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
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
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
In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using ...In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using the method of the next generation matrix.It shows that disease-free equilibrium is globally asymptotically stable when R0<1;the disease is uniformly persistent when R_(0)>1.Secondly,we select dengue fever case data from Guangdong Province from 2006 to 2019 for numerical simulations and predict its development trend.Finally,we conduct parameter sensitivity analysis,and the results show that increasing media publicity can to some extent reduce the number of patients.展开更多
In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of th...In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of the solution to the model under initial conditions are proven.Secondly,it is proven that when R_(0)<1,the disease-free equilibrium is locally and globally asymptotically stable;and when R_(0)>1,the disease is uniformly persistent and there is at least a positive equilibrium.Finally,the effectiveness of the theoretical results is demonstrated by numerical simulation,and the impact of vaccination on disease transmission is predicted.展开更多
Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis mo...Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.展开更多
This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its gl...This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its global dynamics in terms of R0,which predicts the extinction or persistence of diseases.More precisely,the disease-free steady state is globally attractive if R_(0)<1,while the system admits at least one positive periodic solution and the disease is uniformly persistent if R_(0)>1.Moreover,we carry out some numerical simulations to illustrate the long-term behaviors of solutions and explore the influence of environmental pollution and seasonality on the spread of waterborne diseases.展开更多
This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was ...This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was introduced in this paper, which took the gross domestic product(GDP) of each region as one of the factors that affect the spread speed of COVID-19 and studied the relationship between the GDP and the infection density of each region(China's Mainland, the United States, and EU countries). In addition, the geographic distance between regions was also considered in this method and the effect of geographic distance on the spread speed of COVID-19 was studied. Studies have shown that the probability of mutual infection of these two regions decreases with increasing geographic distance. Therefore, this paper proposed an epidemic disease spread index based on GDP and geographic distance to quantify the spread speed of COVID-19 in a region. The analysis results showed a strong correlation between the epidemic disease spread index in a region and the number of confirmed cases. This finding provides reasonable suggestions for the control of epidemics. Strengthening the control measures in regions with higher epidemic disease spread index can effectively control the spread of epidemics.展开更多
Climate is a major driver of vector proliferation and arbovirus transmission, with temperature being a primary focus of research. Unlike other mosquito-borne diseases, Zika virus transmission involves both sexual tran...Climate is a major driver of vector proliferation and arbovirus transmission, with temperature being a primary focus of research. Unlike other mosquito-borne diseases, Zika virus transmission involves both sexual transmission between humans and environmental transmission pathways, a characteristic largely overlooked in existing studies. This paper develops a temperature-dependent transmission model based on the unique transmission characteristics of the Zika virus. We estimated the historical transmission of Zika virus in Brazil using a temperature-dependent basic reproduction number to assess the impact of climate change on Zika virus spread in the region. Results indicate that the temperature range for Zika virus outbreaks is between 23.34˚C and 33.99˚C, peaking at 3.2 at 29.4˚C. This range and peak temperature are approximately 1˚C lower than those found in models that do not consider environmental transmission pathways. By incorporating seasonal variations into the model and categorizing ten Brazilian cities into five climatic types based on temperature changes, we simulated historical and future daily average temperatures using the GFDL-ESM4 temperature model. We analyzed the control periods and virus risks across different regions and projected Zika virus transmission risk in Brazil under four Shared Socioeconomic Pathways (SSP126, SSP245, SSP370, and SSP585). The results suggest that under the SSP126 scenario, the control periods will extend by 2 - 3 months with rising temperatures. This study concludes by discussing the impact of temperature changes on control measures, emphasizing the importance of reducing adult mosquito populations through the Sterile Insect Technique (SIT) to mitigate future risks.展开更多
