On the basic reproduction number and the topological properties of the contact network: An epidemiological study in mainly locally connected cellular automata

Abstract

a b s t r a c tWe study the spreading of contagious diseases in a population of constant size using susceptible-infectiverecovered (SIR) models described in terms of ordinary differential equations (ODEs) and probabilistic cellular automata (PCA). In the PCA model, each individual (represented by a cell in the lattice) is mainly locally connected to others. We investigate how the topological properties of the random network representing contacts among individuals influence the transient behavior and the permanent regime of the epidemiological system described by ODE and PCA. Our main conclusions are: (1) the basic reproduction number (commonly called R 0 ) related to a disease propagation in a population cannot be uniquely determined from some features of transient behavior of the infective group; (2) R 0 cannot be associated to a unique combination of clustering coefficient and average shortest path length characterizing the contact network. We discuss how these results can embarrass the specification of control strategies for combating disease propagations.

Um Modelo Epidemiológico Baseado em Autômatos Celulares Probabilistas Assíncronos

“…Segundo essas regras, o tamanho da população permanece constante, o que é conveniente para representar doenças pouco letais e/ou populações em que mortes são compensadas por nascimentos. Um modelo SIR similar foi proposto por Schimit e Monteiro [13].…”

“…Cada ponto dessas curvas corresponde ao valor médio de 20 simulações. É possível estimar os valores dos parâmetros das EDs a fim de que elas reproduzam a dinâmica do AC [11,13]. Para o modelo aqui analisado, essa estimativa é feita assim: (4) …”

“…Autômatos celulares (ACs) têm sido amplamente usados em modelagem epidemiológica, pois permitem representar a geografia da região estudada e as relações sociais entre os indivíduos de forma natural [2,3,5,11,13]. É simples calcular computacionalmente a evolução temporal de um autômato celular; em contrapartida, costuma ser difícil estudá-los analiticamente.…”

“…Como se percebe, EDs e ACs têm suas vantagens e desvantagens. Talvez, uma abordagem mista seja a mais conveniente [5,11,13].…”

On estimating the impact of information spreading in a consumer market modeled by probabilistic cellular automata and ordinary differential equations

“…Consumer market in cellular automata 2.1 PCA and the contact network Individuals live in a square matrix formed by n 3 n = N cells with periodic boundary conditions (the top edge of the matrix contacts the bottom edge, and the right-hand edge contacts the left-hand edge -the toroidal surface). A network model, used by Schimit and Monteiro, 40 where each cell of the PCA lattice corresponds to an individual and an edge between two cells represents a social contact, configures the neighborhood of each cell. Each cell has social contact with a neighborhood defined as the square matrix of size 2r + 1 centered on such a cell, where r is the maximum radius in which a connection can be made.…”