Ruktanonchai Nick W, Smith David L, De Leenheer Patrick
University of Southampton, Southampton, United Kingdom.
Institute for Health Metrics and Evaluation, Department of Global Health, University of Washington, Seattle WA.
Math Biosci. 2016 Sep;279:90-101. doi: 10.1016/j.mbs.2016.06.012. Epub 2016 Jul 17.
We consider the dynamics of a mosquito-transmitted pathogen in a multi-patch Ross-Macdonald malaria model with mobile human hosts, mobile vectors, and a heterogeneous environment. We show the existence of a globally stable steady state, and a threshold that determines whether a pathogen is either absent from all patches, or endemic and present at some level in all patches. Each patch is characterized by a local basic reproduction number, whose value predicts whether the disease is cleared or not when the patch is isolated: patches are known as "demographic sinks" if they have a local basic reproduction number less than one, and hence would clear the disease if isolated; patches with a basic reproduction number above one would sustain endemic infection in isolation, and become "demographic sources" of parasites when connected to other patches. Sources are also considered focal areas of transmission for the larger landscape, as they export excess parasites to other areas and can sustain parasite populations. We show how to determine the various basic reproduction numbers from steady state estimates in the patched network and knowledge of additional model parameters, hereby identifying parasite sources in the process. This is useful in the context of control of the infection on natural landscapes, because a commonly suggested strategy is to target focal areas, in order to make their corresponding basic reproduction numbers less than one, effectively turning them into sinks. We show that this is indeed a successful control strategy-albeit a conservative and possibly expensive one-in case either the human host, or the vector does not move. However, we also show that when both humans and vectors move, this strategy may fail, depending on the specific movement patterns exhibited by hosts and vectors.
我们考虑了在一个具有流动人类宿主、流动媒介和异质环境的多斑块罗斯 - 麦克唐纳疟疾模型中，由蚊子传播的病原体的动力学。我们证明了全局稳定稳态的存在，以及一个阈值，该阈值决定了病原体是在所有斑块中均不存在，还是在所有斑块中呈地方病状态并以某种水平存在。每个斑块都由一个局部基本繁殖数来表征，其值预测当该斑块孤立时疾病是否会清除：如果局部基本繁殖数小于1，这些斑块被称为“人口统计学汇”，因此如果孤立，疾病会被清除；基本繁殖数大于1的斑块在孤立时会维持地方病感染，并且在与其他斑块相连时会成为寄生虫的“人口统计学源”。源也被视为更大景观中的传播焦点区域，因为它们将多余的寄生虫输出到其他区域并能够维持寄生虫种群。我们展示了如何从斑块网络中的稳态估计和其他模型参数的知识来确定各种基本繁殖数，从而在此过程中识别寄生虫源。这在自然景观感染控制的背景下是有用的，因为一种常见的建议策略是针对焦点区域，以使它们相应的基本繁殖数小于1，从而有效地将它们转变为汇。我们表明，在人类宿主或媒介不移动的情况下，这确实是一种成功的控制策略——尽管是一种保守且可能昂贵的策略。然而，我们也表明，当人类和媒介都移动时，根据宿主和媒介表现出的特定移动模式，这种策略可能会失败。
