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

本文研究了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问题。对于生态系统，这一建议主要关注竞争和捕食的相互作用。本文将重点讨论具有空间异质性和随机性的三种捕食者-猎物（植物-食草动物）系统的种群内捕食行为。对于流行病学系统，建议侧重于传染病传播和控制的建模。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，以及种群在斑块之间的适应性分散。

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.