Multitype Randomized Reed–frost Epidemics and Epidemics upon Random Graphs

Multiple Randomised Reed-Frost Epidemics and Epidemics upon Random Graphs

We consider a multitype epidemic model which is a natural extension of the randomised Reed-Frost epidemic model. The main result is the derivation of an asympotic Gaussian limit theorem for the final size of the epidemic. The method of proof is simpler, and more direct, than is used for similar results elsewhere in the epidemics literature. In particular, the results are specialised to epidemic...

Epidemics on social network graphs

This work is concerned with relaxing the assumption of homogeneous mixing in a Reed-Frost epidemic model. After a thorough presentation of the standard Reed-Frost model we introduce social structure in the population by aid of a social network graph and investigate the effects on the epidemic spread. A number of possible choices for the underlying social network are presented: Bernoulli graphs,...

A Branching Process Approximation of the Final Size of a Multitype Collective Reed-Frost Model

Compound Poisson Limits for Household Epidemics

We consider epidemics in populations that are partitioned into small groups known as households. Whilst infectious, a typical infective makes global and local contact with individuals chosen independently and uniformly from the whole population or their own household, as appropriate. Previously, the classical Poisson approximation for the number of survivors of a severe epidemic has been extend...

Contact tracing and epidemics control in social networks.

A generalization of the standard susceptible-infectious-removed stochastic model for epidemics in sparse random networks is introduced which incorporates contact tracing in addition to random screening. We propose a deterministic mean-field description that yields quantitative agreement with stochastic simulations on random graphs. Both the stochastic simulations and the mean-field equations sh...