Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual ...Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.展开更多
We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartmen...We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.展开更多
Objectives Firstly,according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province,a general population epidemic model is es-tablished.Then,the control reproduction...Objectives Firstly,according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province,a general population epidemic model is es-tablished.Then,the control reproduction number of general population epidemic model is obtained.Based on the epidemic model of general population,the epidemic model of general population and college population is further established,and the control reproduction number is also obtained.Methods For the established epidemic model,firstly,the expression of the control reproduc-tion number is obtained by using the next generation matrix.Secondly,the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model,and the parameters in the model are estimated by least square method and MCMC.Thirdly,the Latin hypercube sampling method and partial rank correlation coefficient(PRCC)are adopted to analyze the sensitivity of the model.Conclusions The control reproduction number remained at 3 from January 23 to January 31,then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China.In order to further control the spread of the epidemic,the following measures can be taken:(i)reducing infection by wearing masks,paying attention to personal hygiene and limiting travel;(i)improving isolation of suspected patients and treatment of symptomatic individuals.In particular,the epidemic model of the collge population and the general population is estab-lished,and the control reproduction number is given,which will provide theoretical basis for the prevention and control of the epidemic in the colleges.展开更多
The classical Kermack-McKendrick homogeneous SIR （susceptible, infected and removed） model is well known, Its general solution is a function of the unique parameter （the reproduction number） that is equal to a mea...The classical Kermack-McKendrick homogeneous SIR （susceptible, infected and removed） model is well known, Its general solution is a function of the unique parameter （the reproduction number） that is equal to a mean number of secondary cases produced by a typical infected individual in a completely susceptible population. If the reproduction number is more than one （the threshold value） its value describes an epidemic scope： larger values correspond to more severe epidemics. In the more complex compartment SIR models the population is divided into several non-overlapping groups. It allows us to partly remove assumptions of the classical model. It is well known that for this kind of models, just as for the classical model there is the threshold parameter R0. Usually it is called by the same name--the reproduction number--though the physical meaning of this parameter has changed. The main purpose of the paper is to show that this new parameter is a not unique measure of an epidemic severity for any compartment SIR model. In particular it means that for such models comparison of the severity of two epidemics by simple comparing values of their reproduction numbers is incorrect. For compartment models these statements were proved with the help of the corresponding ODEs analysis. Very popular now individual-based models （IBMs） are more complex in comparison with the compartment ones since they use overlapping groups （school children are members of families also, for example）. In such a case Diekmann＇s calculation method for the reproduction number used in many papers is inapplicable as well as a presentation the simulation results obtained as functions of this parameter.展开更多
Background Diphtheria,caused by Corynebacterium diphtheriae,remains a serious public health threat in areas with low vaccination coverage,despite global declines due to widespread immunization and improved clinical ma...Background Diphtheria,caused by Corynebacterium diphtheriae,remains a serious public health threat in areas with low vaccination coverage,despite global declines due to widespread immunization and improved clinical management.A major outbreak in Nigeria from 2022 to 2023 underscored the persistent risk in regions with inadequate vaccination.This study aims to assess the transmission dynamics of diphtheria in Kano State,the epicenter of the outbreak,by estimating key epidemiological parameters,including the generation time(GT),approximated in our study by serial interval,and effective reproduction number(R).Methods We analyzed diphtheria case-based data from Kano State,Nigeria,collected between August 18,2022,and November 29,2023.Generation time was approximated using serial intervals in confirmed cases within the same geographical areas.The effective reproduction number(R)was calculated using four methods:Maximum Likelihood Estimation(MLE),Exponential Growth(EG),Sequential Bayesian(SB),and Time-Dependent(TD),focusing on the period of maximum exponential growth.A sensitivity analysis was conducted to quantify the impact of uncertainties in the GT derived from our data on the estimation of R.Results Over the 469-day outbreak period,13,899 diphtheria cases were reported,with complete data available for 9406 cases.The estimated mean generation time was 2.8 days(SD=3.48 days),with 97%of cases having a GT of less than 21 days.The Restimates varied across methods,with the TD method producing the highest reproduction number of 2.21 during the peak growth period.Sensitivity analysis showed that Restimates increased with longer generation times.The models,except for the SB method,demonstrated a generally strong fit with the outbreak exponential growth period.Conclusion The ongoing diphtheria outbreak in Nigeria highlights the critical threat posed by declining vaccination coverage.This study provides valuable insights into the transmission dynamics of diphtheria during a prolonged and widespread outbreak,enhancing our understanding of disease spread in this context.While certain limitations may influence the interpretation of our estimates,the findings offer valuable information for future diphtheria outbreak preparedness and response in the African context.展开更多
In this paper,we introduce a SEIR-type COVID-19 model where the infected class is further divided into subclasses with individuals in intensive care(ICUs)and ventilation units.The model is calibrated with the symptoma...In this paper,we introduce a SEIR-type COVID-19 model where the infected class is further divided into subclasses with individuals in intensive care(ICUs)and ventilation units.The model is calibrated with the symptomatic COVID-19 cases,deaths,and the number of patients in ICUs and ventilation units as reported by Republic of Turkey,Ministry of Health for the period 11 March 2020 through 30 May 2020 when the nationwide lockdown is in order.COVID-19 interventions in Turkey are incorporated into the model to detect the future trend of the outbreak accurately.We tested the effect of underreporting and we found that the peaks of the disease differ significantly depending on the rate of underreporting,however,the timing of the peaks remains constant.The lockdown is lifted on 1 June,and the model is modified to include a time-dependent transmission rate which is linked to the effective reproduction number mi𝑡through basic reproduction number mi0.The modified model captures the changing dynamics and peaks of the outbreak successfully.With the onset of vaccination on 13 January 2021,we augment the model with the vaccination class to investigate the impact of vaccination rate and efficacy.We observe that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.展开更多
