The investigator undertakes mathematical studies of questions arising in ecology and population biology, focusing on host-parasite systems and structured populations. With their rapid turnover, parasitic populations are ideal objects to study the principles of evolution; in turn, it is important to understand these principles to control infectious diseases effectively. Mathematical models and their analysis are very much needed for a deeper understanding and as a theoretical laboratory to devise control and management strategies. In fact, many of the arguments on the adaptive dynamics of virulence have become so complex that they can be more easily formulated mathematically than verbally. While the health aspects of parasite-host interactions are of immediate concern, their impact on biological diversity may be as important. The mediation of species coexistence through chaotic dynamics has gained a lot of attention recently, but coexistence at equilibrium mediated by parasites and by population structure may be far more prominent. In the context of competition, coexistence, and evolution in host-parasite systems, the investigator studies: Coexistence and evolution of endophytic fungi, Parasite mediated coexistence and competition, and Prey-predator-parasite interactions. Using structured population models, he studies: The evolution of parasite virulence in structured host populations, Apparent Allee effects in structured predator-prey systems, and The evolution of polymorphism in amphibians. Emerging and re-emerging infectious diseases and the danger of bioterrorism have led to a renewed interest in host-parasite systems. The fact that infectious diseases afflict not only humans and their food sources (domestic animals and agronomic plants), but also natural animal and plant populations, has directed attention to the important and fascinating role of parasites in ecosystems and in the maintenance of biological diversity. Studying mathematical host-parasite models enhances our insight in evolution in general and in evolution of hosts and parasites in particular (evolution of virulence, co-evolution of hosts and parasites). These models help to design disease control strategies that avoid parasite resistance and decrease parasite virulence (virulence management). They also lead to environmental management strategies that are compatible with species preservation. They can be used as educational tools in graduate and undergraduate instruction and for effective communication with the scientific community, public health officers, and an educated public audience.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Michael H. Steuerwalt
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Arizona State University
United States
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