A stochastic differential equation approach for an SIS model with non-linear incidence rate

J. S. Builes; Cristian F. Coletti; Leon A. Valencia

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arXiv · 2404.13469

A stochastic differential equation approach for an SIS model with non-linear incidence rate

J. S. Builes·Cristian F. Coletti·Leon A. Valencia

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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.

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J. S. Builes, Cristian F. Coletti, Leon A. Valencia. 2024-04-20. A stochastic differential equation approach for an SIS model with non-linear incidence rate. https://arxiv.org/abs/2404.13469

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