The outbreak of infectious diseases is the result of a combination of various factors,including season,the movement of individuals,non-pharmaceutical interventions(NPIs)and the effectiveness and availability of vaccin...The outbreak of infectious diseases is the result of a combination of various factors,including season,the movement of individuals,non-pharmaceutical interventions(NPIs)and the effectiveness and availability of vaccines.Taking these key elements into consideration,an almost periodic SVEIR warning model in the patch environment is here proposed.First,in terms of reproduction numbers,our results imply that if the effective reproduction numbers are R_(e)<1,then the disease dies out;if R_(e)>1,then the disease spreads and leads to local outbreaks.Second,the relationships between R_(e)and C_(s1),C_(a1)(see Section 2)are given by numerical simulations.The numerical results show that even if all people are vaccinated,NPIs are still needed because of the potentially low efficacy of vaccines.Furthermore,the numerical results suggest that NPIs and the strengthening of the effective rate of vaccination are essential in order to achieve herd immunity.Theories involving this model effectively explain the transmission mechanism of most infectious diseases,and provide a valuable theoretical basis for analyzing new infectious diseases in the future.Moreover,this model is helpful for the prevention and control of infectious diseases and the formulation of public health safety policies.展开更多
In this paper,we consider a delayed diffusive SVEIR model with general incidence.We first establish the threshold dynamics of this model.Using a Nonstandard Finite Difference(NSFD) scheme,we then give the discretizati...In this paper,we consider a delayed diffusive SVEIR model with general incidence.We first establish the threshold dynamics of this model.Using a Nonstandard Finite Difference(NSFD) scheme,we then give the discretization of the continuous model.Applying Lyapunov functions,global stability of the equilibria are established.Numerical simulations are presented to validate the obtained results.The prolonged time delay can lead to the elimination of the infectiousness.展开更多
The lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection...The lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this paper, we assess the impact of vaccination in the control of spread of poliomyelitis via a deterministic SVEIR (Susceptible-Vaccinated-Latent-Infectious-Removed) model of infectious disease transmission, where vaccinated individuals are also susceptible, although to a lesser degree. Using Lyapunov-Lasalle methods, we prove the global asymptotic stability of the unique endemic equilibrium whenever ?. Numerical simulations, using poliomyelitis data from Cameroon, are conducted to approve analytic results and to show the importance of vaccinate coverage in the control of disease spread.展开更多
As of May 2024,the main strains of COVID-19 caused hundreds of millions of infection cases and millions of deaths worldwide.In this study,we consider the COVID-19 epidemics with the main strains in the Chinese mainlan...As of May 2024,the main strains of COVID-19 caused hundreds of millions of infection cases and millions of deaths worldwide.In this study,we consider the COVID-19 epidemics with the main strains in the Chinese mainland.We study complex interactions among hosts,non-pharmaceutical interventions,and vaccinations for the main strains by a differential equation model called SVEIR.The disease transmission model incorporates two strains and protection awareness of the susceptible population.Results of this study show that the protection awareness plays a crucial role against infection of the population,and that the vaccines are effective against the circulation of the earlier strains,but ineffective for emerging strains.By using the next generation matrix method,the basic reproduction number of the SVEIR model is firstly obtained.Our analysis by Hurwitz criterion and LaSalle's invariance principle shows that the disease free-equilibrium point is locally and globally asymptotically stable when the threshold value is below one.The existences of endemic equilibrium points are also established,and the global asymptotic stabilities are analyzed using the Lyapunov function method.Further,the SVEIR model is confirmed to satisfy the principle of competitive exclusion,of which the strain with the larger value of the basic reproduction number is dominant.Numerically,the surveillance data with the Omicron strain and the XBB strain are split by the cubic spline interpolation method.The fitting curves against the surveillance data are plotted using the least-squares method from MATLAB.The results indicate that the XBB strain dominates in this study.Moreover,a global sensitivity analysis of the key parameters is performed by using of PRCC.The numerical simulations imply that combination control strategy positively impacts on the infection scale than what separate control strategy does,and that the earlier time producing protection awareness for the public creates less infection scale,further that the increment of protection awareness also reduces the infection scale.Therefore,the policymakers of the local government are suggested to concern the changes of protection awareness of the public.展开更多
