Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control

Abstract

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.

The Stochastic Stability of Internal HIV Models with Gaussian White Noise and Gaussian Colored Noise

“…Early models of HIV infection [4][5][6] were studied analytically and numerically by defining ordinary differential equations which are deterministic models. There are many authors to investigate how to control and predict HIV virus, based on deterministic HIV models [7][8][9][10].…”

Threshold Dynamics of the Switched Multicity Epidemic Models with Pulse Control

“…There have been numerous attempts to control and eradicate the infectious disease, such as use of condos, sex education, and treatments with cocktails of drugs [27][28][29]. Pulse vaccination strategy, due to its highly successful application in the control of the transmission of diseases, such as measles, hepatitis, parotitis, smallpox, and phthisis, has been further considered in the literatures [30][31][32][33][34][35]. Pulse vaccination strategy distinguishes from the traditional constant vaccination.…”

Effects of two types of noise and switching on the asymptotic dynamics of an epidemic model

“…Liu and Stechlinski [17] analyzed infectious disease models with time-varying parameters and obtained some sufficient conditions to ensure the stability of the disease-free equilibrium. Wang et al [18] assumed that incidence functions are time-varying functions and switching functional forms in time, analyzed the extinction of the disease. Motivated by the discussion, assume that both the infection rate and viral production rate are time-varying function and switching forms in time.…”