|Title||Reply to "Comment on 'Linking population-level models with growing networks: a class of epidemic models'"|
|Publication Type||Journal Article|
|Year of Publication||2006|
|Authors||Breban, R , Vardavas R , Blower S |
|Journal||Phys Rev E Stat Nonlin Soft Matter Phys|
|Keywords||Fundamentals of Theoretical Epidemiology |
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.