Mathematical analysis of HIV models with switching nonlinear incidence functions and pulse control. (English) Zbl 1406.92632

Wang, Xiying; Xu, Wei; Cui, Yujun; Wang, Xiaomei

Abstr. Appl. Anal. 2014, Article ID 853960, 8 p. (2014).

Summary: This paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time-varying functions and switching functional forms in time, which have more realistic significance to model infectious disease models. New threshold conditions with the periodic switching term are obtained to guarantee eradication of the disease, by using the novel type of common Lyapunov function. Furthermore, pulse vaccination is applied to the above model, and new sufficient conditions for the eradication of the disease are presented in terms of the pulse effect and the switching effect. Finally, several numerical examples are given to show the effectiveness of the proposed results, and future directions are put forward.

MSC:

92D30	Epidemiology
92C60	Medical epidemiology

Keywords:

HIV models; pulse vaccination; switching nonlinear incidence functions

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