Ecological and epidemiological modelling across multiple spatial scales

我建议考虑制定和数学和计算分析耦合的数学模型在不同的空间尺度上运行，每个模型描述的运动模式和所产生的范围内的不同物种的相互作用，在竞争资源，捕食关系或传染性病原体的传播。 事实上，当考虑两个或两个以上物种之间的相互作用时，所涉及的物种通常以非常不同的方式占据空间并在空间中移动。例如，对资源的竞争可能涉及移徙物种和非移徙物种;许多捕食者的活动范围远远超过其被捕食物种的活动范围;在病媒传播的疾病中，宿主通常具有高度移动的性，而病媒的活动范围非常小。 因此，必须制定处理这些不同幅度的方法。这将通过考虑不同的模型类型（普通或偏微分方程，离散或连续马尔可夫链，网络模型）来实现，每个模型都适合于描述给定物种的范围和运动，耦合项用于描述物种之间的局部相互作用。 为了理解可能发生的不同类型的耦合，我将使用三个我可以访问数据的示例。 1.在北美洲和巴西的越冬地之间的紫色马丁（P. subis）的年度迁徙。这个问题的数据来自K。弗雷泽（马尼托巴大学）。 2.利用雪蟹（C. opilio）在大西洋加拿大。捕鱼船队分为合作和竞争两类。这个问题的数据来自D。Gillis（马尼托巴大学）。 3.科摩罗群岛内部和之间的疟疾传播。通过与C。Rogier（法国军人卫生服务处），我有几种恶性疟原虫（疟疾的病原寄生虫）在群岛五个岛屿之间传播的数据。还提供了关于岛屿之间的人类活动和病媒密度的信息。 这些例子将需要不同的模型类型组合：在P. subis的情况下，离散和连续时间确定性，在C. subis的情况下，连续时间确定性和随机性。opilio和组合的离散和连续的确定性和随机的恶性疟原虫的情况下。从这些不同的例子中，我将推导出管理不同类型模型的使用和耦合的一般原则。我将考虑这种多尺度混合模型的数学分析，并设计计算机代码进行计算分析。 这一新颖的跨学科项目将培训至少10名HQP，并将有助于缩小空间生态学和流行病学中基于模型和数据的方法之间的差距，为考虑这些领域中的数据驱动问题提供坚实的理论背景。

I propose to consider the formulation and mathematical and computational analysis of coupled mathematical models operating across distinct spatial scales, with each model describing the movement patterns and resulting range of the different species interacting in competition for resources, prey-predator relationships or the transmission of an infectious pathogen. Indeed, when considering interactions between two or more species, it is common that the species involved occupy and move through space in very different ways. For instance, competition for resources can involve migrating and non-migrating species; the range of many predators far exceeds the range of their prey species; and in vector-borne diseases, hosts are typically highly mobile while vectors have very small ranges. It is therefore important to formulate methodologies to deal with these varying ranges. This will be achieved by considering different model types (ordinary or partial differential equations, discrete or continuous Markov chains, network models), each suitable for the description of the range and movement of a given species, with coupling terms to describe local interactions between species. To understand the different types of couplings that can occur, I will work with three examples for which I have access to data. 1. Annual migration of the purple martin (P. subis) between North America and its overwintering site in Brazil. The data for this problem comes from K. Fraser (University of Manitoba). 2. Utilization of a stock of snow crabs (C. opilio) in Atlantic Canada. The fishing fleet divides itself between cooperative and competitive groups. The data for this problem comes from D. Gillis (University of Manitoba). 3. Spread of malaria in and between the Comoros Islands. Through a collaboration with C. Rogier (Service de Santé des Armées, France), I have data on the spread of several strains of P. falciparum, the causative parasite of malaria, between the five islands in the archipelago. Information is also available about human movement between the islands and about vector densities. These examples will require different combinations of model types: discrete and continuous time deterministic in the case of P. subis, continuous time deterministic and stochastic in the case of C. opilio and a combination of discrete and continuous deterministic and stochastic in the case of P. falciparum. From these different examples, I will derive general principles that govern the use and coupling of models of different types. I will consider the mathematical analysis of such multiscale hybrid models and will devise computer code for their computational analysis. This novel interdisciplinary program will train at least 10 HQP and will help reduce the gap between model- and data-based approaches in spatial ecology and epidemiology, providing a firm theoretic background to consider data driven problems in these fields.