COVID-19 is a worldwide pandemic that poses a great threat to people’s health and has a huge impact on economic and social life. The epidemic is currently at a low level, but is still prevalent worldwide. Therefore, ...COVID-19 is a worldwide pandemic that poses a great threat to people’s health and has a huge impact on economic and social life. The epidemic is currently at a low level, but is still prevalent worldwide. Therefore, it is still important to study the prevention and control of the spread of the COVID-19 epidemic. We collected the numbers of COVID-19 infections in China during the past three years, and obtained the regional distribution of outbreaks through analysis. To assess the capacity of medical resources in these regions in response to the outbreaks of COVID-19, we developed a model of COVID-19 transmission dynamics including mild and severe cases. The simulation showed that 11 regions, Beijing, Shanghai, Heilongjiang, Yunnan, Xinjiang, Inner Mongolia, Liaoning, Jilin, Hainan, Guangdong and Fujian, all have a serious shortage of medical beds in reserve. When facing the next new outbreak, these areas will have insufficient medical resources. We simulated the effects of drug effectiveness and the proportion of asymptomatic infected individuals on the spread of the epidemic, and obtained that an accurate determination of the proportion of asymptomatic patients in the population is crucial to the impact on healthcare resources, while improving the effectiveness of drugs can significantly reduce the burden on healthcare resources. Regions should invest more in healthcare and increase more medical resources, including medical beds. Government should accelerate the development of effective COVID-19 drugs to effectively control the scale of the outbreak. The proportion of asymptomatic patients in the population has a significant impact on the allocation of healthcare resources. The monitoring of antibody levels in the population should be strengthened to better control the spread of the epidemic.展开更多
This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disea...This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.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
Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infection...Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infections and heavy financial losses.The disease has become a major public health concern.In this paper,we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment,which couples virus-to-animals and animals-to-animals transmission pathways,and investigate the dynamics of the disperal.The basic reproduction number R_(0)is defined as the spectral radius of the next generation operator R(x)by a renewal equation.The relationship between R_(0)and a principal eigenvalue of an operator L_(0)is built.Moreover,the proposed system exhibits threshold dynamics in terms of R_(0),in the sense that R_(0)determines whether or not foot-and-mouth disease invades the hosts.Through numerical simulations,we have found that increasing animals'movements is an effective control measure for preventing prevalence of the disease.展开更多
In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,...In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,non-dangerous male,and female.By mathematical analysis,we obtain the basic reproduction number for the existence of endemic equilibrium and study the effects of various immunization schemes about different groups.Furthermore,numerical simulations are undertaken to verify more conclusions.展开更多
Investigating the stability of information spreading over SNS helps to understand the principles inherent in the spreading behavior.This paper explores the mechanisms of information spreading including stifling mechan...Investigating the stability of information spreading over SNS helps to understand the principles inherent in the spreading behavior.This paper explores the mechanisms of information spreading including stifling mechanism,latent mechanism and forgetting mechanism,establishes a refined SEIR model,and builds the corresponding mean-field equations.The methods of the differential dynamics and the next generation matrix are used to calculate the equilibriums and the basic reproductive number,and the asymptotical stability of the network equilibriums are proved theoretically.Simulation experiments are carried out to analyze the effect of the spreading mechanisms on the information spreading process and the results support our conclusions.展开更多
Current public-opinion propagation research usually focused on closed network topologies without considering the fluctuation of the number of network users or the impact of social factors on propagation. Thus, it rema...Current public-opinion propagation research usually focused on closed network topologies without considering the fluctuation of the number of network users or the impact of social factors on propagation. Thus, it remains difficult to accurately describe the public-opinion propagation rules of social networks. In order to study the rules of public opinion spread on dynamic social networks, by analyzing the activity of social-network users and the regulatory role of relevant departments in the spread of public opinion, concepts of additional user and offline rates are introduced, and the direct