Applied Probability Trust (August 7, 2000) STOCHASTIC MULTITYPE SIR EPIDEMICS AMONG A POPULA- TION PARTITIONED INTO HOUSEHOLDS
نویسندگان
چکیده
We consider a stochastic model for the spread of an SIR (susceptible ! infective ! removed) epidemic among a closed, nite population that contains several types of individuals and is partitioned into households. The infection rate between two individuals depends on the types of the transmitting and receiving individuals and also on whether the infection is local (i.e. within a household) or global (i.e. between households). The exact distribution of the nal outcome of the epidemic is outlined. A branching process approximation for the early stages of the epidemic is described and made fully rigorous, by considering a sequence of epidemics in which the number of households tends to innnity and using a coupling argument. This leads to a threshold theorem for the epidemic model. A central limit theorem for the nal outcome of epidemics which take oo is derived, by exploiting an embedding representation.
منابع مشابه
Epidemics among a Population of Households
This paper considers SIR and SIS epidemics among a population partitioned into households. This heterogeneity has important implications for the threshold behaviour of epidemics and optimal vaccination strategies. It is shown that taking into account household structures when modelling public health problems is valuable. An overview of households models is given, including a determination of th...
متن کاملStochastic multitype epidemics in a community of households: estimation of threshold parameter R and secure vaccination coverage
This paper is concerned with a stochastic model for the spread of an SIR (susceptible ! infective ! removed) epidemic among a closed, nite population that contains several types of individuals and is partitioned into households. Previously obtained probabilistic and inferential results for the model are used to estimate the threshold parameter R , which determines whether or not a major outbrea...
متن کاملAn Introduction to Stochastic Epidemic Models
A brief introduction to the formulation of various types of stochastic epidemic models is presented based on the well-known deterministic SIS and SIR epidemic models. Three different types of stochastic model formulations are discussed: discrete time Markov chain, continuous time Markov chain and stochastic differential equations. Properties unique to the stochastic models are presented: probab...
متن کاملStochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes.
This paper treats a stochastic model for an SIR (susceptible-->infective-->removed) multitype household epidemic. The community is assumed to be closed, individuals are of different types and each individual belongs to a household. Previously obtained probabilistic and inferential results for the model are used to derive the optimal vaccination scheme. By this is meant the scheme that vaccinate...
متن کاملOptimal vaccination policies for stochastic epidemics among a population of households.
This paper considers stochastic epidemics among a population partitioned into households, with mixing locally within households and globally throughout the population. The two levels of mixing have important implications for the threshold behaviour of the epidemic and consequently for the form and construction of optimal vaccination policies. Optimality is considered in terms of the cost of the...
متن کامل