Mathematical Modeling and Analysis of an HIV/AIDS Model with Treatment and Time Delay

Abstract

A nonlinear mathematical model to study the effect of treatment and time delay on the spread of HIV/AIDS in a population with variable size structure is proposed and analyzed. The model divides the population into four subclasses namely susceptibles,
asymptomatic infectives, symptomatic infectives and AIDS population. The delay is used to represent the time from the start of treatment in the symptomatic stage until the treatment effects become visible. The analysis of the model is carried out using stability theory of differential equations. The model exhibits two equilibria, the disease - free and the endemic equilibrium. Some inferences have been drawn regarding disease spread by establishing the local and global asymptotic stability of the equilibria. Model analysis reveals that with increase in the treatment rate, the population of symptomatic infectives decreases which results to increase the population of asymptomatic infectives. This decrease in symptomatic infectives population, as a result of treatment, ultimately decreases AIDS population. The time delay, however, produces oscillations which increases its amplitude with increase in delay period. Numerical analysis of the model is also performed to investigate the influence of certain key parameters on the spread of the disease and to support the analytical results.