Dynamics of a stochastic cholera epidemic model with Lévy process

Abstract

In this paper, a stochastic cholera epidemic model subjected to a Brownian motion noise and a Lévy jump process noise is formulated. The asymptotic behaviors around the equilibriums of the corresponding deterministic model are investigated. It is shown that the expected time average of the distance between the stochastic solution and the equilibriums of the associated deterministic model is small when the noise intensities are small, and the solution will oscillate around these steady states. The amplitude of vibration not only depends on the intensities of the Brownian motion noise but also the Lévy noise. Numerical examples are carried out to illustrate the theoretical results.