A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the origina...A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population modeling.By making corresponding Lyapunov function and using It formula,the condition for the solution of the model tending to the disease free equilibrium asymptotically was obtained.Under this condition,the epidemics will die out as time goes by.Based on this,almost surely exponential stability was analyzed.展开更多
Due to the heterogeneity of contact structure,it is more reasonable to model on networks for epidemics.Because of the stochastic nature of events and the discrete number of individuals,the spread of epidemics is more ...Due to the heterogeneity of contact structure,it is more reasonable to model on networks for epidemics.Because of the stochastic nature of events and the discrete number of individuals,the spread of epidemics is more appropriately viewed as a Markov chain.Therefore,we establish stochastic SIRS models with vaccination on networks to study the mean and variance of the number of susceptible and infected individuals for large-scale populations.Using van Kampen's system-size expansion,we derive a high-dimensional deterministic system which describes the mean behaviour and a Fokker-Planck equation which characterizes the variance around deterministic trajectories.Utilizing the qualitative analysis technique and Lyapunov function,we demonstrate that the disease-free equilibrium of the deterministic system is globally asymptotically stable if the basic reproduction number R_(0)<1;and the endemic equilibrium is globally asymptotically stable if R_(0)>1.Through the analysis of the Fokker-Planck equation,we obtain the asymptotic expression for the variance of the number of susceptible and infected individuals around the endemic equilibrium,which can be approximated by the elements of principal diagonal of the solution of the corresponding Lyapunov equation.Here,the solution of Lyapunov equation is expressed by vectorization operator of matrices and Kronecker product.Finally,numerical simulations illustrate that vaccination can reduce infections and increase fluctuations of the number of infected individuals and show that individuals with greater degree are more easily infected.展开更多
A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally as...A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.展开更多
In this paper,a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases.Nonlinear incidence and vaccination strategies are also considered in the propo...In this paper,a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases.Nonlinear incidence and vaccination strategies are also considered in the proposed model.By using the method of stochastic analysis,we point out the key parameters that determine the persistence and extinction of the diseases.Specifically,if R0^s is greater than 0,the stochastic system has a unique ergodic stationary distribution;while if R ^* is less than 0,the diseases will be extinct at an exponential rate.展开更多
Influenza remains a global challenge,imposing a significant burden on society and the economy.Many influenza cases are asymptomatic,leading to greater uncertainty and the under-reporting of cases in influenza transmis...Influenza remains a global challenge,imposing a significant burden on society and the economy.Many influenza cases are asymptomatic,leading to greater uncertainty and the under-reporting of cases in influenza transmission and preventing authorities from taking effective control measures.In this study,we propose a Bayesian hierarchical approach to model and correct under-reporting of influenza cases in Hong Kong,incorporating a discrete-time stochastic,Susceptible-Infected-Recovered-Susceptible(DT-SIRS)model that allows transmission rate to vary over time.The incidence of influenza exhibits seasonality.To examine the relationship between meteorological factors and seasonal influenza activity in subtropical areas,five meteorological factors are included in the model.The proposed model explores the effects of meteorological factors on transmission rates and disease detection covariates on under-reporting,and the inclusion of the DT-SIRS model enables more accurate inference regarding true disease counts.The results demonstrate that under-reporting rates of influenza cases vary significantly in different years and epidemic seasons.In conclusion,our method effectively captures the dynamic behavior of the disease,and we can accurately estimate under-reporting and provide new possibilities for early warning of influenza based on meteorological data and routine surveillance data.展开更多
基金Foundation of Shanghai for Outstanding Young Teachers in University,China(No.B-5300-08-007)the 085 Knowledge Innovation Project of Shanghai Municipal Education Commission,China(No.Z08509008-01)Humanities and SocialScience Fund General Project of Ministry of Education,China(No.08JA630051)
文摘A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population modeling.By making corresponding Lyapunov function and using It formula,the condition for the solution of the model tending to the disease free equilibrium asymptotically was obtained.Under this condition,the epidemics will die out as time goes by.Based on this,almost surely exponential stability was analyzed.