immune-susceptible, contacted, infected, and refractory (DI-SCIR) public-opinion propagation model based on real-time online users is established. The interventional force of relevant departments, credibility of real information, and time of intervention are considered, and a public-opinion propagation control strategy based on direct immunity is proposed. The equilibrium point and the basic reproduction number of the model are theoretically analyzed to obtain boundary conditions for public-opinion propagation. Simulation results show that the new model can accurately reflect the propagation rules of public opinion. When the basic reproduction number is less than 1, public opinion will eventually disappear in the network. Social factors can significantly influence the time and scope of public opinion spread on social networks. By controlling social factors, relevant departments can analyze the rules of public opinion spread on social networks to suppress the propagate of negative public opinion and provide a powerful tool to ensure security and stability of society.展开更多
Dengue disease is the most common vector borne infectious disease transmitted to humans by infected adult female Aedes mosquitoes. Over the past several years the disease has been increasing remarkably and it has beco...Dengue disease is the most common vector borne infectious disease transmitted to humans by infected adult female Aedes mosquitoes. Over the past several years the disease has been increasing remarkably and it has become a major public health concern. Dengue viruses have increased their geographic range into new human population due to travel of humans from one place to the other. In the present paper, we have proposed a multi patch SIR-SI model to study the host-vector dynamics of dengue disease in different patches including the travel of human population among the patches. We have considered different disease prevalences in different patches and different travel rates of humans. The dimensionless number, basic reproduction number R0 which shows that the disease dies out if R0 < 1 and the disease takes hold if R0 ≥ 1, is calculated. Local and global stability of the disease free equilibrium are analyzed. Simulations are observed considering the two patches only. The results show that controlling the travel of infectious hosts from high disease dominant patch to low disease dominant patch can help in controlling the disease in low disease dominant patch while high disease dominant becomes even more disease dominant. The understanding of the effect of travel of humans on the spatial spread of the disease among the patches can be helpful in improving disease control and prevention measures. In the present study, a patch may represent a city, a village or some biological habitat.展开更多
In this paper, we are concerned with a reaction-diffusion SIR epidemic model with nonlinear incidence rate and non-local delay effect in a continuous bounded spatial domain. We introduce the basic reproduction number ...In this paper, we are concerned with a reaction-diffusion SIR epidemic model with nonlinear incidence rate and non-local delay effect in a continuous bounded spatial domain. We introduce the basic reproduction number R_0 of the model by the idea of next generation operator. By means of the theory of dynamical systems and uniform persistence, we investigate the global dynamics of the model in terms of R_0. Finally, we implement numerical simulations to show the feasibility of our results and explore some epidemiological insights.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.
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Supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2022JM-023)。
文摘In this paper,we establish an ShIhAhSvIvW model to investigate the impact of media communication on the transmission mechanism of dengue fever.Firstly,the basic reproduction number R0of the model is obtained by using the method of the next generation matrix.It shows that disease-free equilibrium is globally asymptotically stable when R0<1;the disease is uniformly persistent when R_(0)>1.Secondly,we select dengue fever case data from Guangdong Province from 2006 to 2019 for numerical simulations and predict its development trend.Finally,we conduct parameter sensitivity analysis,and the results show that increasing media publicity can to some extent reduce the number of patients.
基金supported by the Natural Science Foundation of Xinjiang(No.2022D01E41)the National Natural Science Foundation of China(No.12261087)the Open Project of Key Laboratory of Applied Mathematics of Xinjiang Autonomous Region(No.2021D04014)。
文摘In this paper,we study the epidemic model of respiratory syncytial virus SIRS with age structure.Firstly,the basic reproduction number R_(0) of the model is calculated and the positivity and ultimate boundedness of the solution to the model under initial conditions are proven.Secondly,it is proven that when R_(0)<1,the disease-free equilibrium is locally and globally asymptotically stable;and when R_(0)>1,the disease is uniformly persistent and there is at least a positive equilibrium.Finally,the effectiveness of the theoretical results is demonstrated by numerical simulation,and the impact of vaccination on disease transmission is predicted.
