On a Stochastic Approach to Extensions of the Susceptible‐Infected‐Susceptible (SIS) Model Applied to Malaria

Abstract

This work presents a stochastic model of malaria spread. We first calculated the basic reproduction number R0 of the models ShIhRhSh‐SvIv and ShLhIhRhSh‐SvLvIv in order to show that the malaria-free equilibrium is asymptotically stable; then, we used a finite Markov chain model to describe the interactions between the different compartments of the model SeLeIeReSe‐SaLaIaRaSa‐SvIv. We carried out numerical simulations of our results for two types of transmission zones: a zone with low malaria transmission and an endemic zone. Through these simulations, we first determined the invariant stationary distribution π∗ of the model, and then, we found that the use of the indoor residual spraying (IRS) method by regular application of insecticides is more effective for the elimination of malaria than the use of long-acting impregnated mosquito nets (LLINs).