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Conference Papers Year : 2023

Compartment model with retarded transition rates

Abstract

Our study is devoted to a four-compartment epidemic model of a constant population of independent random walkers. Each walker is in one of four compartments (S-susceptible, C-infected but not infectious (period of incubation), I-infected and infectious, R-recovered and immune) characterizing the states of health. The walkers navigate independently on a periodic 2D lattice. Infections occur by collisions of susceptible and infectious walkers. Once infected, a walker undergoes the delayed cyclic transition pathway S → C → I → R → S. The random delay times between the transitions (sojourn times in the compartments) are drawn from independent probability density functions (PDFs). We analyze the existence of the endemic equilibrium and stability of the globally healthy state and derive a condition for the spread of the epidemics which we connect with the basic reproduction number R0 > 1. We give quantitative numerical evidence that a simple approach based on random walkers offers an appropriate microscopic picture of the dynamics for this class of epidemics.
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Dates and versions

hal-04193140 , version 1 (01-09-2023)

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Téo Granger, Thomas M. Michelitsch, Bernard A Collet, Michael Bestehorn, Alejandro Perez P. Riascos. Compartment model with retarded transition rates. OttoChaos: From the nonlinear dynamical systems theory to observational chaos, Sylvain Mangiarotti, Christophe Letellier, Denisse Sciamarella, Oct 2023, Toulouse, France. ⟨hal-04193140⟩
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