PrefaceNational Science Foundation for its financial support over the years which helped sustain and encourage our work in this area. Finally, we thank our wives, Bonnie and Margaret, for their support and for their cheerful tolerance of the long working hours that were needed to complete this book. We hope that some of their exemplary patience and loyalty has been vertically transmitted to our offspring.
An S----I----R----S epidemiological model with vital dynamics in a population of varying size is discussed. A complete global analysis is given which uses a new result to establish the nonexistence of periodic solutions. Results are discussed in terms of three explicit threshold parameters which respectively govern the increase of the total population, the existence and stability of an endemic proportion equilibrium and the growth of the infective population. These lead to two distinct concepts of disease eradication which involve the total number of infectives and their proportion in the population.
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