Impact of Lévy Noise with Infinite Activity on the Dynamics of Measles Epidemics

Abstract

This research article investigates the application of Lévy noise to understand the dynamic aspects of measles epidemic modeling and seeks to explain the impact of vaccines on the spread of the disease. After model formulation, the study utilises uniqueness and existence techniques to derive a positive solution to the underlying stochastic model. The Lyapunov function is used to investigate the stability results associated with the proposed stochastic model. The model’s dynamic characteristics are analyzed in the vicinity of the infection-free and endemic states of the associated ODEs model. The stochastic threshold Rs that ensures disease’s extinction whenever Rs<1 is calculated. We utilized data from Pakistan in 2019 to estimate the parameters of the model and conducted simulations to forecast the future behavior of the disease. The results were compared to actual data using standard curve fitting tools.