CONICET | Buscador de Institutos y Recursos Humanos

Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models isespecially important to understand and address many relevant ecological and public health questions, e.g., when wanting todifferentiate transmission patterns across geographical regions or when considering spatially heterogeneous interventionmeasures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics andhence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplifiedcomputational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitablyaccounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellularautomata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization ofthe population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infectedindividuals either present a severe form of the disease, thus requiring hospitalization, or belong to the so-called mild/asymptomatic class. The critical transmission threshold is derived analytically in the nonspatial SHAR formulation, and thisgeneralizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of keymodel parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infectionclusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we concludethat the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.

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