Ecological and epidemiological modelling across multiple spatial scales

我建议考虑在不同的空间尺度上运行的耦合数学模型的表述以及数学和计算分析，每个模型描述不同物种在争夺资源、捕食者-捕食者关系或传染性病原体的传播中相互作用的运动模式和结果范围。例如，对资源的竞争可能涉及迁徙和非迁徙物种；许多捕食者的活动范围远远超出其猎物物种的活动范围；在病媒传播的疾病中，宿主通常具有高度流动性，而传播媒介的活动范围非常小。*因此，重要的是制定方法来处理这些不同的范围。这将通过考虑不同的模型类型(常微分方程组或偏微分方程式，离散或连续的马尔可夫链，网络模型)来实现，每种模型都适用于描述给定物种的范围和运动，并使用耦合术语来描述物种之间的局部相互作用。*为了了解可能发生的不同类型的耦合，我将用三个我可以获得数据的例子来工作。*1.紫色马丁(P.subis)在北美和它在巴西的越冬地点之间的年度迁徙。这个问题的数据来自加拿大马尼托巴大学的K.Fraser。*2。加拿大大西洋地区雪蟹种群的利用。捕鱼船队分为合作小组和竞争小组。这个问题的数据来自D.Gillis(马尼托巴大学)。*3.疟疾在科摩罗群岛内部和之间的传播。通过与C.Rogier(法国圣战者服务局)的合作，我掌握了几种恶性疟原虫在群岛五个岛屿之间传播的数据。恶性疟原虫是导致疟疾的寄生虫。*这些例子将需要不同类型的模型组合：在亚种疟原虫的情况下，离散和连续时间确定性的情况下；在小疟原虫的情况下，连续时间确定性和随机的情况下；在恶性疟原虫的情况下，离散和连续的确定性和随机的情况下。从这些不同的例子中，我将得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，并为它们的计算分析设计计算机代码。*这个新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基于数据的方法之间的差距，为考虑这些领域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.