Introduction Tuberculosis(TB)is one of the most prevalent infectious diseases in the world,causing major public health problems in developing countries.The rate of TB incidence in Iran was estimated to be 13 per 100,0...Introduction Tuberculosis(TB)is one of the most prevalent infectious diseases in the world,causing major public health problems in developing countries.The rate of TB incidence in Iran was estimated to be 13 per 100,000 in 2021.This study aimed to estimate the reproduction number and serial interval for pulmonary tuberculosis in Iran.Material and methods The present national historical cohort study was conducted from March 2018 to March 2022 based on data from the National Tuberculosis and Leprosy Registration Center of Iran's Ministry of Health and Medical Education(MOHME).The study included 30,762 tuberculosis cases and 16,165 new smear-positive pulmonary tuberculosis patients in Iran.We estimated the reproduction number of pulmonary tuberculosis in a Bayesian framework,which can incorporate uncertainty in estimating it.Statistical analyses were accomplished in R software.Results The mean age at diagnosis of patients was 52.3±21.2 years,and most patients were in the 35–63 age group(37.1%).Among the data,9121(56.4%)cases were males,and 7044(43.6%)were females.Among patients,7459(46.1%)had a delayed diagnosis between 1 and 3 months.Additionally,3039(18.8%)cases were non-Iranians,and 2978(98%)were Afghans.The time-varying reproduction number for pulmonary tuberculosis disease was calculated at an average of 1.06±0.05(95%Crl 0.96–1.15).Conclusions In this study,the incidence and the time-varying reproduction number of pulmonary tuberculosis showed the same pattern.The mean of the time-varying reproduction number indicated that each infected person is causing at least one new infection over time,and the chain of transmission is not being disrupted.展开更多
We focus on distinctive data-driven measures of the fate of ongoing epidemics.The relevance of our pursuit is suggested by recent results proving that the short-term temporal evolution of infection spread is described...We focus on distinctive data-driven measures of the fate of ongoing epidemics.The relevance of our pursuit is suggested by recent results proving that the short-term temporal evolution of infection spread is described by an epidemicity index related to the maximum instantaneous growth rate of new infections,echoing concepts and tools developed to study the reactivity of ecosystems.Suitable epidemicity indices can showcase the dynamics of infections,together with commonly employed effective reproduction numbers,especially when the latter assume values less than 1.In particular,epidemicity evaluates the short-term reactivity to perturbations of a disease-free equilibrium.Here,we show that sufficient epidemicity thresholds to prevent transient epidemic outbreaks in a spatially connected setting can be estimated by generalizing existing analogues derived when spatial effects are neglected.We specifically account for the discrete nature,in both space and time,of surveillance data of the type typically employed to estimate effective reproduction numbers that formed the bulk of the communication of the state of the COVID-19 pandemic and its controls.After analyzing the effects of spatial heterogeneity on the considered prognostic indicators,we perform a short-and long-term analysis on the COVID-19 pandemic in Italy,showing that endemic conditions were maintained throughout the duration of our simulation despite stringent control measures.Our method provides a portfolio of prognostic indices that are essential to pinpoint the ongoing pandemic in both a qualitative and quantitative manner,as our results demonstrate.We base our conclusions on extended investigations of the effects of spatial fragmentation of communities of different sizes owing to connectivity by human mobility and contact scenarios,within real geographic contexts and synthetic setups designed to test our framework.展开更多
The study of the propagation of infectious diseases in urban centers finds a close connection with their population's social characteristics and behavior.This work performs a spatial analysis of dengue cases in ur...The study of the propagation of infectious diseases in urban centers finds a close connection with their population's social characteristics and behavior.This work performs a spatial analysis of dengue cases in urban centers based on the basic reproduction numbers,R0,and incidence by planning areas(PAs),as well as their correlations with the Human Development Index(HDI)and the number of trips.We analyzed dengue epidemics in 2002 at two Brazilian urban centers,Belo Horizonte(BH)and Rio de Janeiro(RJ),using PAs as spatial units.Our results reveal heterogeneous spatial scenarios for both cities,with very weak correlations between R0 and both the number of trips and the HDI;in BH,the values of R0 show a less spatial heterogeneous pattern than in RJ.For BH,there are moderate correlations between incidence and both the number of trips and the HDI;meanwhile,they weakly correlate for RJ.Finally,the absence of strong correlations between the considered measures indicates that the transmission process should be treated considering the city as a whole.展开更多
The estimation methods of reproduction numbers and serial intervals are important in the early stages of infectious diseases.During the COVID pandemic,China implemented a dynamic zero-COVID policy on the Chinese mainl...The estimation methods of reproduction numbers and serial intervals are important in the early stages of infectious diseases.During the COVID pandemic,China implemented a dynamic zero-COVID policy on the Chinese mainland until the end of 2022.This study compares three estimation methods of basic repro-duction numbers on small-scale,short-duration COVID-19 epidemics in Fujian Province.Basic reproduc-tion numbers were investigated using a varying-strain model via a next-generation matrix method.Serial intervals were derived using the infector-infectee pairs of two epidemics from the Fujian Provincial Center for Disease Control and Prevention.Basic reproduction numbers were estimated using the maxi-mum likelihood estimation method and the exponential growth method.The curves of the effective reproduction numbers of the three epidemics were plotted by utilizing daily cases and the EpiEstim R package.The spatial heterogeneity of infection cases was described using the Gini coefficient.This study provides significant insights on the estimation methods of reproduction numbers for policymakers in the local government.The results reveal that social contacts between infectors and susceptible individuals should be reduced to avoid an increase in deaths and to fight against the spread of infectious diseases.展开更多
This primer article focuses on the basic reproduction number,ℛ0,for infectious diseases,and other reproduction numbers related toℛ0 that are useful in guiding control strategies.Beginning with a simple population mode...This primer article focuses on the basic reproduction number,ℛ0,for infectious diseases,and other reproduction numbers related toℛ0 that are useful in guiding control strategies.Beginning with a simple population model,the concept is developed for a threshold value ofℛ0 determining whether or not the disease dies out.The next generation matrix method of calculatingℛ0 in a compartmental model is described and illustrated.To address control strategies,type and target reproduction numbers are defined,as well as sensitivity and elasticity indices.These theoretical ideas are then applied to models that are formulated for West Nile virus in birds(a vector-borne disease),cholera in humans(a disease with two transmission pathways),anthrax in animals(a disease that can be spread by dead carcasses and spores),and Zika in humans(spread by mosquitoes and sexual contacts).Some parameter values from literature data are used to illustrate the results.Finally,references for other ways to calculateℛ0 are given.These are useful for more complicated models that,for example,take account of variations in environmental fluctuation or stochasticity.展开更多
