A stochastic SIS epidemic with demography: initial stages and time to extinction |
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Authors: | Patrik Andersson David Lindenstrand |
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Institution: | (1) School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, UK |
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Abstract: | We study an open population stochastic epidemic model from the time of introduction of the disease, through a possible outbreak
and to extinction. The model describes an SIS (susceptible–infective–susceptible) epidemic where all individuals, including
infectious ones, reproduce at a given rate. An approximate expression for the outbreak probability is derived using a coupling
argument. Further, we analyse the behaviour of the model close to quasi-stationarity, and the time to disease extinction,
with the aid of a diffusion approximation. In this situation the number of susceptibles and infectives behaves as an Ornstein–Uhlenbeck
process, centred around the stationary point, for an exponentially distributed time before going extinct. |
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Keywords: | |
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