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

本文主要研究生态学模型和流行病学模型中的非线性发展方程的瞬态和渐近动力学问题。对于生态系统，这一建议主要涉及竞争和捕食的相互作用。重点将放在行会内捕食涉及三个物种，捕食者-猎物（植物-草食动物）系统的空间异质性和随机性。对于流行病学系统，该提案侧重于传染病的传播和控制建模。特别是，两个广泛的问题将被调查：细胞，病原体和宿主内的免疫反应的相互作用，以及补丁之间的人口的适应性扩散。

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.