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
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.
