Linking population-level models with growing networks: A class of epidemic models
- 11 October 2005
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 72 (4), 046110
- https://doi.org/10.1103/physreve.72.046110
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.Keywords
This publication has 36 references indexed in Scilit:
- Transmission of severe acute respiratory syndrome in dynamical small-world networksPhysical Review E, 2004
- Properties of highly clustered networksPhysical Review E, 2003
- Spread of epidemic disease on networksPhysical Review E, 2002
- Percolation and epidemics in a two-dimensional small worldPhysical Review E, 2002
- Epidemic dynamics and endemic states in complex networksPhysical Review E, 2001
- Epidemic Spreading in Scale-Free NetworksPhysical Review Letters, 2001
- Epidemics and percolation in small-world networksPhysical Review E, 2000
- Stochastic Processes in Demography and Their Computer ImplementationPublished by Springer Science and Business Media LLC ,1985
- A general age-dependent branching process. IIJournal of Mathematical Analysis and Applications, 1969
- A general age-dependent branching process. IJournal of Mathematical Analysis and Applications, 1968