A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness.
A simple epidemiological model for populations in the wild with Allee effects and disease-modified fitness.
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DOI：
10.3934/dcdsb.2014.19.89
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发表时间：
2014-01
期刊：
影响因子：
--
通讯作者：
Castillo-Chavez C
中科院分区：
文献类型：
--
作者：
Kang Y;Castillo-Chavez C
使用确定性模型对人类传染病动力学进行研究，通常是在假定有一定数量的人参与传播过程的情况下进行的。然而，在动物疾病动力学的研究中，人口因素往往起着重要作用，这一假设必须削弱。动物种群动态模型通常很自然地假设，为了避免灭绝，最小数量的个体是必不可少的。在生态学文献中，这种先验要求通常被认为是阿尔利效应。这里的重点是在假设易感个体的临界质量以保证种群生存的前提下研究疾病动态。具体来说，重点是研究Allee效应在易感-感染（SI）模型中的作用，其中易感和感染个体繁殖的可能性，其中s级最适合。进一步假设受感染的个体失去了争夺资源的能力，这是疾病造成的代价。这些功能都是在尽可能简单的模型中设置的。它们最终会导致一系列丰富的动态结果。这个玩具模型支持多重稳定性（迟滞）、鞍节点和Hopf分岔以及灾难性事件（疾病引起的灭绝）的可能性。分析提供了无病动态下系统的全貌，包括疾病引起的灭绝，并继续确定疾病持续存在的必要条件。我们的结论是，增加(i)一个物种的最大出生率，或（ii）受感染个体的相对繁殖能力，或（iii）受感染个体在低密度水平下的竞争能力，或（iv）受感染个体的人均死亡率（包括疾病引起的），可以稳定系统（导致疾病持续存在）。我们进一步得出结论，(a) Allee效应阈值的增加，或(b)疾病传播率的增加，或(c)高密度水平下受感染个体的竞争能力的增加，都可能破坏系统的稳定，最终可能导致种群的崩溃。从这个玩具模型的分析中得到的结果强调了像Allee效应这样的因素对动物种群的生存和持久性可能起的重要作用。从事生物保护和病虫害管理或对寻找可持续性解决方案感兴趣的科学家可能会发现，这项研究的这些结果足以令人信服，从而建议对疾病在动物种群的调节和持久性中的作用进行进一步的重点研究。濒危物种面临的风险可能比最初想象的要高得多。
The study of the dynamics of human infectious disease using deterministic models is typically carried out under the assumption that a critical mass of individuals is available and involved in the transmission process. However, in the study of animal disease dynamics where demographic considerations often play a significant role, this assumption must be weakened. Models of the dynamics of animal populations often naturally assume that the presence of a minimal number of individuals is essential to avoid extinction. In the ecological literature, this a priori requirement is commonly incorporated as an Allee effect. The focus here is on the study disease dynamics under the assumption that a critical mass of susceptible individuals is required to guarantee the population's survival. Specifically, the emphasis is on the study of the role of an Allee effect on a Susceptible-Infectious (SI) model where the possibility that susceptible and infected individuals reproduce, with the S-class the best fit. It is further assumed that infected individuals loose some of their ability to compete for resources, the cost imposed by the disease. These features are set in motion in as simple model as possible. They turn out to lead to a rich set of dynamical outcomes. This toy model supports the possibility of multi-stability (hysteresis), saddle node and Hopf bifurcations, and catastrophic events (disease-induced extinction). The analyses provide a full picture of the system under disease-free dynamics including disease-induced extinction and proceed to identify required conditions for disease persistence. We conclude that increases in (i) the maximum birth rate of a species, or (ii) in the relative reproductive ability of infected individuals, or (iii) in the competitive ability of a infected individuals at low density levels, or in (iv) the per-capita death rate (including disease-induced) of infected individuals, can stabilize the system (resulting in disease persistence). We further conclude that increases in (a) the Allee effect threshold, or (b) in disease transmission rates, or in (c) the competitive ability of infected individuals at high density levels, can destabilize the system, possibly leading to the eventual collapse of the population. The results obtained from the analyses of this toy model highlight the significant role that factors like an Allee effect may play on the survival and persistence of animal populations. Scientists involved in biological conservation and pest management or interested in finding sustainability solutions, may find these results of this study compelling enough to suggest additional focused research on the role of disease in the regulation and persistence of animal populations. The risk faced by endangered species may turn out to be a lot higher than initially thought.
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影响因子：
4.3
作者：
Del Valle, S;Hethcote, H;Castillo-Chavez, C
通讯作者：
Castillo-Chavez, C
DOI：
10.1098/rspb.1995.0201
发表时间：
1995-11-22
影响因子：
4.7
作者：
BURROWS, R;HOFER, H;EAST, ML
通讯作者：
EAST, ML
DOI：
10.1016/j.jmaa.2004.05.045
发表时间：
2004-10-15
影响因子：
1.3
作者：
Brauer, F
通讯作者：
Brauer, F
影响因子：
4.3
作者：
Alvarez, LHR
通讯作者：
Alvarez, LHR
影响因子：
4.3
作者：
Castillo-Chavez, C;Yakubu, AA
通讯作者：
Yakubu, AA