Mathematical Models of Epidemics for Public Health Applications

Abstract: In this article we develop both deterministic and stochastic models for microparasitic infection to study (1) the static and dynamical behaviours of epidemics and (2) the effects of immunization on epidemiological and demographic parameters. For the static aspect, such key parameters as the basic reproductive rate, incidence rate, transmission rate, recovery rate and death rate are derived in terms of the mean age at infection, mean age at death and mean duration of the infectious period under two assumed distributions of the lifelength in the stationary population. For the dynamical aspect, the deterministic models are used to analyze periodicities in the incidence of endemic infection. Stochastic models are used to analyze the effects on the persistence of the epidemic and on the eradication of endemic infection. The degree of realism of the models so developed are demonstrated by adequately fitting the models to the incidence curve, prevalence curve and the curve of proportion seropositive arising from epidemiological data. The ultimate goals of the models are to develop strategies for optimizing vaccination programs, to answer public health questions for decision makers and to provide broad scenarios for monitoring, prediction and planning.