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- W4299786064 abstract "Consider a large uniformly mixing dynamic population, which has constant birth rate and exponentially distributed lifetimes, with mean population size $n$. A Markovian SIR (susceptible $to$ infective $to$ recovered) infectious disease, having importation of infectives, taking place in this population is analysed. The main situation treated is where $ntoinfty$, keeping the basic reproduction number $R_0$ as well as the importation rate of infectives fixed, but assuming that the quotient of the average infectious period and the average lifetime tends to 0 faster than $1/log n$. It is shown that, as $ n to infty$, the behaviour of the 3-dimensional process describing the evolution of the fraction of the population that are susceptible, infective and recovered, is encapsulated in a 1-dimensional regenerative process $S={ S(t);tge 0}$ describing the limiting fraction of the population that are susceptible. The process $S$ grows deterministically, except at one random time point per regenerative cycle, where it jumps down by a size that is completely determined by the waiting time since the previous jump. Properties of the process $S$, including the jump size and stationary distributions, are determined." @default.
- W4299786064 created "2022-10-03" @default.
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- W4299786064 date "2015-06-08" @default.
- W4299786064 modified "2023-09-26" @default.
- W4299786064 title "An epidemic in a dynamic population with importation of infectives" @default.
- W4299786064 doi "https://doi.org/10.48550/arxiv.1506.02540" @default.
- W4299786064 hasPublicationYear "2015" @default.
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