Abstract
Mathematical models play an important role in epidemiology. The inclusion of a spatial component in epidemiological models is especially important to understand and address many relevant ecological and public health questions, e.g., when wanting to differentiate transmission patterns across geographical regions or when considering spatially heterogeneous intervention measures. However, the introduction of spatial effects can have significant consequences on the observed model dynamics and hence must be carefully analyzed and interpreted. Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community. In this paper, we describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals 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 this generalizes previously obtained theoretical results for the SIR model. We present simulation results discussing the effect of key model parameters and of spatial correlations on model outputs and propose an algorithm for tracking the evolution of infection clusters within the considered population. Focusing on the role of import and criticality on the overall dynamics, we conclude that the current spatial setting increases the critical transmission threshold in comparison to the nonspatial model.
Highlights
Infectious diseases have shaped the global population throughout history, and they have been—and often still are—responsible for a large number of deaths worldwide
Cellular automata epidemiological models typically rely on simplified computational grids but can provide valuable insight into the spatial dynamics of transmission within a population by suitably accounting for the connections between individuals in the considered community
We describe a stochastic cellular automata disease model based on an extension of the traditional Susceptible-Infected-Recovered (SIR) compartmentalization of the population, namely, the Susceptible-Hospitalized-Asymptomatic-Recovered (SHAR) formulation, in which infected individuals either present a severe form of the disease, requiring hospitalization, or belong to the so-called mild/ asymptomatic class
Summary
Infectious diseases have shaped the global population throughout history, and (whether through devastating epidemics or recurrent outbreaks of endemic diseases) they have been—and often still are—responsible for a large number of deaths worldwide. The temporal evolution of the number of individuals in each disease-related category is described mathematically via a set of three ordinary differential equations involving three rates describing the probability of susceptible individuals becoming infected, of infected individuals to fight off the disease and recover, and of recovered individuals to become susceptible once again, that is, the so-called infection, recovery, and waning immunity rates, respectively This model and its many variations (SI, SIS, SEIR, etc.) give the basic framework for the vast majority of epidemiological models found in the literature, and as such, they have been analyzed in detail and extensively used to describe disease transmission dynamics in many contexts (e.g., [3,4,5] just to name a few). We introduce the concept of infection clusters and investigate their evolution (in terms of the amount of clusters present in the system as well as their individual size) as a function of different parameter combinations
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