The coronavirus disease 2019(COVID-19)has become a life-threatening pandemic.The epidemic trends in different countries vary considerably due to different policy-making and resources mobilization.We calculated basic r...The coronavirus disease 2019(COVID-19)has become a life-threatening pandemic.The epidemic trends in different countries vary considerably due to different policy-making and resources mobilization.We calculated basic reproduction number(R0)and the time-varying estimate of the effective reproductive number(Rt)of COVID-19 by using the maximum likelihood method and the sequential Bayesian method,respectively.European and North American countries possessed higher (R0)and unsteady Rt fluctuations,whereas some heavily affected Asian countries showed relatively low (R0)and declining Rt now.The numbers of patients in Africa and Latin America are still low,but the potential risk of huge outbreaks cannot be ignored.Three scenarios were then simulated,generating distinct outcomes by using SEIR(susceptible,exposed,infectious,and removed)model.First,evidence-based prompt responses yield lower transmission rate followed by decreasing Rt.Second,implementation of effective control policies at a relatively late stage,in spite of huge casualties at early phase,can still achieve containment and mitigation.Third,wisely taking advantage of the time-window for developing countries in Africa and Latin America to adopt adequate measures can save more people’s life.Our mathematical modeling provides evidence for international communities to develop sound design of containment and mitigation policies for COVID-19.展开更多
Background Coronavirus disease 2019(COVID-19)has caused a serious epidemic around the world,but it has been effectively controlled in the mainland of China.The Chinese government limited the migration of people almost...Background Coronavirus disease 2019(COVID-19)has caused a serious epidemic around the world,but it has been effectively controlled in the mainland of China.The Chinese government limited the migration of people almost from all walks of life.Medical workers have rushed into Hubei province to fight against the epidemic.Any activity that can increase infection is prohibited.The aim of this study was to confirm that timely lockdown,large-scale case-screening and other control measures proposed by the Chinese government were effective to contain the spread of the virus in the mainland of China.Methods Based on disease transmission-related parameters,this study was designed to predict the trend of COVID-19 epidemic in the mainland of China and provide theoretical basis for current prevention and control.An SEIQR epidemiological model incorporating asymptomatic transmission,short term immunity and imperfect isolation was constructed to evaluate the transmission dynamics of COVID-19 inside and outside of Hubei province.With COVID-19 cases confirmed by the National Health Commission(NHC),the optimal parameters of the model were set by calculating the minimum Chi-square value.Results Before the migration to and from Wuhan was cut off,the basic reproduction number in China was 5.6015.From 23 January to 26 January 2020,the basic reproduction number in China was 6.6037.From 27 January to 11 February 2020,the basic reproduction number outside Hubei province dropped below 1,but that in Hubei province remained 3.7732.Because of stricter controlling measures,especially after the initiation of the large-scale case-screening,the epidemic rampancy in Hubei has also been contained.The average basic reproduction number in Hubei province was 3.4094 as of 25 February 2020.We estimated the cumulative number of confirmed cases nationwide was 82186,and 69230 in Hubei province on 9 April 2020.Conclusions The lockdown of Hubei province significantly reduced the basic reproduction number.The large-scale case-screening also showed the effectiveness in the epidemic control.This study provided experiences that could be replicated in other countries suffering from the epidemic.Although the epidemic is subsiding in China,the controlling efforts should not be terminated before May.展开更多
As of March 12th Italy has the largest number of SARS-CoV-2 cases in Europe as well as outside China.The infections,first limited in Northern Italy,have eventually spread to all other regions.When controlling an emerg...As of March 12th Italy has the largest number of SARS-CoV-2 cases in Europe as well as outside China.The infections,first limited in Northern Italy,have eventually spread to all other regions.When controlling an emerging outbreak of an infectious disease it is essential to know the key epidemiological parameters,such as the basic reproduction number R0,i.e.the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak.Previous work has been limited to the assessment of R0 analyzing data from the Wuhan region or China's Mainland.In the present study the R0 value for SARS-CoV-2 was assessed analyzing data derived from the early phase of the outbreak in Italy.In particular,the spread of SARS-CoV-2 was analyzed in 9 cities(those with the largest number of infections)fitting the well-established SIR-model to available data in the interval between February 25–March 12,2020.The findings of this study suggest that R0 values associated with the Italian outbreak may range from 2.43 to 3.10,confirming previous evidence in the literature reporting similar R0 values for SARS-CoV-2.展开更多
BACKGROUND.The effective reproduction number Re(t)is a critical measure of epidemic potential.Re(t)can be calculated in near real time using an incidence time series and the generation time distribution:the time betwe...BACKGROUND.The effective reproduction number Re(t)is a critical measure of epidemic potential.Re(t)can be calculated in near real time using an incidence time series and the generation time distribution:the time between infection events in an infector-infectee pair.In calculating Re(t),the generation time distribution is often approximated by the serial interval distribution:the time between symptom onset in an infector-infectee pair.However,while generation time must be positive by definition,serial interval can be negative if transmission can occur before symptoms,such as in COVID-19,rendering such an approximation improper in some contexts.METHODS.We developed a method to infer the generation time distribution from parametric definitions of the serial interval and incubation period distributions.We then compared estimates of Re(t)for COVID-19 in the Greater Toronto Area of Canada using:negative-permitting versus non-negative serial interval distributions,versus the inferred generation time distribution.RESULTS.We estimated the generation time of COVID-19 to be Gamma-distributed with mean 3.99 and standard deviation 2.96 days.Relative to the generation time distribution,non-negative serial interval distribution caused overestimation of Re(t)due to larger mean,while negative-permitting serial interval distribution caused underestimation of Re(t)due to larger variance.IMPLICATIONS.Approximation of the generation time distribution of COVID-19 with non-negative or negative-permitting serial interval distributions when calculating Re(t)may result in over or underestimation of transmission potential,respectively.展开更多
