Modelling SARS-CoV-2 epidemics via compartmental and cellular automaton&lt;i&gt; SEIRS&lt;/i&gt; model with temporal immunity and vaccination

J. Ilnytskyi; T. Patsahan

doi:10.5488/cmp.29.13501

journal article Open Access Mar 30, 2026

Modelling SARS-CoV-2 epidemics via compartmental and cellular automaton<i> SEIRS</i> model with temporal immunity and vaccination

J. Ilnytskyi T. Patsahan

Condensed Matter Physics Vol. 29 No. 1 pp. 13501 · Yukhnovskii Institute for Condensed Matter Physics

View at Publisher Save 10.5488/cmp.29.13501

Abstract

We consider the SEIRS epidemiology model with such features of the COVID-19 outbreak as: abundance of unidentified infected individuals, limited time of immunity and a possibility of vaccination. The control of the pandemic dynamics is possible by restricting the transmission rate, increasing identification and isolation rate of infected individuals, and via vaccination. For the compartmental version of this model, we found stable diseasefree and endemic stationary states. The basic reproductive number is analysed with respect to balancing quarantine and vaccination measures. The positions and heights of the first peak of outbreak are obtained numerically and fitted to simple in usage algebraic forms. Lattice-based realization of this model is studied by means of the asynchronous cellular automaton algorithm. This permitted to study the effect of social distancing by varying the neighbourhood size of the model. The attempt is made to match the quarantine and vaccination effects.

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Published: Mar 30, 2026
Vol/Issue: 29(1)
Pages: 13501
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Cite This Article

J. Ilnytskyi, T. Patsahan (2026). Modelling SARS-CoV-2 epidemics via compartmental and cellular automaton<i> SEIRS</i> model with temporal immunity and vaccination. Condensed Matter Physics, 29(1), 13501. https://doi.org/10.5488/cmp.29.13501

Modelling SARS-CoV-2 epidemics via compartmental and cellular automaton&lt;i&gt; SEIRS&lt;/i&gt; model with temporal immunity and vaccination

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Modelling SARS-CoV-2 epidemics via compartmental and cellular automaton<i> SEIRS</i> model with temporal immunity and vaccination