期刊
JOURNAL OF MATHEMATICAL BIOLOGY
卷 62, 期 3, 页码 333-348出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-010-0336-x
关键词
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.
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