title: A covering-graph approach to epidemics on SIS and SIS-like networks.
abstract: In this paper, we introduce a new class of epidemics on networks which we call SI(S/I). SI(S/I) networks differ from SIS networks in allowing an infected individual to become reinfected without first passing to the susceptible state. We use a covering-graph construction to compare SIR, SIS, and SI(S/I) networks. Like the SIR networks that cover them, SI(S/I) networks exhibit infection probabilities that are monotone with respect to both transmission probabilities and the initial set of infectives. The same covering-graph construction allows us to characterize the recurrent states in an SIS or SI(S/I) network with reinfection.
authors: Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA. floyd@math.vt.edu
authors: William
authors: W
authors: Floyd
authors: Leslie
authors: L
authors: Kay
authors: Michael
authors: M
authors: Shapiro
mesh_terms: D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology*; D058872:Epidemics; D004812:Epidemiologic Methods; D006801:Humans; D008954:Models, Biological; D013269:Stochastic Processes