基金Project supported by the National Natural Science Foundation of China(Grant No.12101443,12371493)the Natural Science Foundation of Shanxi Province(Grant Nos.20210302124260 and 202303021221024)。
文摘Livestock transportation is a key factor that contributes to the spatial spread of brucellosis.To analyze the impact of sheep transportation on brucellosis transmission,we develop a human–sheep coupled brucellosis model within a metapopulation network framework.Theoretically,we examine the positively invariant set,the basic reproduction number,the existence,uniqueness,and stability of disease-free equilibrium and the existence of the endemic equilibrium of the model.For practical application,using Heilongjiang province as a case study,we simulate brucellosis transmission across 12 cities based on data using three network types:the BA network,the ER network,and homogeneous mixing network.The simulation results indicate that the network's average degree plays a role in the spread of brucellosis.For BA and ER networks,the basic reproduction number and cumulative incidence of brucellosis stabilize when the network's average degree reaches 4 or 5.In contrast,sheep transport in a homogeneous mixing network accelerates the cross-regional spread of brucellosis,whereas transportation in a BA network helps to control it effectively.Furthermore,the findings suggest that the movement of sheep is not always detrimental to controlling the spread of brucellosis.For cities with smaller sheep populations,such as Shuangyashan and Qitaihe,increasing the transport of sheep outward amplifies the spatial spread of the disease.In contrast,in cities with larger sheep populations,such as Qiqihar,Daqing,and Suihua,moderate sheep outflow can help reduce the spread.In addition,cities with large livestock populations play a dominant role in the overall transmission dynamics,underscoring the need for stricter supervision in these areas.
基金supported by the NSFC(12161079)the XSTP(KC2023058)。
文摘This paper concentrates on the dynamics of a waterborne pathogen periodic PDE model with environmental pollution.For this model,we derive the basic reproduction number R0and establish a threshold type result on its global dynamics in terms of R0,which predicts the extinction or persistence of diseases.More precisely,the disease-free steady state is globally attractive if R_(0)<1,while the system admits at least one positive periodic solution and the disease is uniformly persistent if R_(0)>1.Moreover,we carry out some numerical simulations to illustrate the long-term behaviors of solutions and explore the influence of environmental pollution and seasonality on the spread of waterborne diseases.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.62266030 and 61863025)International S & T Cooperation Projects of Gansu province (Grant No.144WCGA166)Longyuan Young Innovation Talents and the Doctoral Foundation of LUT。
文摘This paper first estimated the infectious capacity of COVID-19 based on the time series evolution data of confirmed cases in multiple countries. Then, a method to infer the cross-regional spread speed of COVID-19 was introduced in this paper, which took the gross domestic product(GDP) of each region as one of the factors that affect the spread speed of COVID-19 and studied the relationship between the GDP and the infection density of each region(China's Mainland, the United States, and EU countries). In addition, the geographic distance between regions was also considered in this method and the effect of geographic distance on the spread speed of COVID-19 was studied. Studies have shown that the probability of mutual infection of these two regions decreases with increasing geographic distance. Therefore, this paper proposed an epidemic disease spread index based on GDP and geographic distance to quantify the spread speed of COVID-19 in a region. The analysis results showed a strong correlation between the epidemic disease spread index in a region and the number of confirmed cases. This finding provides reasonable suggestions for the control of epidemics. Strengthening the control measures in regions with higher epidemic disease spread index can effectively control the spread of epidemics.
文摘Climate is a major driver of vector proliferation and arbovirus transmission, with temperature being a primary focus of research. Unlike other mosquito-borne diseases, Zika virus transmission involves both sexual transmission between humans and environmental transmission pathways, a characteristic largely overlooked in existing studies. This paper develops a temperature-dependent transmission model based on the unique transmission characteristics of the Zika virus. We estimated the historical transmission of Zika virus in Brazil using a temperature-dependent basic reproduction number to assess the impact of climate change on Zika virus spread in the region. Results indicate that the temperature range for Zika virus outbreaks is between 23.34˚C and 33.99˚C, peaking at 3.2 at 29.4˚C. This range and peak temperature are approximately 1˚C lower than those found in models that do not consider environmental transmission pathways. By incorporating seasonal variations into the model and categorizing ten Brazilian cities into five climatic types based on temperature changes, we simulated historical and future daily average temperatures using the GFDL-ESM4 temperature model. We analyzed the control periods and virus risks across different regions and projected Zika virus transmission risk in Brazil under four Shared Socioeconomic Pathways (SSP126, SSP245, SSP370, and SSP585). The results suggest that under the SSP126 scenario, the control periods will extend by 2 - 3 months with rising temperatures. This study concludes by discussing the impact of temperature changes on control measures, emphasizing the importance of reducing adult mosquito populations through the Sterile Insect Technique (SIT) to mitigate future risks.
