A mathematical model with delays for schistosomiasis japonicum transmission
type: Item
instance of: scholarly article
title: A mathematical model with delays for schistosomiasis japonicum transmission
zbMATH Open document ID: 1213.34103
author: Yu Yang
author: Dongmei Xiao
published in: Chinese Annals of Mathematics. Series B
publication date: 2010-11-17T00:00:00Z
review text: The authors incorporate the incubation period into \textit{A. D. Barbour}'s schistosomiasis model [Am. J. Trop. Med. Hyg. 55, (5 Suppl.) 135--143 (1996)]. The model consists of four delay differential equations. The basic reproductive number \(R_0\) is given. They show that the disease free equilibrium \(E_0\) is globally stable if \(R_0<1\). If \(R_0>1\), the endemic equilibrium \(E_1\) exists, and it is globally stable if there are no delays. For two other cases with nonzero delays, they show \(E_1\) undergoes Hopf bifurcation and a periodic orbit emerges. Their results suggest that prepatent periods in infection affect the prevalence of schistosomiasis, and it is an effective strategy schistosomiasis control to extend the prepatent period for infected definitive hosts by drug treatment (or extend the prepatent period for infected intermediate snails by lower water temperature).
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34K21
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 5816608
zbMATH Keywords: schistosomiasis model
zbMATH Keywords: delay differential equations
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: stability
reviewed by: Peixuan Weng
MaRDI profile type: Publication
full work available at URL: s11401-010-0596-1
OpenAlex ID: W2067257199
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DOI: 10.1007/S11401-010-0596-1
description: scientific article; zbMATH DE number 5816608