A stochastic SIS epidemic with demography: initial stages and time to extinction

作者：Andersson Patrik; Lindenstrand David^*

来源：Journal of Mathematical Biology, 2011, 62(3): 333-348.

DOI：10.1007/s00285-010-0336-x

• Stochastic epidemic model
• Quasi stationarity
• SIS model
• Coupling
• Ornstein-Uhlenbeck
• Diffusion approximation
• Outbreak probability

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.

• 出版日期2011-3