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

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Ecological Modelling
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Schimit P.H.T.
Monteiro L.H.A.
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In epidemiology, the basic reproduction number R 0 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, R 0 is related to the initial stage of the spreading of a contagious disease. However, from epidemiological models based on ordinary differential equations (ODE), R 0 is commonly derived from a linear stability analysis and interpreted as a bifurcation parameter: typically, when R 0>1, the contagious disease tends to persist in the population because the endemic stationary solution is asymptotically stable; when R 0<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 R 0 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 R 0 obtained from both approaches are compared, showing good agreement. © 2012 Elsevier B.V.
Assuntos Scopus
Asymptotically stable , Average numbers , Basic reproduction number , Bifurcation parameter , Complex networks , Contagious disease , Epidemiological models , Initial stages , Numerical values , Probabilistic cellular automatons , Random network , Stability analysis , Stationary solutions , Steady state , Susceptible population