Abstract
A general formulation of the discrete-time epidemic model with permanent immunity is presented, following the general format of a model developed in the Soviet Union. This paper presents a stochastic form of the model on a discrete state space and a deterministic form on a continuous state space. An epidemic threshold theorem is derived for the deterministic form. Bounds are found for the final infection attack rate, and the relative error of these bounds is investigated for varying parameter values. A number of discrete-time epidemic models proposed by others are shown to be special cases of the general model formulated. Methods for parameter estimation are given for small populations when the data are in either sequential or final value form and for large populations when the data are in sequential form. Examples are given of analysis of epidemic influenza data from small and large populations.
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