Nonlinear stochastic cholera epidemic model under the influence of noise

Abstract

Epidemic cholera is the term for acute diarrhea brought on by the pathogen’s abundance within the human body. A mathematical model for the epidemic cholera is created by analyzing when an individual becomes ill and exhibits signs following exposure to the pathogen concentration. The model is first developed from a deterministic viewpoint and then converted into a model containing stochastic differential equations. Besides offering a biological explanation for the stochastic system, we prove that the corresponding deterministic model has potential equilibria. As such, we introduce stability theorems. The research shows that there is a unique global solution for the proposed stochastic model. Necessary conditions are defined by using the Lyapunov function theory, which ensures that the model remains stable in the average for Rs0 > 1. When Rs < 1, our evidence suggests that the illness is probably gone from the population. To strengthen the validity of the acquired analytical results, graphical solutions were created. This work provides a solid theoretical framework for a thorough comprehension of a range of chronic communicable diseases. In addition, we will provide a method for developing Lyapunov functions that may be used to analyze the stationary distributions of models with nonlinear random disruptions.