title: On the exact measure of disease spread in stochastic epidemic models.
abstract: The basic reproduction number, R₀, is probably the most important quantity in epidemiology. It is used to measure the transmission potential during the initial phase of an epidemic. In this paper, we are specifically concerned with the quantification of the spread of a disease modeled by a Markov chain. Due to the occurrence of repeated contacts taking place between a typical infective individual and other individuals already infected before, R₀ overestimates the average number of secondary infections. We present two alternative measures, namely, the exact reproduction number, Re0, and the population transmission number, Rp, that overcome this difficulty and provide valuable insight. The applicability of Re0 and Rp to control of disease spread is also examined.
authors.affiliation: Department of Statistics and Operations Research, Faculty of Mathematics, Complutense University of Madrid, 28040 Madrid, Spain. jesus_artalejo@mat.ucm.es
authors.forename: J R
authors.initials: JR
authors.lastname: Artalejo
authors.forename: M J
authors.initials: MJ
authors.lastname: Lopez-Herrero
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D017053:Infection Control / Q000379:methods / Q000706:statistics & numerical data; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D013269:Stochastic Processes