Mathematical Modelling of HIV/AIDS and Transmission Dynamics

Abstract

A nonlinear deterministic mathematical model for the problem is proposed and analysed qualitatively using the stability theory of differential equations. We investigate the HIV/AIDS epidemic in a varied population. We derive and analyze a mathematical model that describes the dynamics of HIV infection among the susceptible population. The model was developed by adopting the compartmental modeling approach where the population was partitioned into; Susceptible, Infected and Aids sub-populations is found that completely determines the stability dynamics and outcome of the disease. It is found that if the basic reproduction number is less than one the disease free equilibrium is stable and the disease dies out. However, if the basic reproduction number is more than one, there exists a unique endemic equilibrium that is locally asymptotically stable. Numerical simulation of the model is also performed by using fourth order Runge - Kutta method. It is concluded from our analysis that public health education is more efficient if the susceptible individuals are educated in time and followed up by treatment in the exposed sub-population.