Causes of backward bifurcations in some epidemiological models
Causes of backward bifurcations in some epidemiological models
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DOI：
10.1016/j.jmaa.2012.04.077
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发表时间：
2012-11-01
影响因子：
1.3
通讯作者：
Gumel, A. B.
中科院分区：
文献类型：
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作者：
Gumel, A. B.
在疾病传播模型中，当再生数小于1时，存在稳定的地方病平衡点和稳定的无病平衡点，这一现象在许多疾病传播模型中被观察到.后向分叉的流行病学后果是，对于疾病消除来说，经典的繁殖数小于1的要求只是必要的，但不是充分的（因此，疾病传播动力学中这种现象的存在使其在社区中难以有效控制）。本文讨论了在一些标准的确定性模型中寻找一些新出现和重新出现的疾病传播的后向分支的原因的问题（它包含了一些常见的原因，以及一些新的原因，在一些标准的疾病传播模型中的后向分支的简要回顾）。结果表明，除了常见的原因（如使用不完善的疫苗和结核病中的外源性再感染）外，其他一些生物学或流行病学机制，如疫苗免疫衰减速度慢于自然免疫、病媒传播疾病中的疾病诱导死亡率和风险结构模型中的差异易感性，也可能导致疾病传播模型的后向分岔。(C)2012 Elsevier Inc. All rights reserved.
The phenomenon of backward bifurcation in disease transmission models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has been observed in a number of disease transmission models. The epidemiological consequence of backward bifurcation is that the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, for disease elimination (hence, the presence of this phenomenon in the transmission dynamics of a disease makes its effective control in the community difficult). This paper addresses the problem of finding the causes of backward bifurcation in some standard deterministic models for the spread of some emerging and re-emerging diseases (it contains a brief review of some common causes, as well as some new causes, of backward bifurcation in some standard disease transmission models). It is shown that, in addition to the usual causes (such as the use of imperfect vaccine and exogenous re-infection in TB disease), a number of other biological or epidemiological mechanisms, such as vaccine-derived immunity waning at a slower rate than natural immunity, disease-induced mortality in vector-borne diseases and differential susceptibility in risk-structured models, could also cause backward bifurcation in disease transmission models. (C) 2012 Elsevier Inc. All rights reserved.