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On the stochastic engine of contagious diseases in exponentially growing populations
Linnaeus University, Faculty of Technology, Department of Mathematics. Linnaeus University, Linnaeus Knowledge Environments, Water.ORCID iD: 0000-0002-7261-0399
2024 (English)In: Nonlinear Analysis: Real World Applications, ISSN 1468-1218, Vol. 77, article id 104045Article in journal (Refereed) Published
Abstract [en]

The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth and death rates in comparison to disease parameters like the contact rate and the removal rate ensures that the globally stable endemic equilibrium corresponds to a tiny average proportion of infected individuals. Asymptotic equilibrium levels corresponding to low numbers of individuals invalidate the deterministic results.

Diffusion effects force probability mass functions of the stochastic model to possess similar stability properties as the deterministic model. Particular simulations of the stochastic model predict, however, oscillatory patterns. Small and isolated populations show longer periods, more violent oscillations, and larger probabilities of extinction.

We prove that evolution maximizes the infectiousness of the disease as measured by the ability to increase the proportion of infected individuals. This holds provided the stochastic oscillations are moderate enough to keep the proportion of susceptible individuals near a deterministic equilibrium.

We close our paper with a discussion of the herd-immunity concept and stress its close relation to vaccination-programs.

Place, publisher, year, edition, pages
Elsevier, 2024. Vol. 77, article id 104045
National Category
Mathematical Analysis
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-125806DOI: 10.1016/j.nonrwa.2023.104045ISI: 001125982500001Scopus ID: 2-s2.0-85183379977OAI: oai:DiVA.org:lnu-125806DiVA, id: diva2:1815094
Available from: 2023-11-28 Created: 2023-11-28 Last updated: 2025-02-06Bibliographically approved

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Lindström, Torsten

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