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- Andersson, Patrik, et al.
(författare)
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A stochastic SIS epidemic with demography : initial stages and time to extinction
- 2011
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Ingår i: Journal of Mathematical Biology. - : Springer Science and Business Media LLC. - 0303-6812 .- 1432-1416. ; 62:3, s. 333-348
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Tidskriftsartikel (refereegranskat)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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