The epidemiological characteristics and distributions of two epidemics in Fujian Province of Southeast China were attributed to the complex interactions among variant,host,and non-pharmaceutical interventions(NPIs).Al...The epidemiological characteristics and distributions of two epidemics in Fujian Province of Southeast China were attributed to the complex interactions among variant,host,and non-pharmaceutical interventions(NPIs).All reported cases in the Putian epidemic(September 8–October 2,2021,Delta variant B.1.617.2)and Fuzhou epidemic(October 22–November 18,2022,Omicron variant BA.5.2)were classified by sex,age group,occupation,and location in this study.Using surveillance data from the Fujian Provincial Center for Disease Control and Prevention,we established a virus-oriented SVEIR(Susceptible–Vaccinated–Exposed–Infected–Recovered)model to investigate the dynamic evolution features of these two variants and the effects of NPIs.The optimal simulations were carried out with variants and scenario investigations.The scenario investigations showed that NPIs significantly reduced the transmission risk and infection scales of COVID-19,and that the Omicron variant was more infectious than the Delta variant.Moreover,the dynamic investigations revealed the increasing tendencies from Delta to Omicron,such as the basic reproduction number,infection rate,percentage of high-risk cases,and the growth rate.Decreasing tendencies were also identified,such as the average recovery period,the awareness delay,and the percentage of symptomatic cases.This study highlighted that NPIs played critical roles in successfully containing the two epidemics.Such interventions are strongly recommended to public health policymakers.展开更多
In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics a...In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.展开更多
The complex interactions were performed among non-pharmaceutical interventions,vaccinations,and hosts for all epidemics in China's Mainland during the spread of COVID-19.Specially,the small-scale epidemic in the c...The complex interactions were performed among non-pharmaceutical interventions,vaccinations,and hosts for all epidemics in China's Mainland during the spread of COVID-19.Specially,the small-scale epidemic in the city described by SVEIR model was less found in the current studies.The SVEIR model with control was established to analyze the dynamical and epidemiological features of two epidemics in Jinzhou City led by Omicron variants before and after Twenty Measures.In this study,the total population(N)of Jinzhou City was divided into five compartments:the susceptible(S),the vaccinated(V),the exposed(E),the infected(I),and the recovered(R).By surveillance data and the SVEIR model,three methods(maximum likelihood method,exponential growth rate method,next generation matrix method)were governed to estimate basic reproduction number,and the results showed that an increasing tendency of basic reproduction number from Omicron BA.5.2 to Omicron BA.2.12.1.Meanwhile,the effective reproduction number for two epidemics were investigated by surveillance data,and the results showed that Jinzhou wave 1 reached the peak on November 1 and was controlled 7 days later,and that Jinzhou wave 2 reached the peak on November 28 and was controlled 5 days later.Moreover,the impacts of non-pharmaceutical interventions(awareness delay,peak delay,control intensity)were discussed extensively,the variations of infection scales for Omicron variant and EG.5 variant were also discussed.Furthermore,the investigations on peaks and infection scales for two epidemics in dynamic zero-COVID policy were operated by the SVEIR model with control.The investigations on public medical requirements of Jinzhou City and Liaoning Province were analyzed by using SVEIR model without control,which provided a possible perspective on variant evolution in the future.展开更多
The global dynamics of an SVEIR epidemic model with age-dependent waning immu- nity, latency and relapse are studied. Sharp threshold properties for global asymptotic stability of both disease-free equilibrium and end...The global dynamics of an SVEIR epidemic model with age-dependent waning immu- nity, latency and relapse are studied. Sharp threshold properties for global asymptotic stability of both disease-free equilibrium and endemic equilibrium are given. The asymptotic smoothness, uniform persistence and the existence of interior global attractor of the semi-flow generated by a family of solutions of the system are also addressed. Furthermore, some related strategies for controlling the spread of diseases are discussed.展开更多
基金supported by the NSFC(11501269)and the Natural Science Foundation of Gansu Province(23JRRA1041).