We demonstrate a methodology for replicating and projecting the path of COVID-19 using a simple epidemiology model.We fit the model to daily data on the number of infected cases in China,Italy,the United States,and Br...We demonstrate a methodology for replicating and projecting the path of COVID-19 using a simple epidemiology model.We fit the model to daily data on the number of infected cases in China,Italy,the United States,and Brazil.These four countries can be viewed as representing different stages,from later to earlier,of a COVID-19 epidemic cycle.We solve for a model-implied effective reproduction number R t each day so that the model closely replicates the daily number of currently infected cases in each country.For out-of-sample projections,we fit a behavioral function to the in-sample data that allows for the endogenous response of R t to movements in the lagged number of infected cases.We show that declines in measures of population mobility tend to precede declines in the model-implied reproduction numbers for each country.This pattern suggests that mandatory and voluntary stay-at-home behavior and social distancing during the early stages of the epidemic worked to reduce the effective reproduction number and mitigate the spread of COVID-19.展开更多
The basic reproduction number,R0,is defined as the expected number of secondary cases of a disease produced by a single infection in a completely susceptible population,and can be estimated in several ways.For example...The basic reproduction number,R0,is defined as the expected number of secondary cases of a disease produced by a single infection in a completely susceptible population,and can be estimated in several ways.For example,from the stability analysis of a compartmental model;through the use of the matrix of next generation,or from the final size of an epidemic,etc.In this paper we applied the method for estimating R0 of dengue fever from the initial growth phase of an outbreak,without assuming exponential growth of cases,a common assumption in many studies.We used three different methods of calculating R0 to compare the techniques'details and to evaluate how these techniques estimate the value of R0 of dengue using data from the city of Ribeir^ao Preto(SE of Brazil)in two outbreaks.The results of the three methods are numerically different but,when we compare them using a system of differential equations developed for modeling only the first generation time,we can observe that the methods differ little in the initial growth phase.We conclude that the methods predict that dengue will spread in the city studied and the analysis of the data shows that the estimated values of R0 have an equal pattern overtime.展开更多
Transmission potential of a pathogen,often quantified by the time-varying reproduction number R t,provides the current pace of infection for a disease and indicates whether an emerging epidemic is under control.In thi...Transmission potential of a pathogen,often quantified by the time-varying reproduction number R t,provides the current pace of infection for a disease and indicates whether an emerging epidemic is under control.In this study,we proposed a novel method,EpiMix,for R t estimation,wherein we incorporated the impacts of exogenous factors and random effects under a Bayesian regression framework.Using Integrated Nested Laplace Approx-imation,EpiMix is able to efficiently generate reliable,deterministic R t estimates.In the simulations and case studies performed,we further demonstrated the method's robust-ness in low-incidence scenarios,together with other merits,including its flexibility in selecting variables and tolerance of varying reporting rates.All these make EpiMix a potentially useful tool for real-time R t estimation provided that the serial interval distri-bution,time series of case counts and external influencing factors are available.展开更多
Background:Monitoring the transmission of coronavirus disease 2019(COVID-19)requires accurate estimation of the effective reproduction number(Rt).However,existing methods for calculating Rt may yield biased estimates ...Background:Monitoring the transmission of coronavirus disease 2019(COVID-19)requires accurate estimation of the effective reproduction number(Rt).However,existing methods for calculating Rt may yield biased estimates if important real-world factors,such as delays in confirmation,pre-symptomatic transmissions,or imperfect data observation,are not considered.Method:To include real-world factors,we expanded the susceptible-exposed-infectiousrecovered(SEIR)model by incorporating pre-symptomatic(P)and asymptomatic(A)states,creating the SEPIAR model.By utilizing both stochastic and deterministic versions of the model,and incorporating predetermined time series of Rt,we generated simulated datasets that simulate real-world challenges in estimating Rt.We then compared the performance of our proposed particle filtering method for estimating Rt with the existing EpiEstim approach based on renewal equations.Results:The particle filtering method accurately estimated Rt even in the presence of data with delays,pre-symptomatic transmission,and imperfect observation.When evaluating via the root mean square error(RMSE)metric,the performance of the particle filtering method was better in general and was comparable to the EpiEstim approach if perfectly deconvolved infection time series were provided,and substantially better when Rt exhibited short-term fluctuations and the data was right truncated.Conclusions:The SEPIAR model,in conjunction with the particle filtering method,offers a reliable tool for predicting the transmission trend of COVID-19 and assessing the impact of intervention strategies.This approach enables enhanced monitoring of COVID-19 transmission and can inform public health policies aimed at controlling the spread of the disease.展开更多
Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks.In this study,we impr...Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks.In this study,we improve the estimation of the effective reproduction number through two main approaches.First,we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework.We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme.By doing so,we enhance the accuracy of approximating the underlying epidemic process compared to previous methods,even when the counting period is similar to the mean generation time of an infectious disease.Second,we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion.Specifically,given that observed incidence counts follow a negative binomial distribution,the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution.With this formulation,we establish posterior uncertainty bounds for the effective reproduction number.Finally,we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.展开更多
文摘Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
基金The work has been supported by a grant received from the Ministry of Education,Government of India under the Scheme for the Promotion of Academic and Research Collaboration(SPARC)(ID:SPARC/2019/1396).
文摘We have proposed a new mathematical method,the SEIHCRD model,which has an excellent potential to predict the incidence of COVID-19 diseases.Our proposed SEIHCRD model is an extension of the SEIR model.Three-compartments have added death,hospitalized,and critical,which improves the basic understanding of disease spread and results.We have studiedCOVID-19 cases of six countries,where the impact of this disease in the highest are Brazil,India,Italy,Spain,the United Kingdom,and the United States.After estimating model parameters based on available clinical data,the modelwill propagate and forecast dynamic evolution.Themodel calculates the Basic reproduction number over time using logistic regression and the Case fatality rate based on the selected countries’age-category scenario.Themodel calculates two types of Case fatality rate one is CFR daily,and the other is total CFR.The proposed model estimates the approximate time when the disease is at its peak and the approximate time when death cases rarely occur and calculate how much hospital beds and ICU beds will be needed in the peak days of infection.The SEIHCRD model outperforms the classic ARXmodel and the ARIMA model.RMSE,MAPE,andRsquaredmatrices are used to evaluate results and are graphically represented using Taylor and Target diagrams.The result shows RMSE has improved by 56%–74%,and MAPE has a 53%–89%improvement in prediction accuracy.