基金supported by National Natural Science Foundation of China(Nos.12371494,12231012,11971279)Shanxi Provincial Key Research and Development Project(No.202202020101010).
文摘Due to the heterogeneity of contact structure,it is more reasonable to model on networks for epidemics.Because of the stochastic nature of events and the discrete number of individuals,the spread of epidemics is more appropriately viewed as a Markov chain.Therefore,we establish stochastic SIRS models with vaccination on networks to study the mean and variance of the number of susceptible and infected individuals for large-scale populations.Using van Kampen's system-size expansion,we derive a high-dimensional deterministic system which describes the mean behaviour and a Fokker-Planck equation which characterizes the variance around deterministic trajectories.Utilizing the qualitative analysis technique and Lyapunov function,we demonstrate that the disease-free equilibrium of the deterministic system is globally asymptotically stable if the basic reproduction number R_(0)<1;and the endemic equilibrium is globally asymptotically stable if R_(0)>1.Through the analysis of the Fokker-Planck equation,we obtain the asymptotic expression for the variance of the number of susceptible and infected individuals around the endemic equilibrium,which can be approximated by the elements of principal diagonal of the solution of the corresponding Lyapunov equation.Here,the solution of Lyapunov equation is expressed by vectorization operator of matrices and Kronecker product.Finally,numerical simulations illustrate that vaccination can reduce infections and increase fluctuations of the number of infected individuals and show that individuals with greater degree are more easily infected.
基金Supported by National Natural Science Foundation of China (Grant No. 10971021)the Ministry of Education of China (Grant No. 109051)+1 种基金the Ph.D. Programs Foundation of Ministry of China (Grant No. 200918)the Graduate Innovative Research Project of NENU (Grant No. 09SSXT117)
文摘A stochastic two-group SIR model is presented in this paper. The existence and uniqueness of its nonnegative solution is obtained, and the solution belongs to a positively invariant set. Further- more, the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 〈 1, which means the disease will die out. While if R0 〉 1, we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average. In addition, the intensity of the fluctuation is proportional to the intensity of the white noise. When the white noise is small, we consider the disease will prevail. At last, we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.
基金Z.Qiu is supported by the National Natural Science Foundation of China(NSFC)grant No.11671206X.Zhao is supported by the Scholarship Foundation of China Scholarship Council grant No.201906840072+2 种基金T.Feng is supported by the Scholarship Foundation of China Scholarship Council grant No.201806840120the Out-standing Chinese and Foreign Youth Exchange Program of China Association of Science and Technologythe Fundamental Research Funds for the Central Universities grant No.30918011339.
文摘In this paper,a stochastic epidemic system with both switching noise and white noise is proposed to research the dynamics of the diseases.Nonlinear incidence and vaccination strategies are also considered in the proposed model.By using the method of stochastic analysis,we point out the key parameters that determine the persistence and extinction of the diseases.Specifically,if R0^s is greater than 0,the stochastic system has a unique ergodic stationary distribution;while if R ^* is less than 0,the diseases will be extinct at an exponential rate.
文摘Influenza remains a global challenge,imposing a significant burden on society and the economy.Many influenza cases are asymptomatic,leading to greater uncertainty and the under-reporting of cases in influenza transmission and preventing authorities from taking effective control measures.In this study,we propose a Bayesian hierarchical approach to model and correct under-reporting of influenza cases in Hong Kong,incorporating a discrete-time stochastic,Susceptible-Infected-Recovered-Susceptible(DT-SIRS)model that allows transmission rate to vary over time.The incidence of influenza exhibits seasonality.To examine the relationship between meteorological factors and seasonal influenza activity in subtropical areas,five meteorological factors are included in the model.The proposed model explores the effects of meteorological factors on transmission rates and disease detection covariates on under-reporting,and the inclusion of the DT-SIRS model enables more accurate inference regarding true disease counts.The results demonstrate that under-reporting rates of influenza cases vary significantly in different years and epidemic seasons.In conclusion,our method effectively captures the dynamic behavior of the disease,and we can accurately estimate under-reporting and provide new possibilities for early warning of influenza based on meteorological data and routine surveillance data.
