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

Yao Simplice Kouame and Modeste Nzi

Journal of Mathematics Research, 2021, vol. 13, issue 4, 1

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 Ñ‚-periodic stochastic intensity of time t has been given, for some Ñ‚> 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.

Date: 2021
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