Study of Public Health Education Effect on Spread of HIV Infection in a Density-Dependent Transmission Model

Abstract

A nonlinear density-dependent mathematical model is proposed to study the effect of public health education on spread of HIV infection. In this model the host population is divided into seven sub-classes of educated and non-educated susceptibles, HIV infective in asymptomatic and symptomatic phases, and that of AIDS patients. The model exhibits two equilibrium points namely, a disease free and an endemic equilibrium. The model has been studied qualitatively using stability theory of nonlinear differential equations. We have found threshold parameters, the basic reproduction number \(\mathcal {R}_{0}\) for the HIV/AIDS in the absence of public health education and education-including basic reproduction number \(\mathcal {R}_{E}\) for the model with public health education. We have proved that if education-including basic reproduction number is less than one, the disease free equilibrium is locally asymptotically stable otherwise for \(\mathcal {R}_{E}>1\) the infection will be prevalent in the population. By comparing threshold parameters \(\mathcal {R}_{0}\) and \(\mathcal {R}_{E}\), the effect of public health education can be observed. Based upon the presented results of this paper, we can conclude that in a population where public health education is not effective or when the basic reproduction number \(R_0\) is large, HIV/AIDS can not be controlled using public health education alone. Numerical study of the model is also performed to investigate the influence of certain key parameters on the spread of the disease.