Clancy Damian
Department of Actuarial Mathematics and Statistics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
J Math Biol. 2018 Sep;77(3):545-570. doi: 10.1007/s00285-018-1222-1. Epub 2018 Feb 23.
For a susceptible-infectious-susceptible infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to extinction of infection. Our model may be interpreted as describing an infection spreading through either (1) a population with heterogeneity in individuals' susceptibility and/or infectiousness; or (2) a heterogeneous directed network. Using our asymptotic formulae, we show that such heterogeneity can only reduce (to leading order) the mean persistence time compared to a corresponding homogeneous population, and that the greater the degree of heterogeneity, the more quickly infection will die out.
对于异质人群中的易感-感染-易感感染模型，我们给出了简单公式，这些公式给出了从地方病状态到感染灭绝的平均持续时间的主导阶渐近（大群体）行为。我们的模型可以解释为描述感染通过以下两种情况传播：（1）个体易感性和/或传染性存在异质性的人群；（2）异质有向网络。使用我们的渐近公式，我们表明，与相应的同质人群相比，这种异质性只会（在主导阶上）减少平均持续时间，并且异质性程度越高，感染消失得越快。
