Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynami...Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynamical behavior of this model and define the basic reproductive number R0. The authors also prove that the diseased-free equilibrium is globally asymptotically stable if R0 〈 1. The endemic equilibrium is locally asymptotically stable if K1 〉 α and R0 〉 1.展开更多
In this paper,we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI)age-infection-structured human immunodeficiency virus(HIV)model with heterogeneous transmission.Mathematical analysis ...In this paper,we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI)age-infection-structured human immunodeficiency virus(HIV)model with heterogeneous transmission.Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number R_(0).If R_(0)<1,disease-free equilibrium is globally asymptotically stable.If R_(0)>1,it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable.The proofs of global stability utilize Lyapunov functions.Besides,the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for is R_(0)performed by the method of partial rank correlation coefficient(PRCC).展开更多
We present an epidemic model which can incorporate essential biological detail as well as the intrinsic demographic stochastieity of the epidemic process, yet is very simple, enabling rapid generation of a large numbe...We present an epidemic model which can incorporate essential biological detail as well as the intrinsic demographic stochastieity of the epidemic process, yet is very simple, enabling rapid generation of a large number of simulations, A deterministic version of the model is also derived, in the limit of infinitely large populations, and a final-size formula for the deterministic model is proved. A key advantage of the model proposed is that it is possible to write down an explicit likelihood functions for it, which enables a systematic procedure for fitting parameters to real incidence data, using maximum likelihood.展开更多
In this paper, nonlinear incidence rate is incorporated into an age-of-infection SVIR epidemiological model. By the method of Lyapunov functionals, it is shown that the basic reproduction number R0 of the model is a t...In this paper, nonlinear incidence rate is incorporated into an age-of-infection SVIR epidemiological model. By the method of Lyapunov functionals, it is shown that the basic reproduction number R0 of the model is a threshold parameter in the sense that if R0 〈 1, the disease dies out, while if R0〉1, the disease persists.展开更多
基金the National Natural Sciences Foundation of China (10471040)the University Foundation of Yuncheng University (20060218)
文摘Saturating contact rate of individual contacts is crucial in an epidemiology model. A mathematical SIR model with saturation incidence and age of infection is formulated in this paper. In addition, we study the dynamical behavior of this model and define the basic reproductive number R0. The authors also prove that the diseased-free equilibrium is globally asymptotically stable if R0 〈 1. The endemic equilibrium is locally asymptotically stable if K1 〉 α and R0 〉 1.
基金This work is partly supported by the National Sciences Foundation of China(Nos.11971278,61873154)The 1331 Engineering Project of Shanxi Province,China.Health Commission of Shanxi Province(2020XM18).
文摘In this paper,we analyze the global asymptotic behaviors of a mathematical susceptible-infected(SI)age-infection-structured human immunodeficiency virus(HIV)model with heterogeneous transmission.Mathematical analysis shows that the local and global dynamics are completely determined by the basic reproductive number R_(0).If R_(0)<1,disease-free equilibrium is globally asymptotically stable.If R_(0)>1,it shows that disease-free equilibrium is unstable and the unique endemic equilibrium is globally asymptotically stable.The proofs of global stability utilize Lyapunov functions.Besides,the numerical simulations are illustrated to support these theoretical results and sensitivity analysis of each parameter for is R_(0)performed by the method of partial rank correlation coefficient(PRCC).
文摘We present an epidemic model which can incorporate essential biological detail as well as the intrinsic demographic stochastieity of the epidemic process, yet is very simple, enabling rapid generation of a large number of simulations, A deterministic version of the model is also derived, in the limit of infinitely large populations, and a final-size formula for the deterministic model is proved. A key advantage of the model proposed is that it is possible to write down an explicit likelihood functions for it, which enables a systematic procedure for fitting parameters to real incidence data, using maximum likelihood.
基金Acknowledgments We are very grateful to the two anonymous reviewers for their very valuable comments and suggestions, based on which we have revised our manuscript. Research is partially supported by the National Natural Science Foundation of China （Nos. 61573016, 61203228）, China Scholarship Council （201308140016）, Shanxi Scholarship Council of China （2015-094）, Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi, Shanxi ＂131＂ Talents Program, Shanxi ＂100＂ Talent Program.
文摘In this paper, nonlinear incidence rate is incorporated into an age-of-infection SVIR epidemiological model. By the method of Lyapunov functionals, it is shown that the basic reproduction number R0 of the model is a threshold parameter in the sense that if R0 〈 1, the disease dies out, while if R0〉1, the disease persists.
