Transient and Asymptotic Dynamics of Some Evolution Equations from Ecology and Epidemiology

本研究将研究生态模型和流行病学模型中一些非线性演化方程的瞬态和渐近动力学。对于生态系统，该建议主要涉及竞争和捕食的相互作用。重点将放在涉及三个物种的行会内捕食，即具有空间异质性和随机性的捕食者-被捕食者（植物-草食动物）系统。对于流行病学系统，该提案的重点是对传染病的传播和控制进行建模。特别是，将研究两个广泛的问题：宿主内细胞、病原体和免疫反应的相互作用，以及斑块之间种群的适应性扩散。

Transient and asymptotic dynamics of some nonlinear evolution equations from ecological modeling and epidemiological modeling will be studied in this proposed research. For ecological systems, this proposal mainly concerns the interplay of competition and predation. An emphasis will be placed on intra-guild predation involving three species, predator-prey (plant-herbivore) systems with spatial heterogeneities and stochasticity. For epidemiological systems, the proposal focuses on modeling the transmission and control of infectious diseases. In particular, two broad problems will be investigated: interactions of cells, pathogens and immune responses within a host, and adaptive dispersal of a population between patches.