The Predictive Power of R ₀ in an Epidemic Probabilistic System

Abstract

An important issue in theoretical epidemiology is the epidemic thresholdphenomenon, which specify the conditions for an epidemic to grow or die out.In standard (mean-field-like) compartmental models the concept of the basic reproductive number, R ₀, has been systematically employed as apredictor for epidemic spread and as an analytical tool to study thethreshold conditions. Despite the importance of this quantity, there are nogeneral formulation of R ₀ when one considers the spread of a disease ina generic finite population, involving, for instance, arbitrary topology ofinter-individual interactions and heterogeneous mixing of susceptible andimmune individuals. The goal of this work is to study this concept in ageneralized stochastic system described in terms of global and localvariables. In particular, the dependence of R ₀ on the space ofparameters that define the model is investigated; it is found that near ofthe `classical' epidemic threshold transition the uncertainty about thestrength of the epidemic process still is significantly large. Theforecasting attributes of R ₀ for a discrete finite system is discussedand generalized; in particular, it is shown that, for a discrete finitesystem, the pretentious predictive power of R ₀ is significantlyreduced.