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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Andersson, P., Lindenstrand, D. A stochastic SIS epidemic with demography: initial stages and time to extinction. J. Math. Biol. 62, 333–348 (2011). https://doi.org/10.1007/s00285-010-0336-x
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DOI: https://doi.org/10.1007/s00285-010-0336-x
Keywords
- Stochastic epidemic model
- Quasi stationarity
- SIS model
- Coupling
- Ornstein–Uhlenbeck
- Diffusion approximation
- Outbreak probability