SIR epidemic model taking into account the spatial heterogeneity of the location of individuals

Authors: Razumov T.E.
Published in issue: #6(35)/2019
DOI: 10.18698/2541-8009-2019-6-490
Category: Mathematics | Chapter: Computational Mathematics
Keywords: SIR model, homogeneous model, heterogeneous model, population, state probability, Markov chain, pandemic, epidemic modeling
Published: 10.06.2019

In this paper, the author showed based on Markov chains method a generalization of the classical homogeneous SIR model to the case of a spatial non-uniform distribution of individuals (heterogeneous model). The state of each individual is determined by the probabilities of being in the three groups of the SIR model. The decrease in the intensity of infection with increasing distance between individuals is taken into account; the characteristic time of virus degeneration inside the individual is taken into account. The author presented the results of numerical modeling of the development of infectious diseases for different ways of placing susceptible and infected individuals. Based on numerical modeling, the author showed a fundamental difference in the epidemic scenarios for homogeneous and heterogeneous models.

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