基金Supported by the Fundamental Research Funds for the Central Universities,CHD(300102129201)the Nat ural Science Basic Research Plan in Shaanxi Province of China(2018JM1011)the National Natural Science Foundation of China(11701041)。
文摘Objectives Firstly,according to the characteristics of COVID-19 epidemic and the control measures of the government of Shaanxi Province,a general population epidemic model is es-tablished.Then,the control reproduction number of general population epidemic model is obtained.Based on the epidemic model of general population,the epidemic model of general population and college population is further established,and the control reproduction number is also obtained.Methods For the established epidemic model,firstly,the expression of the control reproduc-tion number is obtained by using the next generation matrix.Secondly,the real-time reported data of COVID-19 in Shaanxi Province is used to fit the epidemic model,and the parameters in the model are estimated by least square method and MCMC.Thirdly,the Latin hypercube sampling method and partial rank correlation coefficient(PRCC)are adopted to analyze the sensitivity of the model.Conclusions The control reproduction number remained at 3 from January 23 to January 31,then gradually decreased from 3 to slightly greater than 0.2 by using the real-time reports on the number of COVID-19 infected cases from Health Committee of Shaanxi Province in China.In order to further control the spread of the epidemic,the following measures can be taken:(i)reducing infection by wearing masks,paying attention to personal hygiene and limiting travel;(i)improving isolation of suspected patients and treatment of symptomatic individuals.In particular,the epidemic model of the collge population and the general population is estab-lished,and the control reproduction number is given,which will provide theoretical basis for the prevention and control of the epidemic in the colleges.
基金Acknowledgements This work was assisted through participation in ＂Optimal Control and Optimization for Individual- based and Agent-based Models＂ Investigative Workshop at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation, the U.S. Department of Homeland Security, and the U.S. Department of Agriculture through NSF Award #EF-0832858, with additional support from The University of Tennessee, Knoxville.
文摘The classical Kermack-McKendrick homogeneous SIR （susceptible, infected and removed） model is well known, Its general solution is a function of the unique parameter （the reproduction number） that is equal to a mean number of secondary cases produced by a typical infected individual in a completely susceptible population. If the reproduction number is more than one （the threshold value） its value describes an epidemic scope： larger values correspond to more severe epidemics. In the more complex compartment SIR models the population is divided into several non-overlapping groups. It allows us to partly remove assumptions of the classical model. It is well known that for this kind of models, just as for the classical model there is the threshold parameter R0. Usually it is called by the same name--the reproduction number--though the physical meaning of this parameter has changed. The main purpose of the paper is to show that this new parameter is a not unique measure of an epidemic severity for any compartment SIR model. In particular it means that for such models comparison of the severity of two epidemics by simple comparing values of their reproduction numbers is incorrect. For compartment models these statements were proved with the help of the corresponding ODEs analysis. Very popular now individual-based models （IBMs） are more complex in comparison with the compartment ones since they use overlapping groups （school children are members of families also, for example）. In such a case Diekmann＇s calculation method for the reproduction number used in many papers is inapplicable as well as a presentation the simulation results obtained as functions of this parameter.
文摘Background Diphtheria,caused by Corynebacterium diphtheriae,remains a serious public health threat in areas with low vaccination coverage,despite global declines due to widespread immunization and improved clinical management.A major outbreak in Nigeria from 2022 to 2023 underscored the persistent risk in regions with inadequate vaccination.This study aims to assess the transmission dynamics of diphtheria in Kano State,the epicenter of the outbreak,by estimating key epidemiological parameters,including the generation time(GT),approximated in our study by serial interval,and effective reproduction number(R).Methods We analyzed diphtheria case-based data from Kano State,Nigeria,collected between August 18,2022,and November 29,2023.Generation time was approximated using serial intervals in confirmed cases within the same geographical areas.The effective reproduction number(R)was calculated using four methods:Maximum Likelihood Estimation(MLE),Exponential Growth(EG),Sequential Bayesian(SB),and Time-Dependent(TD),focusing on the period of maximum exponential growth.A sensitivity analysis was conducted to quantify the impact of uncertainties in the GT derived from our data on the estimation of R.Results Over the 469-day outbreak period,13,899 diphtheria cases were reported,with complete data available for 9406 cases.The estimated mean generation time was 2.8 days(SD=3.48 days),with 97%of cases having a GT of less than 21 days.The Restimates varied across methods,with the TD method producing the highest reproduction number of 2.21 during the peak growth period.Sensitivity analysis showed that Restimates increased with longer generation times.The models,except for the SB method,demonstrated a generally strong fit with the outbreak exponential growth period.Conclusion The ongoing diphtheria outbreak in Nigeria highlights the critical threat posed by declining vaccination coverage.This study provides valuable insights into the transmission dynamics of diphtheria during a prolonged and widespread outbreak,enhancing our understanding of disease spread in this context.While certain limitations may influence the interpretation of our estimates,the findings offer valuable information for future diphtheria outbreak preparedness and response in the African context.
文摘In this paper,we introduce a SEIR-type COVID-19 model where the infected class is further divided into subclasses with individuals in intensive care(ICUs)and ventilation units.The model is calibrated with the symptomatic COVID-19 cases,deaths,and the number of patients in ICUs and ventilation units as reported by Republic of Turkey,Ministry of Health for the period 11 March 2020 through 30 May 2020 when the nationwide lockdown is in order.COVID-19 interventions in Turkey are incorporated into the model to detect the future trend of the outbreak accurately.We tested the effect of underreporting and we found that the peaks of the disease differ significantly depending on the rate of underreporting,however,the timing of the peaks remains constant.The lockdown is lifted on 1 June,and the model is modified to include a time-dependent transmission rate which is linked to the effective reproduction number mi𝑡through basic reproduction number mi0.The modified model captures the changing dynamics and peaks of the outbreak successfully.With the onset of vaccination on 13 January 2021,we augment the model with the vaccination class to investigate the impact of vaccination rate and efficacy.We observe that vaccination rate is a more critical parameter than the vaccine efficacy to eliminate the disease successfully.
基金This study was financially supported by the Vice-chancellor for Research and Technology,Mashhad University of Medical Sciences,Iran(project No.4001759).
