Periodic Solutions for Stochastic Differential Equations Driven by General Counting Processes: Application to Malaria

Abstract

In this paper, a class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied. First, an existence-uniqueness result for the solution of general SDEsGp based on Poisson processes with т-periodic stochastic intensity of time t has been given, for some  т> 0. Then, using the properties of periodic Markov processes, sufficient conditions for the existence and uniqueness of a periodic solution of the considered equations are obtained. We will then apply the obtained results to the propagation of malaria in a periodic environment.