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.
Highlights
In stochastic modeling, a dynamical system is the set constituted by a system and stochastic evolution equations describing the random evolution of its trajectories
A class of periodic stochastic differential equations driven by general counting processes (SDEsGp) is studied
We study here periodic solutions for stochastic differential equations based on counting processes with periodic stochastic intensity
Summary
A dynamical system is the set constituted by a system and stochastic evolution equations describing the random evolution of its trajectories. The theoretical development of stochastic process based on Poisson processes has be seen in recent years and several results have been proven: Existence and uniqueness of the solution of Eq(3) are proved under more general conditions (Anderson, D.F and Kurtz, T.G, 2015), (Guy,R and all, 2014), (Guy,R and all, 2014). This result is discussed in more detail in Kurtz (Kurtz, T.G, 1980). An example is provided to demonstrate the obtained results and apply the previous analytical results to study stochastic dynamic for malaria epidemic model under periodic environment
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