Threshold behaviour for a chain-binomial S-I-S infectious disease
type: Item
instance of: scholarly article
title: Threshold behaviour for a chain-binomial S-I-S infectious disease
zbMATH Open document ID: 0611.92019
DOI: 10.1007/BF00275720
published in: Journal of Mathematical Biology
publication date: 1986-01-01T00:00:00Z
review text: The paper is concerned with a discrete time model for the spread of an infection. Like in the classical Reed-Frost model an infectious individual can transmit the disease to any susceptible with a constant probability p (the infectious period is assumed to be very small). If an individual was infected, it itself becomes infectious after a certain period of fixed length, the latent period, which is taken as the time unit. After another time unit the individual returns to the susceptible state (SIS-epidemic). During the infectious period each susceptible makes a random number of contacts with other individuals; it is assumed that the j-th contact of a not yet infected individual with an infective will result in an infection with probability \(\beta_ j\). The process of infection is formulated stochastically and then the associated deterministic model is derived. For this model, which is essentially a first-order difference equation, it is studied under what conditions the disease becomes endemic. Besides some general results a detailed discussion is presented for the specific case where at least \(K+1\) (K\(\geq 1)\) contacts with infectives are needed for an infection to occur.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 3989159
zbMATH Keywords: chain-binomial deterministic model
zbMATH Keywords: threshold behaviour
zbMATH Keywords: endemic disease
zbMATH Keywords: discrete time model
zbMATH Keywords: SIS-epidemic
zbMATH Keywords: first-order difference equation
Wikidata QID: Q69550754
author: Claude Lefèvre
MaRDI profile type: Publication
cites work: Q4101645
cites work: Q3908199
cites work: Q5847520
cites work: Q3713901
cites work: Q5653524
cites work: A chain binomial model of endemicity
cites work: Togetherness among schistosomes: Its effects on the dynamics of the infection
cites work: Asymptotic final-size distribution for some chain-binomial processes
cites work: Threshold limit theorems for some epidemic processes
full work available at URL: https://doi.org/10.1007/bf00275720
OpenAlex ID: W2010164640
description: scientific article; zbMATH DE number 3989159