Between-host HIV model: stability analysis and solution using memetic computing

Abstract

HIV poses a great threat to humanity for two major reasons. First it attacks the immunity system of thebody and second, it is epidemic in nature. Mathematical models of HIV have been instrumental in understanding andcontrolling the infection. In this paper, we solve the between host epidemic model of HIV, described by nonlinear coupleddifferential equations, by using memetic computing. Under this model, the sexually active population is divided intofour classes and we investigate the transfer of individuals from one class to another. The solution consists of Bernsteinpolynomials whose parameters have been optimized by using differential evolution as global and sequential quadraticprogramming as local optimizer. Our second contribution is the stability analysis of this model. The disease-freeequilibrium is stable while endemic equilibrium is unstable within the practical range of the values of parameters.