City Research Online

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 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.

Publication Type:	Article
Additional Information:	This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/https://doi.org/10.1007/s00285-025-02204-1.
Publisher Keywords:	Switching diffusion, Epidemic model, Ergodicity, Invariant measure, Quarantine, Temporary immunity
Subjects:	Q Science > QA Mathematics Q Science > QH Natural history > QH301 Biology R Medicine > RA Public aspects of medicine > RA0421 Public health. Hygiene. Preventive Medicine
Departments:	School of Policy & Global Affairs School of Policy & Global Affairs > Economics
SWORD Depositor:	Symplectic Administrator

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