Applications of branching processes to the final size of SIR epidemics

摘要: This paper considers applications of branching processes to a model for the spread an SIR (susceptible \(\to\) infective removed) epidemic among closed, homogeneously mixing population, consisting initially m and n susceptible individuals. Each remains infectious period sampled independently from arbitrary but specified distribution, during which he/she contacts individuals with rate \(n^{-1}\lambda\) each susceptible. The well-known approximation early stages this by process is outlined. main thrust use obtain, when constant, new probabilistically direct proofs central limit theorems size becomes established. Two asymptotic situations are considered: (i) many initial infectives, where both become large, establishment asymptotically certain; (ii) few held fixed only not certain may be possible. constant periods closely related Erdos-Reenyi random graph our methodology provides alternative proof theorem giant component in that graph.