Neal, Peter (2008) The SIS Great Circle Epidemic model. Journal of Applied Probability, 45 (2). pp. 513-530.Full text not available from this repository.
We consider a stochastic SIS model for the spread of an epidemic amongst a population of n individuals that are equally spaced upon the circumference of a circle. Whilst infectious, an individual, i say, makes both local and global infectious contacts at the points of homogeneous Poisson point processes. Global contacts are made uniformly at random with members of the entire population, whilst local contacts are made according to a contact distribution centred upon the infective. Individuals at the end of their infectious period return to the susceptible state and can be reinfected. The emphasis of the paper is on asymptotic results as the population size n → ∞. Therefore, a contact process with global infection is introduced representing the limiting behaviour as n → ∞ of the circle epidemics. A branching process approximation for the early stages of the epidemic is derived and the endemic equilibrium of a major outbreak is obtained. Furthermore, assuming exponential infectious periods, the probability of a major epidemic outbreak and the proportion of the population infectious in the endemic equilibrium are shown to satisfy the same equation which characterises the epidemic process.
|Journal or Publication Title:||Journal of Applied Probability|
|Uncontrolled Keywords:||SIS epidemic ; contact process ; great circle model ; endemic equilibrium ; branching process|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||05 Nov 2012 11:25|
|Last Modified:||15 Mar 2016 01:22|
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