title: Linking population-level models with growing networks: a class of epidemic models.
abstract: We introduce a class of growing network models that are directly applicable to epidemiology. We show how to construct a growing network model (individual-level model) that generates the same epidemic-level outcomes as a population-level ordinary differential equation (ODE) model. For concreteness, we analyze the susceptible-infected (SI) ODE model of disease invasion. First, we give an illustrative example of a growing network whose population-level variables are compatible with those of this ODE model. Second, we demonstrate that a growing network model can be found that is equivalent to the Crump-Mode-Jagers (CMJ) continuous-time branching process of the SI ODE model of disease invasion. We discuss the computational advantages that our growing network model has over the CMJ branching process.
authors.affiliation: Department of Biomathematics, University of California, Los Angeles, California 90095-1555, USA.
authors.forename: Romulus
authors.initials: R
authors.lastname: Breban
authors.forename: Raffaele
authors.initials: R
authors.lastname: Vardavas
authors.forename: Sally
authors.initials: S
authors.lastname: Blower
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000453:epidemiology* / Q000503:physiopathology*; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000706:statistics & numerical data*; D004198:Disease Susceptibility / Q000453:epidemiology* / Q000503:physiopathology*; D004812:Epidemiologic Methods; D006801:Humans; D015994:Incidence; D008954:Models, Biological; D011157:Population Dynamics; D015995:Prevalence; D013223:Statistics as Topic