Asymptotic behaviour of a logistic epidemic model with stochastic disease transmission

摘要

A simple model of the dynamics of an infectious disease, taking into account environmental variability in the form of Gaussian white noise in the disease transmission rate, has been investigated. The probability distribution for the proportion of infected animals, plus its mean, mode and variance are found explicitly. The results are presented using data from bovine tuberculosis in possum populations in New Zealand as an example.