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Journal of Applied Mathematics and Computation

ISSN Online: 2576-0653 Downloads: 328502 Total View: 3034173
Frequency: quarterly ISSN Print: 2576-0645 CODEN: JAMCEZ
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ArticleOpen Access http://dx.doi.org/10.26855/jamc.2023.06.003

Mathematical Analysis of an SIR Model with Local and Global Infections Based on Trinomial Distribution

Mengke Ren

School of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei, China.

*Corresponding author: Mengke Ren

Published: July 21,2023

Abstract

Infectious disease can be transmitted either through some fixed contacts or through some casual contacts. As the prevention and control measures (like contact restrictions and lock-downs) of an infectious disease change, the contact behavior among people may change. In this paper, by introducing a locality parameter, we consider the classical SIR model with two types of contacts: local contacts (individuals only contact their nearest neighbours on the lattice) and global contacts (individuals contact some other unknown people by chance). Then, we adopt the pair approximation approach to get a deterministic mean-field SIR model on square lattice by assuming that the distribution for errors (comparing with the expected value of the number of neighbours in a given state) follows trinomial. We calculate the basic reproduction number of the model, and establish the local stability of the disease-free equilibrium. In particular, three cases are focused: only global contact exists, only local contact exists, and both contacts exist. The existence and uniqueness of an endemic equilibrium in the first two cases, and the local stability of endemic equilibrium when only global contact exists are analyzed. Numerical simulations are performed to explore the effect of different interactions on the transmission dynamics.

Keywords

Pair-wise SIR model, Trinomial distribution, Basic reproduction number, Stability, Numerical simulations

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How to cite this paper

Mathematical Analysis of an SIR Model with Local and Global Infections Based on Trinomial Distribution

How to cite this paper: Mengke Ren. (2023) Mathematical Analysis of an SIR Model with Local and Global Infections Based on Trinomial Distribution. Journal of Applied Mathematics and Computation7(2), 224-233.

DOI: http://dx.doi.org/10.26855/jamc.2023.06.003