Study of some systems from population dynamics and disease transmission dynamics with heterogeneity

点击翻译按钮获取中文摘要

This proposed research program consists of two parts. (A) Study spatial temporal dynamics of two classes of systems under spatially shifting heterogeneity that may account for environment/resource shifting caused by climate change or industrialization. One class are scalar delay differential equations for mature populations with maturation delay, and the other class are systems for population dynamics of interacting species including competing species and predator-prey species. (B) Explore various fear effects in predator-prey systems and the corresponding notion of fear effects in transmission dynamics of infectious diseases. For (A), the focus will be on how the shifting speed and the profile, together with the biological characteristics of the species involved, will affect the spatial temporal dynamics of governing systems. These characteristics include the type of birth functions, death rate, maturation delays, and type of interaction, rate of dispersal  and strengths of interaction. The possible topics include extinction/persistence, pattern of coexistence, spreading speed, pushed traveling waves and their stability, and impact of initial distribution. We will encounter some new dynamical systems with a special type of spatial-temporal heterogeneity with delay. I expect to develop some new approaches/methods, abd to modify and improve some existing ones to achieve our objectives. Thus, the results may contribute to the theory and methods for spatial dynamical systems, and they may also help understand the impact of climate change and industrialization. Part (B) is real world problem driven. We extend the notion of "fear effects" in predator-prey (P-P) systems to "susceptible-infectious" (S-I) interactions in modeling transmission dynamics of infectious diseases to reflect the reality that during the epidemic of an infectious disease, human beings behaviors (e.g., social activities and travel) will change and such changes are due to the fear of disease and may evolve with the epidemic. The focus in this part will be on how a prey's dispersal, foraging and production strategies evolve in response to perceiving its predator(s); and how human being's precaution level will evolve and the impact of such an evolution of precaution level on the long term and short term disease dynamics. I expect the results of this proposed research will have potential applications in agriculture and public health: the results on fear effect in P-P system may suggest new and environmentally friendly approaches for controlling some agriculture rodent pests; and the results on "fear effects" (e.g. represented by media coverage and public health agents' warning) on human's behavior change and its impacts may help inform decision makers,  in public health,  of valuable guidelines for controlling or mitigating the epidemics of an infectious disease.