Ongoing estimation of the epidemic parameters of a stochastic, spatial, discrete-time model for a 1983-84 avian influenza epidemic.

We formulate a stochastic, spatial, discrete-time model of viral "Susceptible, Exposed, Infectious, Recovered" animal epidemics and apply it to an avian influenza epidemic in Pennsylvania in 1983-84. Using weekly data for the number of newly infectious cases collected during the epidemic, we find estimates for the latent period of the virus and the values of two parameters within the transmission kernel of the model. These data are then jackknifed on a progressive weekly basis to show how our estimates can be applied to an ongoing epidemic to generate continually improving values of certain epidemic parameters.

Conditions determining the local stability of populations.

The conditions that determine the local stability classification of an equilibrium population configuration are analyzed. The population investigated is age-structured and density-dependent, where density is determined by an age-weighted population size. 2 demographic parameters are introduced: the marginal birth rate and the marginal death rate, which describe the marginal density-dependence of the birth and death rates of the equilibrium population. Certain necessary and/or sufficient conditions determining stability are developed, most of them involving the net reproduction rate of the population, and examples illustrating these conditions are presented.