文摘Introduction Tuberculosis(TB)is one of the most prevalent infectious diseases in the world,causing major public health problems in developing countries.The rate of TB incidence in Iran was estimated to be 13 per 100,000 in 2021.This study aimed to estimate the reproduction number and serial interval for pulmonary tuberculosis in Iran.Material and methods The present national historical cohort study was conducted from March 2018 to March 2022 based on data from the National Tuberculosis and Leprosy Registration Center of Iran's Ministry of Health and Medical Education(MOHME).The study included 30,762 tuberculosis cases and 16,165 new smear-positive pulmonary tuberculosis patients in Iran.We estimated the reproduction number of pulmonary tuberculosis in a Bayesian framework,which can incorporate uncertainty in estimating it.Statistical analyses were accomplished in R software.Results The mean age at diagnosis of patients was 52.3±21.2 years,and most patients were in the 35–63 age group(37.1%).Among the data,9121(56.4%)cases were males,and 7044(43.6%)were females.Among patients,7459(46.1%)had a delayed diagnosis between 1 and 3 months.Additionally,3039(18.8%)cases were non-Iranians,and 2978(98%)were Afghans.The time-varying reproduction number for pulmonary tuberculosis disease was calculated at an average of 1.06±0.05(95%Crl 0.96–1.15).Conclusions In this study,the incidence and the time-varying reproduction number of pulmonary tuberculosis showed the same pattern.The mean of the time-varying reproduction number indicated that each infected person is causing at least one new infection over time,and the chain of transmission is not being disrupted.
基金C.T.,and A.R.acknowledge funding from the Swiss National Science Foundation via the project”Optimal control of intervention strategies for waterborne disease epidemics”(grant number 200021-172578)L.M.acknowledges funding from the Italian Ministry of University and Research through the project”Epidemiological data assimilation and optimal control for short-term forecasting and emergency management of COVID-19 in Italy”(FISR_2020IP_04249).
文摘We focus on distinctive data-driven measures of the fate of ongoing epidemics.The relevance of our pursuit is suggested by recent results proving that the short-term temporal evolution of infection spread is described by an epidemicity index related to the maximum instantaneous growth rate of new infections,echoing concepts and tools developed to study the reactivity of ecosystems.Suitable epidemicity indices can showcase the dynamics of infections,together with commonly employed effective reproduction numbers,especially when the latter assume values less than 1.In particular,epidemicity evaluates the short-term reactivity to perturbations of a disease-free equilibrium.Here,we show that sufficient epidemicity thresholds to prevent transient epidemic outbreaks in a spatially connected setting can be estimated by generalizing existing analogues derived when spatial effects are neglected.We specifically account for the discrete nature,in both space and time,of surveillance data of the type typically employed to estimate effective reproduction numbers that formed the bulk of the communication of the state of the COVID-19 pandemic and its controls.After analyzing the effects of spatial heterogeneity on the considered prognostic indicators,we perform a short-and long-term analysis on the COVID-19 pandemic in Italy,showing that endemic conditions were maintained throughout the duration of our simulation despite stringent control measures.Our method provides a portfolio of prognostic indices that are essential to pinpoint the ongoing pandemic in both a qualitative and quantitative manner,as our results demonstrate.We base our conclusions on extended investigations of the effects of spatial fragmentation of communities of different sizes owing to connectivity by human mobility and contact scenarios,within real geographic contexts and synthetic setups designed to test our framework.
基金support of the National Council of Technological and Scientific Development,CNPq,Brazil(grant no.305941/2021-6)support of Coordenação de Aperfeiçoamento de Pessoal de Nível Superior/Programa de Excelência Acadêmica(CAPES/PROEX)for the publication charge.
文摘The study of the propagation of infectious diseases in urban centers finds a close connection with their population's social characteristics and behavior.This work performs a spatial analysis of dengue cases in urban centers based on the basic reproduction numbers,R0,and incidence by planning areas(PAs),as well as their correlations with the Human Development Index(HDI)and the number of trips.We analyzed dengue epidemics in 2002 at two Brazilian urban centers,Belo Horizonte(BH)and Rio de Janeiro(RJ),using PAs as spatial units.Our results reveal heterogeneous spatial scenarios for both cities,with very weak correlations between R0 and both the number of trips and the HDI;in BH,the values of R0 show a less spatial heterogeneous pattern than in RJ.For BH,there are moderate correlations between incidence and both the number of trips and the HDI;meanwhile,they weakly correlate for RJ.Finally,the absence of strong correlations between the considered measures indicates that the transmission process should be treated considering the city as a whole.
基金supported by the Special Projects of the Central(2021L3018)the Natural Science Foundation of Fujian Province ported by the Major Health Research Project of Fujian Province KCZ and GMC were supported by the Fujian Science and Technol-the Government Guiding Local Science and Technology Development of China(2021J01621)+2 种基金the Consultancy Project by the Chinese Academy of Engineering(2022-JB-06,2023-JB-12)JFX was sup-(2021ZD01001).We would like to thank Fujian Research and Training Grants for Young and Middle-aged Leaders in Healthcare.ogy Innovation Platform Construction Project(2019Y2001)Health Science and Technology Project of Fujian Province(2020GGB019).
文摘The estimation methods of reproduction numbers and serial intervals are important in the early stages of infectious diseases.During the COVID pandemic,China implemented a dynamic zero-COVID policy on the Chinese mainland until the end of 2022.This study compares three estimation methods of basic repro-duction numbers on small-scale,short-duration COVID-19 epidemics in Fujian Province.Basic reproduc-tion numbers were investigated using a varying-strain model via a next-generation matrix method.Serial intervals were derived using the infector-infectee pairs of two epidemics from the Fujian Provincial Center for Disease Control and Prevention.Basic reproduction numbers were estimated using the maxi-mum likelihood estimation method and the exponential growth method.The curves of the effective reproduction numbers of the three epidemics were plotted by utilizing daily cases and the EpiEstim R package.The spatial heterogeneity of infection cases was described using the Gini coefficient.This study provides significant insights on the estimation methods of reproduction numbers for policymakers in the local government.The results reveal that social contacts between infectors and susceptible individuals should be reduced to avoid an increase in deaths and to fight against the spread of infectious diseases.
基金The research of PvdD is partially funded by an NSERC Discovery grant.Thanks to CM Saad-Roy for discussions on this article.
