季节性宿主出生率对疾病持续存在的影响。

The effect of seasonal host birth rates on disease persistence.

作者信息

Ireland J M, Mestel B D, Norman R A

机构信息

Department of Computing Science and Mathematics, University of Stirling, Stirling, Scotland FK9 4LA, UK.

出版信息

Math Biosci. 2007 Mar;206(1):31-45. doi: 10.1016/j.mbs.2006.08.028. Epub 2006 Sep 26.

DOI:10.1016/j.mbs.2006.08.028

PMID:17316708

Abstract

In this paper, we add seasonality to the birth rate of an SIR model with density dependence in the death rate. We find that disease persistence can be explained by considering the average value of the seasonal term. If the basic reproductive ratio R(0)>1 with this average value then the disease will persist and if R(0)<1 with this average value then the disease will die out. However, if the underlying non-seasonal model displays oscillations towards the equilibrium then the dynamics of the seasonal model can become more complex. In this case, the seasonality can interact with the underlying oscillations, resonate and the population can display a range of complex behaviours including chaos. We discuss these results in terms of two examples, Cowpox in bank voles and Rabbit Haemorrhagic disease in rabbits.

摘要

在本文中，我们在死亡率具有密度依赖性的SIR模型的出生率中加入季节性因素。我们发现，通过考虑季节性项的平均值可以解释疾病的持续存在。如果基于该平均值的基本繁殖数R(0)>1，那么疾病将会持续存在；如果基于该平均值的R(0)<1，那么疾病将会消亡。然而，如果基础非季节性模型朝着平衡点呈现振荡，那么季节性模型的动态变化可能会变得更加复杂。在这种情况下，季节性因素可以与基础振荡相互作用、产生共振，并且种群可能会表现出一系列复杂行为，包括混沌。我们通过两个例子来讨论这些结果，即银行田鼠中的牛痘和兔子中的兔出血性疾病。