文摘The outbreak of infectious diseases is the result of a combination of various factors,including season,the movement of individuals,non-pharmaceutical interventions(NPIs)and the effectiveness and availability of vaccines.Taking these key elements into consideration,an almost periodic SVEIR warning model in the patch environment is here proposed.First,in terms of reproduction numbers,our results imply that if the effective reproduction numbers are R_(e)<1,then the disease dies out;if R_(e)>1,then the disease spreads and leads to local outbreaks.Second,the relationships between R_(e)and C_(s1),C_(a1)(see Section 2)are given by numerical simulations.The numerical results show that even if all people are vaccinated,NPIs are still needed because of the potentially low efficacy of vaccines.Furthermore,the numerical results suggest that NPIs and the strengthening of the effective rate of vaccination are essential in order to achieve herd immunity.Theories involving this model effectively explain the transmission mechanism of most infectious diseases,and provide a valuable theoretical basis for analyzing new infectious diseases in the future.Moreover,this model is helpful for the prevention and control of infectious diseases and the formulation of public health safety policies.
文摘In this paper,we consider a delayed diffusive SVEIR model with general incidence.We first establish the threshold dynamics of this model.Using a Nonstandard Finite Difference(NSFD) scheme,we then give the discretization of the continuous model.Applying Lyapunov functions,global stability of the equilibria are established.Numerical simulations are presented to validate the obtained results.The prolonged time delay can lead to the elimination of the infectiousness.
文摘The lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this paper, we assess the impact of vaccination in the control of spread of poliomyelitis via a deterministic SVEIR (Susceptible-Vaccinated-Latent-Infectious-Removed) model of infectious disease transmission, where vaccinated individuals are also susceptible, although to a lesser degree. Using Lyapunov-Lasalle methods, we prove the global asymptotic stability of the unique endemic equilibrium whenever ?. Numerical simulations, using poliomyelitis data from Cameroon, are conducted to approve analytic results and to show the importance of vaccinate coverage in the control of disease spread.
基金supported by the Natural Science Foundation of Fujian Province of China(2021J01621)Special Projects of the Central Government Guiding Local Science and Technology Development(2021L3018)+1 种基金Consultancy Project by the Chinese Academy of Engineering(2022-JB-06,2023-JB-12)Project for epidemiological characteristics analysis and clustering epidemics analysis of COVID-19 in Jinzhou City(JZ2024B066).
文摘As of May 2024,the main strains of COVID-19 caused hundreds of millions of infection cases and millions of deaths worldwide.In this study,we consider the COVID-19 epidemics with the main strains in the Chinese mainland.We study complex interactions among hosts,non-pharmaceutical interventions,and vaccinations for the main strains by a differential equation model called SVEIR.The disease transmission model incorporates two strains and protection awareness of the susceptible population.Results of this study show that the protection awareness plays a crucial role against infection of the population,and that the vaccines are effective against the circulation of the earlier strains,but ineffective for emerging strains.By using the next generation matrix method,the basic reproduction number of the SVEIR model is firstly obtained.Our analysis by Hurwitz criterion and LaSalle's invariance principle shows that the disease free-equilibrium point is locally and globally asymptotically stable when the threshold value is below one.The existences of endemic equilibrium points are also established,and the global asymptotic stabilities are analyzed using the Lyapunov function method.Further,the SVEIR model is confirmed to satisfy the principle of competitive exclusion,of which the strain with the larger value of the basic reproduction number is dominant.Numerically,the surveillance data with the Omicron strain and the XBB strain are split by the cubic spline interpolation method.The fitting curves against the surveillance data are plotted using the least-squares method from MATLAB.The results indicate that the XBB strain dominates in this study.Moreover,a global sensitivity analysis of the key parameters is performed by using of PRCC.The numerical simulations imply that combination control strategy positively impacts on the infection scale than what separate control strategy does,and that the earlier time producing protection awareness for the public creates less infection scale,further that the increment of protection awareness also reduces the infection scale.Therefore,the policymakers of the local government are suggested to concern the changes of protection awareness of the public.
基金supported by Consultancy Project by the Chinese Academy of Engineering(2022-JB-06)supported by Special Projects of the Central Government Guiding Local Science and Technology Development(2021L3018)+2 种基金supported by the Natural Science Foundation of Fujian ProvinceProvince of China(2021J01621)supported by Fujian Science and Technology Innovation Platform Construction Project(2019Y2001)Health Science and Technology Project of Fujian Province(2020GGB019).