文摘This primer article focuses on the basic reproduction number,ℛ0,for infectious diseases,and other reproduction numbers related toℛ0 that are useful in guiding control strategies.Beginning with a simple population model,the concept is developed for a threshold value ofℛ0 determining whether or not the disease dies out.The next generation matrix method of calculatingℛ0 in a compartmental model is described and illustrated.To address control strategies,type and target reproduction numbers are defined,as well as sensitivity and elasticity indices.These theoretical ideas are then applied to models that are formulated for West Nile virus in birds(a vector-borne disease),cholera in humans(a disease with two transmission pathways),anthrax in animals(a disease that can be spread by dead carcasses and spores),and Zika in humans(spread by mosquitoes and sexual contacts).Some parameter values from literature data are used to illustrate the results.Finally,references for other ways to calculateℛ0 are given.These are useful for more complicated models that,for example,take account of variations in environmental fluctuation or stochasticity.
基金This work is funded by Medicine and Engineering Interdisciplinary Research Fund of Shanghai Jiao Tong University(No.YG2020YQ06)the National Key Research and Development Project(Nos.2018YFC1705100,2018YFC1705103,and 2018YFC2000700)+1 种基金the National Natural Science Foundation of China(Nos.71673187 and 81630086)the Key Research Program(No.ZDRW-ZS-2017-1)of the Chinese Academy of Sciences,Innovative research team of high-level local universities in Shanghai.
文摘The coronavirus disease 2019(COVID-19)has become a life-threatening pandemic.The epidemic trends in different countries vary considerably due to different policy-making and resources mobilization.We calculated basic reproduction number(R0)and the time-varying estimate of the effective reproductive number(Rt)of COVID-19 by using the maximum likelihood method and the sequential Bayesian method,respectively.European and North American countries possessed higher (R0)and unsteady Rt fluctuations,whereas some heavily affected Asian countries showed relatively low (R0)and declining Rt now.The numbers of patients in Africa and Latin America are still low,but the potential risk of huge outbreaks cannot be ignored.Three scenarios were then simulated,generating distinct outcomes by using SEIR(susceptible,exposed,infectious,and removed)model.First,evidence-based prompt responses yield lower transmission rate followed by decreasing Rt.Second,implementation of effective control policies at a relatively late stage,in spite of huge casualties at early phase,can still achieve containment and mitigation.Third,wisely taking advantage of the time-window for developing countries in Africa and Latin America to adopt adequate measures can save more people’s life.Our mathematical modeling provides evidence for international communities to develop sound design of containment and mitigation policies for COVID-19.
文摘Background Coronavirus disease 2019(COVID-19)has caused a serious epidemic around the world,but it has been effectively controlled in the mainland of China.The Chinese government limited the migration of people almost from all walks of life.Medical workers have rushed into Hubei province to fight against the epidemic.Any activity that can increase infection is prohibited.The aim of this study was to confirm that timely lockdown,large-scale case-screening and other control measures proposed by the Chinese government were effective to contain the spread of the virus in the mainland of China.Methods Based on disease transmission-related parameters,this study was designed to predict the trend of COVID-19 epidemic in the mainland of China and provide theoretical basis for current prevention and control.An SEIQR epidemiological model incorporating asymptomatic transmission,short term immunity and imperfect isolation was constructed to evaluate the transmission dynamics of COVID-19 inside and outside of Hubei province.With COVID-19 cases confirmed by the National Health Commission(NHC),the optimal parameters of the model were set by calculating the minimum Chi-square value.Results Before the migration to and from Wuhan was cut off,the basic reproduction number in China was 5.6015.From 23 January to 26 January 2020,the basic reproduction number in China was 6.6037.From 27 January to 11 February 2020,the basic reproduction number outside Hubei province dropped below 1,but that in Hubei province remained 3.7732.Because of stricter controlling measures,especially after the initiation of the large-scale case-screening,the epidemic rampancy in Hubei has also been contained.The average basic reproduction number in Hubei province was 3.4094 as of 25 February 2020.We estimated the cumulative number of confirmed cases nationwide was 82186,and 69230 in Hubei province on 9 April 2020.Conclusions The lockdown of Hubei province significantly reduced the basic reproduction number.The large-scale case-screening also showed the effectiveness in the epidemic control.This study provided experiences that could be replicated in other countries suffering from the epidemic.Although the epidemic is subsiding in China,the controlling efforts should not be terminated before May.
文摘As of March 12th Italy has the largest number of SARS-CoV-2 cases in Europe as well as outside China.The infections,first limited in Northern Italy,have eventually spread to all other regions.When controlling an emerging outbreak of an infectious disease it is essential to know the key epidemiological parameters,such as the basic reproduction number R0,i.e.the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak.Previous work has been limited to the assessment of R0 analyzing data from the Wuhan region or China's Mainland.In the present study the R0 value for SARS-CoV-2 was assessed analyzing data derived from the early phase of the outbreak in Italy.In particular,the spread of SARS-CoV-2 was analyzed in 9 cities(those with the largest number of infections)fitting the well-established SIR-model to available data in the interval between February 25–March 12,2020.The findings of this study suggest that R0 values associated with the Italian outbreak may range from 2.43 to 3.10,confirming previous evidence in the literature reporting similar R0 values for SARS-CoV-2.
基金The study was supported by:the Natural Sciences and Engineering Research Council of Canada(NSERC CGS-D)Ontario Early Researcher Award No.ER17-13-043(Canada)the 2020 COVID-19 Centred Research Award from the St Michael’s Hospital Foundation Research Innovation Council(Canada).
文摘BACKGROUND.The effective reproduction number Re(t)is a critical measure of epidemic potential.Re(t)can be calculated in near real time using an incidence time series and the generation time distribution:the time between infection events in an infector-infectee pair.In calculating Re(t),the generation time distribution is often approximated by the serial interval distribution:the time between symptom onset in an infector-infectee pair.However,while generation time must be positive by definition,serial interval can be negative if transmission can occur before symptoms,such as in COVID-19,rendering such an approximation improper in some contexts.METHODS.We developed a method to infer the generation time distribution from parametric definitions of the serial interval and incubation period distributions.We then compared estimates of Re(t)for COVID-19 in the Greater Toronto Area of Canada using:negative-permitting versus non-negative serial interval distributions,versus the inferred generation time distribution.RESULTS.We estimated the generation time of COVID-19 to be Gamma-distributed with mean 3.99 and standard deviation 2.96 days.Relative to the generation time distribution,non-negative serial interval distribution caused overestimation of Re(t)due to larger mean,while negative-permitting serial interval distribution caused underestimation of Re(t)due to larger variance.IMPLICATIONS.Approximation of the generation time distribution of COVID-19 with non-negative or negative-permitting serial interval distributions when calculating Re(t)may result in over or underestimation of transmission potential,respectively.
