Mathematical modelling of epidemic processes in the case of the contact stepwise infection pattern

Author:

Chigarev A. V.1,Zhuravkov M. A.1,Mikhnovich M. O.2

Affiliation:

1. Belarusian State University

2. Belarusian National Technical University

Abstract

Herein we consider mathematical models of infection in a population consisting of two types of people: those who transmit infection to others (type 1) and those who do not participate in the spread of infection (type 2). On the basis of the percolation theory and a model of the urn test type, a critical value of the proportion of infected persons in the population is determined, after which the infection process may become explosive. The probabilities of continuous infection and the interruption of its transmission are investigated. On the basis of Feigenbaum logistic mapping for the epidemic process, it is possible to estimate the change in the value of the parameter of the number of contacts and the bifurcations arising in this case, which are modelled in accordance with the scenario of transition to deterministic chaos through the doubling of the cycle period. In modes of stochasticity there are local modes of periodicity, the identification of which, if the model is adequate to the real situation, allows predicting and controlling the epidemic process, translating it or keeping the process in a stable cyclic state.

Publisher

Publishing House Belorusskaya Nauka

Reference20 articles.

1. Chigarev A. V., Zhuravkov M. A., Chigarev V. A. Deterministic and stochastic models of infection spread and testing in an isolated contingent. Journal of Belarusian State University. Mathematics. Informatics, 2021, no. 3, pp. 57–67 (in Russian). https://doi.org/10.33581/2520-6508-2021-3-57-67

2. Chigarev A. V., Chigarev V. A., Adzeriho J. E. Kinetic models of distribution and testing of epidemic diseases in an isolated contingent. Russian Journal of Biomechanics, 2021, vol. 25, no. 2, pp. 113–122.

3. Miksch F. Mathematical Modeling for New Insights into Epidemics by Herd Immunity and Serotype Shift. Vienna, ARGESIM Publisher, 2016. https://doi.org/10.11128/fbs.20

4. Harris T. H. The Theory of Branching Processes. Berlin, Heidelberg, Springer-Verlag, 1963. 355 p. https://doi. org/10.1007/978-3-642-51866-9_6

5. Efros A. L. Physics and Geometry of Disorder. Moscow, Nauka Publ., 1982. 112 p. (in Russian).

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