Mathematical modelling of HIV epidemic and stability analysis

Abstract

A nonlinear mathematical model of differential equations with piecewise constant arguments is proposed. This model is analyzed by using the theory of both differential and difference equations to show the spread of HIV in a homogeneous population. Because of the solution of this differential equations being established in a certain subinterval, solutions will be analyzed as a system of difference equations. After that, results will be considered for differential equations as well. The population of the model is divided into three subclasses, which are the HIV negative class, the HIV positive class that do not know they are infected and the HIV positive class that know they are infected. As an application of the model we took the spread of HIV in India into consideration.© 2014 Liu and Jiang; licensee Springer.