A stochastic differential equation approach for an SIS model with non-linear incidence rate
arxiv(2024)
摘要
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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