A stochastic differential equation approach for an SIS model with non-linear incidence rate
Probability
2024-04-23 v1
Abstract
In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive solution, and we study its regularity. We study the persistence and extinction regimes, and we give sufficient conditions under which the disease-free equilibrium point is an asymptotically stable equilibrium point with probability one. We provide sufficient conditions under which the model admits a unique stationary measure. Finally, we illustrate our findings using simulations.
Keywords
Cite
@article{arxiv.2404.13469,
title = {A stochastic differential equation approach for an SIS model with non-linear incidence rate},
author = {J. S. Builes and Cristian F. Coletti and Leon A. Valencia},
journal= {arXiv preprint arXiv:2404.13469},
year = {2024}
}