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

J. Ilnytskyi; T. Patsahan

doi:10.5488/CMP.29.13501

Authors

J. Ilnytskyi Yukhnovskii Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 S. Bandera Str., 79013 Lviv, Ukraine https://orcid.org/0000-0002-1868-5648
T. Patsahan Yukhnovskii Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii Str., 79011 Lviv, Ukraine; Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 S. Bandera Str., 79013 Lviv, Ukraine https://orcid.org/0000-0002-7870-2219

DOI:

https://doi.org/10.5488/CMP.29.13501

Keywords:

compartmental models, cellular automata, epidemics

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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