Population dynamics of mosquito-borne disease: Persistence in a completely heterogeneous environment
type: Item
instance of: scholarly article
title: Population dynamics of mosquito-borne disease: Persistence in a completely heterogeneous environment
zbMATH Open document ID: 0647.92015
DOI: 10.1016/0040-5809(88)90003-2
author: Günther Hasibeder
author: Christopher Dye
published in: Theoretical Population Biology
publication date: 1988-01-01T00:00:00Z
review text: The m/n model of mosquito-borne disease is studied. m/n model means that infected hosts and mosquitos are divided into groups (patches) and a mosquito belonging to any one of n vector patches can take blood from any of m host patches. The condition for extinction or persistence of the infection involves the so-called basic reproductive rate for the m/n model R(m/n). If R(m/n)\(\leq 1\), the infection becomes extinct, whereas the number of infectives and susceptibles approaches constant positive levels in all patches if \(R(m/n)>1\). The basic reproductive rate for the m/n model can be estimated against the basic reproductive rate for the corresponding m/1, 1/1 and 1/m models. On the other hand each of the four R(m/n), R(m/1), R(1/1), R(1/m) is the product of two factors, one is the basic reproductive rate for the 1/1 model, the second is called heterogeneity factor and denoted by f(m/1), f(1/1), f(1/m), respectively. Lower and upper estimates for the heterogeneity factor are given. An accurate analysis of the mathematical model is made. The study of the stability of the 0 solution and the existence and the form of the eigenvalues of a suitable matrix leads to the main results about R(m/n).
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 4057346
zbMATH Keywords: epidemiology
zbMATH Keywords: mosquito-borne disease
zbMATH Keywords: extinction
zbMATH Keywords: persistence
zbMATH Keywords: basic reproductive rate
zbMATH Keywords: heterogeneity factor
zbMATH Keywords: stability
zbMATH Keywords: eigenvalues
Wikidata QID: Q44148947
reviewed by: S. Totaro
MaRDI profile type: Publication
full work available at URL: 0040-5809(88)90003-2
OpenAlex ID: W2088012843
cites work: Q5724331
cites work: Q3958316
cites work: A deterministic model for gonorrhea in a nonhomogeneous population
cites work: Heterogeneity in disease-transmission modeling
cites work: Non-negative matrices and Markov chains. 2nd ed
description: scientific article; zbMATH DE number 4057346