Geodesic
Spatial and temporal dynamics of the emergence of epidemics in the hybrid SIRS+V model of cellular automata
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 31 (2023) no. 3, pp. 271-285

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Purpose of this work is to construct a model of infection spread in the form of a lattice of probabilistic cellular automata, which takes into account the inertial nature of infection transmission between individuals. Identification of the relationship between the spatial and temporal dynamics of the model depending on the probability of migration of individuals. Methods. The numerical simulation of stochastic dynamics of the lattice of cellular automata by the Monte Carlo method. Results. A modified SIRS+V model of epidemic spread in the form of a lattice of probabilistic cellular automata is constructed. It differs from standard models by taking into account the inertial nature of the transmission of infection between individuals of the population, which is realized by introducing a "carrier agent" into the model, which viruses act as. The similarity and difference between the dynamics of the cellular automata model and the previously studied mean field model are revealed. Discussion. The model in the form of cellular automata allows us to study the processes of infection spread in the population, including in conditions of spatially heterogeneous distribution of the disease. The latter situation occurs if the probability of migration of individuals is not too high. At the same time, a significant change in the quantitative characteristics of the processes is possible, as well as the emergence of qualitatively new modes, such as the regime of undamped oscillations.
Keywords: Population dynamics, SIRS model, dynamical systems. 
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     author = {A. V. Shabunin},
     title = {Spatial and temporal dynamics of the emergence of epidemics in the hybrid {SIRS+V} model of cellular automata},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {271--285},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2023_31_3_a3/}
}
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A. V. Shabunin. Spatial and temporal dynamics of the emergence of epidemics in the hybrid SIRS+V model of cellular automata. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 31 (2023) no. 3, pp. 271-285. http://geodesic.mathdoc.fr/item/IVP_2023_31_3_a3/