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

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 a...

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Bibliographic Details
Published inarXiv.org
Main Authors Builes, J S, Coletti, Cristian F, Valencia, Leon A
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.04.2024
Subjects
Differential equations
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Summary: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.
ISSN:2331-8422