Mechanistic models of host movement to understand disease dynamics in variable environments

在加拿大，过去二十年来出现了新的野生动物疾病，现有疾病的模式发生了重大变化。这些变化突出了研究疾病动态的必要性。当易感宿主接触感染性宿主或寄生虫时，疾病就会传播。这些相遇率在很大程度上取决于宿主的移动方式，然而，大多数疾病传播的数学模型并没有明确考虑宿主的移动。此外，温度、湿度等非生物因素既影响寄生虫的传染性，也影响寄生虫在整个生命阶段的成熟速度。季节性的强度和机制都会影响疾病的动态。寄生虫影响宿主的移动方式，这影响寄生虫的传播和寄生虫毒力等特征的进化。我的研究小组将调查宿主运动如何影响由此产生的流行病类型。我们将考虑不同类型的运动模型，包括相关和有偏随机漫步和状态空间模型。我们将调查波动的环境条件对自由生活的寄生虫传播的影响。我们还将通过推导和分析数学模型来研究寄生虫毒力的进化，其中宿主运动和/或寄生虫传染性、寄生虫脱落率和疾病引起的死亡率之间存在权衡。在所有情况下，模型将使用数学和计算技术进行分析。

In Canada, over the last two decades new wildlife diseases have emerged and patterns of existing diseases have changed substantially. These changes highlight the need for research that investigates disease dynamics. Diseases are spread when a susceptible host contacts an infectious host or a parasite. These rates of encounter depend strongly on how hosts move, and yet, most mathematical models of disease spread do not explicitly consider host movement. In addition, temperature, humidity and other abiotic factors affect both the infectivity of parasites and the rate of maturation through parasite life stages. Both the strength and mechanisms of seasonality will affect disease dynamics. Parasites affect how hosts move and this affects parasite spread and the evolution of characteristics such as parasite virulence. My research group will investigate how host movement affects the types of epidemics that result. We will consider different types of movement models including correlated and biased random walks and state-space models. We will investigate the effect of fluctuating environmental conditions on the spread of free-living parasites. We will also investigate the evolution of parasite virulence by deriving and analyzing mathematical models where a trade-off exists between the rate of host movement and/or parasite infectivity, the parasite shedding rate, and the disease-induced death rate. In all cases, the models will be analyzed using mathematical and computational techniques. This research will capitalize on recent progress in developing mechanistic models of animal movement and will contribute new conceptual, quantitative, and computational tools to the study of infectious disease spread. The models that we will derive improve the biological realism of existing theory and are likely to lead to a better understanding of disease dynamics. For a specific case study, we will apply the theory we develop to understand the spread of brain worm in declining herds of caribou in Newfoundland. This research program will support the training of 1 PhD student, 4 MSc students and 4 undergraduate researchers. These students will be trained in mathematical modelling and theoretical biology and will gain valuable experience in interdisciplinary research.