文摘The epidemiological characteristics and distributions of two epidemics in Fujian Province of Southeast China were attributed to the complex interactions among variant,host,and non-pharmaceutical interventions(NPIs).All reported cases in the Putian epidemic(September 8–October 2,2021,Delta variant B.1.617.2)and Fuzhou epidemic(October 22–November 18,2022,Omicron variant BA.5.2)were classified by sex,age group,occupation,and location in this study.Using surveillance data from the Fujian Provincial Center for Disease Control and Prevention,we established a virus-oriented SVEIR(Susceptible–Vaccinated–Exposed–Infected–Recovered)model to investigate the dynamic evolution features of these two variants and the effects of NPIs.The optimal simulations were carried out with variants and scenario investigations.The scenario investigations showed that NPIs significantly reduced the transmission risk and infection scales of COVID-19,and that the Omicron variant was more infectious than the Delta variant.Moreover,the dynamic investigations revealed the increasing tendencies from Delta to Omicron,such as the basic reproduction number,infection rate,percentage of high-risk cases,and the growth rate.Decreasing tendencies were also identified,such as the average recovery period,the awareness delay,and the percentage of symptomatic cases.This study highlighted that NPIs played critical roles in successfully containing the two epidemics.Such interventions are strongly recommended to public health policymakers.
文摘In this paper, based on a class of multi-group epidemic models of SEIR type with bilinear incidences, we introduce a vaccination compartment, leading to multi-group SVEIR model. We establish that the global dynamics are completely determined by the basic reproduction number R0V which is defined by the spectral radius of the next generation matrix. Our proofs of global stability of the equilibria utilize a graph-theoretical approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccines to obtain immunity or the possibility for them to be infected before acquiring immunity is neglected in each group, this condition will be satisfied and the disease can always be eradicated by suitable vaccination strategies. This may lead to over evaluation for the effect of vaccination.
基金This study received was supported by the Natural Science Foundation of Fujian Province of China(2021J01621)Consultancy Project by the Chinese Academy of Engineering(2022-JB-06)Project for epidemiological characteristics analysis and clustering epidemics analysis of COVID-19 in Jinzhou City(JZ2024B066).
文摘The complex interactions were performed among non-pharmaceutical interventions,vaccinations,and hosts for all epidemics in China's Mainland during the spread of COVID-19.Specially,the small-scale epidemic in the city described by SVEIR model was less found in the current studies.The SVEIR model with control was established to analyze the dynamical and epidemiological features of two epidemics in Jinzhou City led by Omicron variants before and after Twenty Measures.In this study,the total population(N)of Jinzhou City was divided into five compartments:the susceptible(S),the vaccinated(V),the exposed(E),the infected(I),and the recovered(R).By surveillance data and the SVEIR model,three methods(maximum likelihood method,exponential growth rate method,next generation matrix method)were governed to estimate basic reproduction number,and the results showed that an increasing tendency of basic reproduction number from Omicron BA.5.2 to Omicron BA.2.12.1.Meanwhile,the effective reproduction number for two epidemics were investigated by surveillance data,and the results showed that Jinzhou wave 1 reached the peak on November 1 and was controlled 7 days later,and that Jinzhou wave 2 reached the peak on November 28 and was controlled 5 days later.Moreover,the impacts of non-pharmaceutical interventions(awareness delay,peak delay,control intensity)were discussed extensively,the variations of infection scales for Omicron variant and EG.5 variant were also discussed.Furthermore,the investigations on peaks and infection scales for two epidemics in dynamic zero-COVID policy were operated by the SVEIR model with control.The investigations on public medical requirements of Jinzhou City and Liaoning Province were analyzed by using SVEIR model without control,which provided a possible perspective on variant evolution in the future.
基金X. Liu is supported by the National Natural Science Foundation of China （11271303）. L. Liu is supported by the National Natural Science Foundation of China （11601293） and Chongqing Graduate Student Research Innovation Project （CYB14053）. We are grateful to the editors and two anonymous referees for their valuable comments and suggestions that led to an improvement of our manuscript.
文摘The global dynamics of an SVEIR epidemic model with age-dependent waning immu- nity, latency and relapse are studied. Sharp threshold properties for global asymptotic stability of both disease-free equilibrium and endemic equilibrium are given. The asymptotic smoothness, uniform persistence and the existence of interior global attractor of the semi-flow generated by a family of solutions of the system are also addressed. Furthermore, some related strategies for controlling the spread of diseases are discussed.