文摘We demonstrate a methodology for replicating and projecting the path of COVID-19 using a simple epidemiology model.We fit the model to daily data on the number of infected cases in China,Italy,the United States,and Brazil.These four countries can be viewed as representing different stages,from later to earlier,of a COVID-19 epidemic cycle.We solve for a model-implied effective reproduction number R t each day so that the model closely replicates the daily number of currently infected cases in each country.For out-of-sample projections,we fit a behavioral function to the in-sample data that allows for the endogenous response of R t to movements in the lagged number of infected cases.We show that declines in measures of population mobility tend to precede declines in the model-implied reproduction numbers for each country.This pattern suggests that mandatory and voluntary stay-at-home behavior and social distancing during the early stages of the epidemic worked to reduce the effective reproduction number and mitigate the spread of COVID-19.
基金This work was partially funded by grants CAPES,CNPq,LIM01-HCFMUSP,DengueTools(Health theme of the Seventh Framework Programme of the European Community,Grant Agreement Number:282589).
文摘The basic reproduction number,R0,is defined as the expected number of secondary cases of a disease produced by a single infection in a completely susceptible population,and can be estimated in several ways.For example,from the stability analysis of a compartmental model;through the use of the matrix of next generation,or from the final size of an epidemic,etc.In this paper we applied the method for estimating R0 of dengue fever from the initial growth phase of an outbreak,without assuming exponential growth of cases,a common assumption in many studies.We used three different methods of calculating R0 to compare the techniques'details and to evaluate how these techniques estimate the value of R0 of dengue using data from the city of Ribeir^ao Preto(SE of Brazil)in two outbreaks.The results of the three methods are numerically different but,when we compare them using a system of differential equations developed for modeling only the first generation time,we can observe that the methods differ little in the initial growth phase.We conclude that the methods predict that dengue will spread in the city studied and the analysis of the data shows that the estimated values of R0 have an equal pattern overtime.
基金suppoted by Singapore’s Ministry of Education(through a Tier 1 grant),the National University of Singapore(through a Reimagine Research grant),and the Singapore Ministry of Health’s National Medical Research Council under its National Epidemic Preparedness and Response R&D Funding Initiative(MOH-001041)Programme for Research in Epidemic Preparedness And REsponse(PREPARE).
文摘Transmission potential of a pathogen,often quantified by the time-varying reproduction number R t,provides the current pace of infection for a disease and indicates whether an emerging epidemic is under control.In this study,we proposed a novel method,EpiMix,for R t estimation,wherein we incorporated the impacts of exogenous factors and random effects under a Bayesian regression framework.Using Integrated Nested Laplace Approx-imation,EpiMix is able to efficiently generate reliable,deterministic R t estimates.In the simulations and case studies performed,we further demonstrated the method's robust-ness in low-incidence scenarios,together with other merits,including its flexibility in selecting variables and tolerance of varying reporting rates.All these make EpiMix a potentially useful tool for real-time R t estimation provided that the serial interval distri-bution,time series of case counts and external influencing factors are available.
基金supported by Government-wide R&D Fund project for infectious disease research (GFID),Republic of Korea (grant number:HG18C0088)National Institute for Mathematical Sciences (NIMS)grant funded by the Korean Government (NIMS-B23730000).
文摘Background:Monitoring the transmission of coronavirus disease 2019(COVID-19)requires accurate estimation of the effective reproduction number(Rt).However,existing methods for calculating Rt may yield biased estimates if important real-world factors,such as delays in confirmation,pre-symptomatic transmissions,or imperfect data observation,are not considered.Method:To include real-world factors,we expanded the susceptible-exposed-infectiousrecovered(SEIR)model by incorporating pre-symptomatic(P)and asymptomatic(A)states,creating the SEPIAR model.By utilizing both stochastic and deterministic versions of the model,and incorporating predetermined time series of Rt,we generated simulated datasets that simulate real-world challenges in estimating Rt.We then compared the performance of our proposed particle filtering method for estimating Rt with the existing EpiEstim approach based on renewal equations.Results:The particle filtering method accurately estimated Rt even in the presence of data with delays,pre-symptomatic transmission,and imperfect observation.When evaluating via the root mean square error(RMSE)metric,the performance of the particle filtering method was better in general and was comparable to the EpiEstim approach if perfectly deconvolved infection time series were provided,and substantially better when Rt exhibited short-term fluctuations and the data was right truncated.Conclusions:The SEPIAR model,in conjunction with the particle filtering method,offers a reliable tool for predicting the transmission trend of COVID-19 and assessing the impact of intervention strategies.This approach enables enhanced monitoring of COVID-19 transmission and can inform public health policies aimed at controlling the spread of the disease.
文摘Accurately estimating the effective reproduction number is crucial for characterizing the transmissibility of infectious diseases to optimize interventions and responses during epidemic outbreaks.In this study,we improve the estimation of the effective reproduction number through two main approaches.First,we derive a discrete model to represent a time series of case counts and propose an estimation method based on this framework.We also conduct numerical experiments to demonstrate the effectiveness of the proposed discretization scheme.By doing so,we enhance the accuracy of approximating the underlying epidemic process compared to previous methods,even when the counting period is similar to the mean generation time of an infectious disease.Second,we employ a negative binomial distribution to model the variability of count data to accommodate overdispersion.Specifically,given that observed incidence counts follow a negative binomial distribution,the posterior distribution of secondary infections is obtained as a Dirichlet multinomial distribution.With this formulation,we establish posterior uncertainty bounds for the effective reproduction number.Finally,we demonstrate the effectiveness of the proposed method using incidence data from the COVID-19 pandemic.
