Analysis of Leptospirosis Disease with Contaminated Environment in Human and Animal Population via Stochastic Mathematical Model

Abstract

This study investigates the impact of contaminated environment on leptospirosis disease using stochastic mathematical models through neural networks. Initially, we demonstrate that the solution exists globally and remains positive. Secondly, we determine the key stochastic reproduction number that will determine whether the disease persists or extinct from the population. If \({R}_{0}^{s}<1\), then the disease will die out from the population. And if \({R}_{0}^{s}>1\), the disease continues to persist in the population. Using numerical simulations, the dynamics of leptospirosis within both human populations and animals was examined. Simulations showed that a contaminated environment plays a critical role in the spread of leptospirosis, thereby increases the disease’s transmission. Meanwhile, treating the disease plays a critical role in controlling it. This highlights the critical importance of a contaminated environment in disease management. Furthermore, neural networks (NNs) were utilized to improve the simulation and validation of disease dynamics. Public health strategists can use the findings of this study to reduce or eliminate leptospirosis infection.