Analysis of a Nonautonomous Hiv/Aids Epidemic Model With Distributed Time Delay

Abstract

Abstract. In this paper, we have considered a nonautonomous stage-structured HIV/AIDS epidemic model through vertical and horizontal transmissions of infections, having two stages of the period of infection according to the developing progress of infection before AIDS defined would be detected, with varying total population size and distributed time delay to become infectious (through horizontal transmission) due to intracellular delay between initial infection of a cell by HIV and the release of new virions. The infected people in the different stages have different ability of transmitting disease. We have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical technique. We have obtained the explicit formula of the eventual lower bounds of infected people. We have introduced some new threshold values R0 and R * and further obtained that the disease will be permanent when R0 > 1 and the disease will be going to extinct when R * < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings.

Analysis of a drinking epidemic model

“…Mathematical studies can be effective as it guides to the evaluation, testing and implementation of strategies over short or long time scales for chronic relapsing diseases such as alcohol addiction, drug abuse etc. There are many mathematical models for epidemic diseases like HIV [4][5][6][7][8][9], SARS [10], gonorrhea [11,12], dengue [13], cancer [14][15][16], Chlamydia [17], HFMD [18][19][20][21] etc. But the mathematical models on alcohol and drug abuse are very small in number though they have been referred to in terms of epidemics.…”

Optimization of Public Health Education Parameters for Controlling the Spread of HIV/AIDS Infection

“…The researchers developed several mathematical models to provide a better understanding of the epidemiological patterns of HIV control, so that researchers can make more accurate short and long-term predictions to control HIV infection. Following the elementary models presented by May and Anderson [1][2][3], various modifications have been applied to these models, and this topic has been addressed by certain researchers [4][5][6][7][8][9][10][11][12][13][14][15]. To reduce HIV infection incidence, the impact of education as a single strategy was investigated by Ostadzad et al [16,17].…”

Threshold Dynamics of the Switched Multicity Epidemic Models with Pulse Control

“…In the real world, due to the seasonal variety, which makes the population behave periodically, the parameters involved with the modeling approach of epidemic systems always fluctuate in time. For instance, Samanta assumed the coefficients of the HIV/AIDS epidemic model are periodic functions and studied its global asymptotic stability [17,18]. Researchers [19][20][21][22][23] added seasonal variety factor into their models.…”