基金funded by the the Guangdong Provincial Key Laboratory of Functional Substances in Medicinal Edible Resources and Healthcare Products(2021B1212040015)Natural Science Foundation of China(NSFC 11901027)+2 种基金China Postdoctoral Science Foundation(No.2021M703426)the Pyramid Talent Training Project of BUCEA(JDYC20200327)the Undergraduate Teaching Practice Program(J1703).
文摘COVID-19 is a worldwide pandemic that poses a great threat to people’s health and has a huge impact on economic and social life. The epidemic is currently at a low level, but is still prevalent worldwide. Therefore, it is still important to study the prevention and control of the spread of the COVID-19 epidemic. We collected the numbers of COVID-19 infections in China during the past three years, and obtained the regional distribution of outbreaks through analysis. To assess the capacity of medical resources in these regions in response to the outbreaks of COVID-19, we developed a model of COVID-19 transmission dynamics including mild and severe cases. The simulation showed that 11 regions, Beijing, Shanghai, Heilongjiang, Yunnan, Xinjiang, Inner Mongolia, Liaoning, Jilin, Hainan, Guangdong and Fujian, all have a serious shortage of medical beds in reserve. When facing the next new outbreak, these areas will have insufficient medical resources. We simulated the effects of drug effectiveness and the proportion of asymptomatic infected individuals on the spread of the epidemic, and obtained that an accurate determination of the proportion of asymptomatic patients in the population is crucial to the impact on healthcare resources, while improving the effectiveness of drugs can significantly reduce the burden on healthcare resources. Regions should invest more in healthcare and increase more medical resources, including medical beds. Government should accelerate the development of effective COVID-19 drugs to effectively control the scale of the outbreak. The proportion of asymptomatic patients in the population has a significant impact on the allocation of healthcare resources. The monitoring of antibody levels in the population should be strengthened to better control the spread of the epidemic.
基金supported by the National Natural Science Foundation of China(No.12171337)the Central Government Guided Local Science and Technology Development Projects(No.2024ZYD0059)+1 种基金the Natural Science Foundation of Sichuan Province(No.2022NSFSC0529)the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province(No.DRN2405)。
文摘This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.
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supported by the National Natural Science Foundation of China(12001339,61573016,11871316)Shanxi Scholarship Council of China(2015-094)+1 种基金the Natural Science Foundation of Shanxi(201801D121006)the Shanxi Province Science Foundation for Youths(201901D211413).
文摘Foot-and-mouth disease is one of the major contagious zoonotic diseases in the world.It is caused by various species of the genus Aphthovirus of the family Picornavirus,and it always brings a large number of infections and heavy financial losses.The disease has become a major public health concern.In this paper,we propose a nonlocal foot-and-mouth disease model in a spatially heterogeneous environment,which couples virus-to-animals and animals-to-animals transmission pathways,and investigate the dynamics of the disperal.The basic reproduction number R_(0)is defined as the spectral radius of the next generation operator R(x)by a renewal equation.The relationship between R_(0)and a principal eigenvalue of an operator L_(0)is built.Moreover,the proposed system exhibits threshold dynamics in terms of R_(0),in the sense that R_(0)determines whether or not foot-and-mouth disease invades the hosts.Through numerical simulations,we have found that increasing animals'movements is an effective control measure for preventing prevalence of the disease.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10901145)the Natural Science Foundation of Shanxi Province,China(Grant Nos. 2009011005-1 and 2012011002-1)the Top Young Academic Leaders of Higher Learning Institutions of Shanxi Province,China
文摘In this paper,a sexually transmitted disease model is proposed on complex networks,where contacts between humans are treated as a scale-free social network.There are three groups in our model,which are dangerous male,non-dangerous male,and female.By mathematical analysis,we obtain the basic reproduction number for the existence of endemic equilibrium and study the effects of various immunization schemes about different groups.Furthermore,numerical simulations are undertaken to verify more conclusions.
