This project will study ways in which heterogeneities associated with age structure, social habits, or genetic variability within the host population can interact with the nonlinearities inherent in the transmission of infectious diseases to produce outcomes that are not easily intuited. The first part of the project focuses on various aspects of specific viral and bacterial infections in the USA and UK; measles, rubella, mumps, polio, pertussis and HIV. Models that account for observed age-specific differences in infection probabilities will be studied tested against epidemiological data and applied to compare different immunization strategies. Equations describing the epidemic spread of HIV infection among populations of homosexual males will be developed, taking account of the AIDS wide distribution reported in degrees of sexual activity; potential applications of the estimation of epidemiological parameters and projected effects of changes in sexual habits will be explored. Second, mathematical models for the transmission dynamics of helminth infections (specially Ascaris and various filarial infections) will be studied with attention to comparing the effects of different control strategies. At a more abstract level, the cyclic and chaotic properties of models for arthropod populations regulated by lethal pathogens will be investigated, partly with the aim of understanding relations between life history parameters and dynamical behavior. Building on earlier work, these studies will be extended to combine population genetics with population biology in pursuit of a better understanding of the coevolution of host-parasite associations. Mathematical models in epidemiology are often based on the qualitative theory of differential equations and constitute a prime example of applied mathematics in life sciences. Dr. May is the most prominent representative of this research direction in the U.S.
