Stochastic analysis for measles transmission with Lévy noise: a case study

Abstract

In this paper, we deal with a Lévy noise-driven epidemic model reflecting the dynamics of measles infection subject to the effect of vaccination. After model formulation, the feasibility of the system was studied by using the underlying existence and uniqueness theory. Moreover, we discussed the behavior of solution around the infection-free and disease-present steady states. To check the persistence and extinction of the infection, we calculated the threshold parameter $ {\bf R_s} $ and it was determined that the disease vanishes whenever $ {\bf R_s} < 1 $. From January to October 2019, the reported measles cases in Pakistan wear used and the model was fitted against this data by using the well-known fitting techniques. The values of the parameter were estimated and future behavior of the infection was predicted by simulating the model. The model was further simulated and theoretical findings of the study were validated.

Keywords

• white noise
• lévy jump
• lyapunov function
• persistence
• parameter estimation
• positive recurrence