Long-term behavior of stochastic SIQRS epidemic models
arxiv(2024)
Abstract
In this paper we analyze and classify the dynamics of SIQRS epidemiological
models with susceptible, infected, quarantined, and recovered classes, where
the recovered individuals can become reinfected. We are able to treat general
incidence functional responses. Our models are more realistic than what has
been studied in the literature since they include two important types of random
fluctuations. The first type is due to small fluctuations of the various model
parameters and leads to white noise terms. The second type of noise is due to
significant environment regime shifts in the that can happen at random. The
environment switches randomly between a finite number of environmental states,
each with a possibly different disease dynamic. We prove that the long-term
fate of the disease is fully determined by a real-valued threshold λ.
When λ < 0 the disease goes extinct asymptotically at an exponential
rate. On the other hand, if λ > 0 the disease will persist
indefinitely. We end our analysis by looking at some important examples where
λ can be computed explicitly, and by showcasing some simulation results
that shed light on real-world situations.
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