The generalized discrete-time epidemic model with immunity: A synthesis
type: Item
instance of: scholarly article
title: The generalized discrete-time epidemic model with immunity: A synthesis
zbMATH Open document ID: 0613.92021
DOI: 10.1016/0025-5564(86)90003-9
published in: Mathematical Biosciences
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 3993364
zbMATH Keywords: general epidemic
zbMATH Keywords: discrete-time epidemic model
zbMATH Keywords: permanent immunity
zbMATH Keywords: epidemic threshold theorem
zbMATH Keywords: parameter estimation
zbMATH Keywords: influenza data
author: Ira M. jun. Longini
MaRDI profile type: Publication
full work available at URL: 0025-5564(86)90003-9
OpenAlex ID: W2009650530
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description: scientific article; zbMATH DE number 3993364