On estimating the basic reproduction number in distinct stages of a contagious disease spreading

P.H.T. Schimit and L.H.A. Monteiro

Ecological Modelling, 2012, vol. 240, issue C, 156-160

Abstract: In epidemiology, the basic reproduction number R0 is usually defined as the average number of new infections caused by a single infective individual introduced into a completely susceptible population. According to this definition, R0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R0>1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable; when R0<1, the corresponding pathogen tends to naturally disappear because the disease-free stationary solution is asymptotically stable. Here we intend to answer the following question: Do these two different approaches for calculating R0 give the same numerical values? In other words, is the number of secondary infections caused by a unique sick individual equal to the threshold obtained from stability analysis of steady states of ODE? For finding the answer, we use a susceptible-infective-recovered (SIR) model described in terms of ODE and also in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. The values of R0 obtained from both approaches are compared, showing good agreement.

Keywords: Basic reproduction number; Complex network; Epidemiology; Ordinary differential equations; Probabilistic cellular automata (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:240:y:2012:i:c:p:156-160

DOI: 10.1016/j.ecolmodel.2012.04.026

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