New Results on the Asymptotic Behaviour of a Stochastic SEI Model of Lymphatic Filariasis

Abstract

The goal of this article is to examine a new stochastic epidemic model for lymphatic filariasis, susceptible-exposed-infected (SEI). Like other diseases, the spread of lymphatic filariasis is subject to a degree of randomness due to fluctuations in the natural environment. This provides us with the opportunity to formulate a mathematical model of lymphatic filariasis that comprehensively considers external stochastic influences. By using carefully designed stochastic Lyapunov functions, we establish sufficient conditions for the eradication of lymphatic filariasis infections. Moreover, under specific conditions regarding the intensity of white noise, we also demonstrate the existence of a unique ergodic stationary distribution and the persistence of the mean for the model. Numerical simulations are conducted to substantiate the validity of our findings.