Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK.
Math Biosci. 2011 Jun;231(2):144-58. doi: 10.1016/j.mbs.2011.02.011. Epub 2011 Mar 3.
Backward bifurcation is a relatively recent yet well-studied phenomenon associated with deterministic epidemic models. It allows for the presence of multiple subcritical endemic equilibria, and is generally found only in models possessing a reasonable degree of complexity. One particular aspect of backward bifurcation that appears to have been virtually overlooked in the literature is the potential influence its presence might have on the behaviour of any analogous stochastic model. Indeed, the primary aim of this paper is to investigate this possibility. Our approach is to compare the theoretical probabilities of extinction, calculated via a particular stochastic formulation of a deterministic model exhibiting backward bifurcation, with those obtained from a series of stochastic simulations. We have found some interesting links in the behaviour between the deterministic and stochastic models, and are able to offer plausible explanations for our observations.
反向分歧是一种相对较新但研究充分的现象，与确定性传染病模型有关。它允许存在多个亚临界地方性平衡点，通常只在具有一定复杂程度的模型中发现。反向分歧的一个特别方面，似乎在文献中几乎被忽视，那就是它的存在可能对任何类似的随机模型的行为产生影响。事实上，本文的主要目的是研究这种可能性。我们的方法是比较通过表现出反向分歧的确定性模型的特定随机形式计算的灭绝理论概率，与从一系列随机模拟中获得的概率。我们已经发现了确定性和随机模型之间的一些有趣的行为联系，并能够对我们的观察结果提供合理的解释。
