Discontinuous stochastic modelling and discrete numerical approximation for Tuberculosis model with relapse

Abstract

The objective of this paper is to study a stochastic epidemiological model with infinite Lévy measure and relapse. Using stochastic tools, we prove the existence and uniqueness of global positive solution. Moreover, we also show the extinction and persistence in mean of the disease by the use of Kunita’s inequality instead of Burkholder–Davis–Gundy inequality for continuous diffusions. The numerical behavior of the considered model is analyzed to understand the impact of environmental transmission on the spread of human and zonotic tuberculosis in Morocco.