基金The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work was supported in part by Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China under Grant No. IRT1078 Key Program of NSFC-Guangdong Union Foundation under Grant No. U1135002+3 种基金 National Science and Technology Major Project of the Ministry of Science and Technology of China under Grant No. 2011ZX03005- 002 National Natural Science Foundation of China under Grant No.61173135 Natural Science Foundation of Shaanxi Province under Grant No.2014JQ8297 Fundamental Research Funds for the Central Universities of Ministry of Education of China under Grant Nos. JY 10000903001, K5051303007, K5051203012.
文摘Investigating the stability of information spreading over SNS helps to understand the principles inherent in the spreading behavior.This paper explores the mechanisms of information spreading including stifling mechanism,latent mechanism and forgetting mechanism,establishes a refined SEIR model,and builds the corresponding mean-field equations.The methods of the differential dynamics and the next generation matrix are used to calculate the equilibriums and the basic reproductive number,and the asymptotical stability of the network equilibriums are proved theoretically.Simulation experiments are carried out to analyze the effect of the spreading mechanisms on the information spreading process and the results support our conclusions.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61471080)the Equipment Development Department Research Foundation of China (Grant No. 61400010303)+2 种基金the Natural Science Research Project of Liaoning Education Department of China (Grant Nos. JDL2019019 and JDL2020002)the Surface Project for Natural Science Foundation in Guangdong Province of China (Grant No. 2019A1515011164)the Science and Technology Plan Project in Zhanjiang, China (Grant No. 2018A06001)。
文摘Current public-opinion propagation research usually focused on closed network topologies without considering the fluctuation of the number of network users or the impact of social factors on propagation. Thus, it remains difficult to accurately describe the public-opinion propagation rules of social networks. In order to study the rules of public opinion spread on dynamic social networks, by analyzing the activity of social-network users and the regulatory role of relevant departments in the spread of public opinion, concepts of additional user and offline rates are introduced, and the direct immune-susceptible, contacted, infected, and refractory (DI-SCIR) public-opinion propagation model based on real-time online users is established. The interventional force of relevant departments, credibility of real information, and time of intervention are considered, and a public-opinion propagation control strategy based on direct immunity is proposed. The equilibrium point and the basic reproduction number of the model are theoretically analyzed to obtain boundary conditions for public-opinion propagation. Simulation results show that the new model can accurately reflect the propagation rules of public opinion. When the basic reproduction number is less than 1, public opinion will eventually disappear in the network. Social factors can significantly influence the time and scope of public opinion spread on social networks. By controlling social factors, relevant departments can analyze the rules of public opinion spread on social networks to suppress the propagate of negative public opinion and provide a powerful tool to ensure security and stability of society.
文摘Dengue disease is the most common vector borne infectious disease transmitted to humans by infected adult female Aedes mosquitoes. Over the past several years the disease has been increasing remarkably and it has become a major public health concern. Dengue viruses have increased their geographic range into new human population due to travel of humans from one place to the other. In the present paper, we have proposed a multi patch SIR-SI model to study the host-vector dynamics of dengue disease in different patches including the travel of human population among the patches. We have considered different disease prevalences in different patches and different travel rates of humans. The dimensionless number, basic reproduction number R0 which shows that the disease dies out if R0 < 1 and the disease takes hold if R0 ≥ 1, is calculated. Local and global stability of the disease free equilibrium are analyzed. Simulations are observed considering the two patches only. The results show that controlling the travel of infectious hosts from high disease dominant patch to low disease dominant patch can help in controlling the disease in low disease dominant patch while high disease dominant becomes even more disease dominant. The understanding of the effect of travel of humans on the spatial spread of the disease among the patches can be helpful in improving disease control and prevention measures. In the present study, a patch may represent a city, a village or some biological habitat.
基金Supported by the Science and Technology Planed Projects of Gansu Province(18JR3RA217)Science Research Foundation for Higher Education Institutions of Gansu Province(2018B-032)
文摘In this paper, we are concerned with a reaction-diffusion SIR epidemic model with nonlinear incidence rate and non-local delay effect in a continuous bounded spatial domain. We introduce the basic reproduction number R_0 of the model by the idea of next generation operator. By means of the theory of dynamical systems and uniform persistence, we investigate the global dynamics of the model in terms of R_0. Finally, we implement numerical simulations to show the feasibility of our results and explore some epidemiological insights.
