There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist ...There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist when other infections are already resident within the population.Invasion reproductive numbers(IRN),which are tied to the stability of boundary endemic equilibria,can address this question.By reinterpreting resident infections epidemiologically,this study extends methods for finding IRNs to periodic systems,and presents some examples which illustrate the often complex computations required.Results identify conditions under which a simple time-average can be used to derive IRNs,and apply the methods to examine how seasonal fluctuations in influenza incidence facilitate the year-round persistence of bacterial respiratory infections.展开更多
Although invasion reproductive numbers(IRNs)are utilized frequently in continuous-time models with multiple interacting pathogens,they are yet to be explored in discrete-time systems.Here,we extend the concept of IRNs...Although invasion reproductive numbers(IRNs)are utilized frequently in continuous-time models with multiple interacting pathogens,they are yet to be explored in discrete-time systems.Here,we extend the concept of IRNs to discrete-time models by showing how to calculate them for a set of two-pathogen SIS models with coinfection.In our exploration,we address how sequencing events impacts the basic reproductive number(BRN)and IRN.As an illustrative example,our models are applied to rhinovirus and respiratory syncytial virus co-circulation.Results show that while the BRN is unaffected by variations in the order of events,the IRN differs.Furthermore,our models predict copersistence of multiple pathogen strains under cross-immunity,which is atypical of analogous continuous-time models.This investigation shows that sequencing events has important consequences for the IRN and can drastically alter competition dynamics.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
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
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
Wastewater surveillance(WWS)can leverage its wide coverage,population-based sampling,and high monitoring frequency to capture citywide pandemic trends independent of clinical surveillance.Here we conducted a nine mont...Wastewater surveillance(WWS)can leverage its wide coverage,population-based sampling,and high monitoring frequency to capture citywide pandemic trends independent of clinical surveillance.Here we conducted a nine months daily WWS for severe acute respiratory syndrome coronavirus 2(SARSCoV-2)from 12 wastewater treatment plants(WWTPs),covering approximately 80%of the population,to monitor infection dynamics in Hong Kong,China.We found that the SARS-CoV-2 virus concentration in wastewater was correlated with the daily number of reported cases and reached two pandemic peaks three days earlier during the study period.In addition,two different methods were established to estimate the prevalence/incidence rates from wastewater measurements.The estimated results from wastewater were consistent with findings from two independent citywide clinical surveillance programmes(rapid antigen test(RAT)surveillance and serology surveillance),but higher than the cases number reported by the Centre for Health Protection(CHP)of Hong Kong,China.Moreover,the effective reproductive number(R_(t))was estimated from wastewater measurements to reflect both citywide and regional transmission dynamics.Our findings demonstrate that large-scale intensive WWS from WWTPs provides cost-effective and timely public health information,especially when the clinical surveillance is inadequate and costly.This approach also provides insights into pandemic dynamics at higher spatiotemporal resolutions,facilitating the formulation of effective control policies and targeted resource allocation.展开更多
This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delay...This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.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 study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R<sub>0</sub>) using the nex...This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R<sub>0</sub>) using the next-generation matrix approach. Applying the Routh-Hurwitz Criterion, we establish that the Disease-Free Equilibrium (DFE) point achieves local asymptotic stability when R<sub>0</sub> α<sub>1</sub> and α<sub>2</sub>) are closely associated with reduced susceptibility in animal populations, underscoring the link between immigrants and susceptibility. Furthermore, our findings emphasize the interplay of disease introduction with population response and adaptation, particularly involving incoming infectious immigrants. Swift interventions are vital due to the limited potential for disease establishment and rapid susceptibility decline. This study offers crucial insights into the complexities of FMD transmission with active immigrants, informing effective disease management strategies.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
In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home ...In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.展开更多
A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was ...A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.展开更多
Mathematical modeling plays a crucial role in understanding the dynamics of malaria transmission and can provide valuable insights for designing effective control strategies. Malaria indeed faces significant challenge...Mathematical modeling plays a crucial role in understanding the dynamics of malaria transmission and can provide valuable insights for designing effective control strategies. Malaria indeed faces significant challenges due to a changing climate, particularly in regions where the disease is endemic. This disease is significantly impacted by changes in climate, especially rising temperatures and fluctuating rainfall patterns. This study explores the influence of temperature and rainfall abundance on malaria transmission dynamics within the context of Burundi. We have constructed a deterministic model that integrates these climatic parameters into the dynamics of the human host-mosquito vector system. The model’s steady states and basic reproduction number, calculated using the next-generation method, reveal important insights. Numerical simulations demonstrate that both temperature and rainfall significantly influence mosquito population dynamics, leading to distinct effects on malaria transmission. Specifically, we observe that temperatures between 20˚C and 32˚C, along with rainfall ranging from 10 to 30 mm per month, create optimal conditions for mosquito development, thus driving malaria transmission in Burundi. Furthermore, our findings indicate a delayed relationship between rainfall and malaria cases. When rainfall peaks in a given month, malaria does not peak immediately but instead shows a lagged response. Similarly, when rainfall decreases, malaria incidence drops after a certain time lag. This same lagged effect is observed when comparing temperature with confirmed malaria cases in Burundi. These findings highlight the urgent need to consider climate factors in malaria control strategies.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
HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not...HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.展开更多
文摘There are many cases within epidemiology where infections compete to persist within a population.In studying models for such cases,one of the goals is to determine which infections can invade a population and persist when other infections are already resident within the population.Invasion reproductive numbers(IRN),which are tied to the stability of boundary endemic equilibria,can address this question.By reinterpreting resident infections epidemiologically,this study extends methods for finding IRNs to periodic systems,and presents some examples which illustrate the often complex computations required.Results identify conditions under which a simple time-average can be used to derive IRNs,and apply the methods to examine how seasonal fluctuations in influenza incidence facilitate the year-round persistence of bacterial respiratory infections.
