A stochastic model for malaria and its behavior under insecticide-treated nets

Abstract

Stochastic model for malaria transmission is introduced, and its behavior under insecticide-treated nets (which is used as a prevention) is considered. A white noise is introduced into the model, representing fluctuations in the environment that manifest themselves naturally on the transmission coefficient rate. Existence and uniqueness of a global positive solution of the stochastic model are proved, as well as the conditions under which extinction and persistence in mean hold are establish. Numerical simulations are provided, which illustrate that the theoretical results and conclusions are derived on the impact of the fluctuations that are caused by the environment.