文章基本信息

标题：The dynamics of an epidemic model with targeted antiviral prophylaxis
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作者：Zhipeng Qiu ; Zhilan Feng
期刊名称：Journal of Biological Dynamics
印刷版ISSN：1751-3758
电子版ISSN：1751-3766
出版年度：2010
卷号：4
期号：5
页码：506-526
DOI：10.1080/17513758.2010.498925
出版社：Taylor & Francis
摘要：Due to the increasing risk of drug resistance and side effects with large-scale antiviral use, it has been suggested to provide antiviral drugs only to susceptibles who have had contacts with infectives. This antiviral distribution strategy is referred to as ‘targeted antiviral prophylaxis’. The question of how effective this strategy is in infection control is of great public heath interest. In this paper, we formulate an ordinary differential equation model to describe the transmission dynamics of infectious disease with targeted antiviral prophylaxis, and provide the analysis of dynamical behaviours of the model. The control reproduction number ℛ c is derived and shown to govern the disease dynamics, and the stability analysis is carried out. The local bifurcation theory is applied to explore the variety of dynamics of the model. Our theoretical results show that the system undergoes two Hopf bifurcations due to the existence of multiple endemic equilibria and the switch of their stability. Numerical results demonstrate that the system may have more complex dynamical behaviours including multiple periodic solutions and a homoclinic orbit. The results of this study suggest that the possibility of complex disease dynamics can be driven by the use of targeted antiviral prophylaxis, and the critical level of prophylaxis which achieves ℛ c =1 is not enough to control the prevalence of a disease.
关键词：epidemic model; targeted prophylaxis; reproduction number; bi-stability; bifurcation