文摘Although invasion reproductive numbers(IRNs)are utilized frequently in continuous-time models with multiple interacting pathogens,they are yet to be explored in discrete-time systems.Here,we extend the concept of IRNs to discrete-time models by showing how to calculate them for a set of two-pathogen SIS models with coinfection.In our exploration,we address how sequencing events impacts the basic reproductive number(BRN)and IRN.As an illustrative example,our models are applied to rhinovirus and respiratory syncytial virus co-circulation.Results show that while the BRN is unaffected by variations in the order of events,the IRN differs.Furthermore,our models predict copersistence of multiple pathogen strains under cross-immunity,which is atypical of analogous continuous-time models.This investigation shows that sequencing events has important consequences for the IRN and can drastically alter competition dynamics.
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.
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.
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financially supported by the Health and Medical Research Fund(COVID1903015)the Food and Health Bureau,the Government of the Hong Kong Special Administrative Region(SAR),China+1 种基金supported by the AIR@InnoHK(KL,GML,and JTW)Health@InnoHK(MP and LLMP)administered by the Innovation and Technology Commission of the Government of the Hong Kong SAR.
文摘Wastewater surveillance(WWS)can leverage its wide coverage,population-based sampling,and high monitoring frequency to capture citywide pandemic trends independent of clinical surveillance.Here we conducted a nine months daily WWS for severe acute respiratory syndrome coronavirus 2(SARSCoV-2)from 12 wastewater treatment plants(WWTPs),covering approximately 80%of the population,to monitor infection dynamics in Hong Kong,China.We found that the SARS-CoV-2 virus concentration in wastewater was correlated with the daily number of reported cases and reached two pandemic peaks three days earlier during the study period.In addition,two different methods were established to estimate the prevalence/incidence rates from wastewater measurements.The estimated results from wastewater were consistent with findings from two independent citywide clinical surveillance programmes(rapid antigen test(RAT)surveillance and serology surveillance),but higher than the cases number reported by the Centre for Health Protection(CHP)of Hong Kong,China.Moreover,the effective reproductive number(R_(t))was estimated from wastewater measurements to reflect both citywide and regional transmission dynamics.Our findings demonstrate that large-scale intensive WWS from WWTPs provides cost-effective and timely public health information,especially when the clinical surveillance is inadequate and costly.This approach also provides insights into pandemic dynamics at higher spatiotemporal resolutions,facilitating the formulation of effective control policies and targeted resource allocation.
基金supported via funding from Prince Sattam bin Abdulaziz University Project Number(PSAU/2023/R/1444)The first author is partially supported by the University Research Fellowship(PU/AD-3/URF/21F37237/2021 dated 09.11.2021)of PeriyarUniversity,SalemThe second author is supported by the fund for improvement of Science and Technology Infrastructure(FIST)of DST(SR/FST/MSI-115/2016).
文摘This research examines the transmission dynamics of the Omicron variant of COVID-19 using SEIQIcRVW and SQIRV models,considering the delay in converting susceptible individuals into infected ones.The significant delays eventually resulted in the pandemic’s containment.To ensure the safety of the host population,this concept integrates quarantine and the COVID-19 vaccine.We investigate the stability of the proposed models.The fundamental reproduction number influences stability conditions.According to our findings,asymptomatic cases considerably impact the prevalence of Omicron infection in the community.The real data of the Omicron variant from Chennai,Tamil Nadu,India,is used to validate the outputs.
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.
文摘This study employs mathematical modeling to analyze the impact of active immigrants on Foot and Mouth Disease (FMD) transmission dynamics. We calculate the reproduction number (R<sub>0</sub>) using the next-generation matrix approach. Applying the Routh-Hurwitz Criterion, we establish that the Disease-Free Equilibrium (DFE) point achieves local asymptotic stability when R<sub>0</sub> α<sub>1</sub> and α<sub>2</sub>) are closely associated with reduced susceptibility in animal populations, underscoring the link between immigrants and susceptibility. Furthermore, our findings emphasize the interplay of disease introduction with population response and adaptation, particularly involving incoming infectious immigrants. Swift interventions are vital due to the limited potential for disease establishment and rapid susceptibility decline. This study offers crucial insights into the complexities of FMD transmission with active immigrants, informing effective disease management strategies.
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In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.
文摘A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.
文摘Mathematical modeling plays a crucial role in understanding the dynamics of malaria transmission and can provide valuable insights for designing effective control strategies. Malaria indeed faces significant challenges due to a changing climate, particularly in regions where the disease is endemic. This disease is significantly impacted by changes in climate, especially rising temperatures and fluctuating rainfall patterns. This study explores the influence of temperature and rainfall abundance on malaria transmission dynamics within the context of Burundi. We have constructed a deterministic model that integrates these climatic parameters into the dynamics of the human host-mosquito vector system. The model’s steady states and basic reproduction number, calculated using the next-generation method, reveal important insights. Numerical simulations demonstrate that both temperature and rainfall significantly influence mosquito population dynamics, leading to distinct effects on malaria transmission. Specifically, we observe that temperatures between 20˚C and 32˚C, along with rainfall ranging from 10 to 30 mm per month, create optimal conditions for mosquito development, thus driving malaria transmission in Burundi. Furthermore, our findings indicate a delayed relationship between rainfall and malaria cases. When rainfall peaks in a given month, malaria does not peak immediately but instead shows a lagged response. Similarly, when rainfall decreases, malaria incidence drops after a certain time lag. This same lagged effect is observed when comparing temperature with confirmed malaria cases in Burundi. These findings highlight the urgent need to consider climate factors in malaria control strategies.
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.
文摘HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.
