Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes

The release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes...

Full description

Saved in:
Bibliographic Details
Main Authors: Xiongwei Liu, Junjun Xu, Xiao Wang, Lizhi Cheng
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/378968
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832566236703096832
author Xiongwei Liu
Junjun Xu
Xiao Wang
Lizhi Cheng
author_facet Xiongwei Liu
Junjun Xu
Xiao Wang
Lizhi Cheng
author_sort Xiongwei Liu
collection DOAJ
description The release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number R0 is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. By theoretical analysis of the dynamic behaviors of the models and numerical simulations, it is verified that malaria can be effectively controlled by the opportune release of transgenic mosquitoes; that is, when R0≤1, malaria will disappear; when R0>1, malaria will become an endemic disease in the target field.
format Article
id doaj-art-dc4e5cd947c644959e2e7123dd8a26b9
institution Kabale University
issn 1085-3375
1687-0409
language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-dc4e5cd947c644959e2e7123dd8a26b92025-02-03T01:04:52ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/378968378968Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic MosquitoesXiongwei Liu0Junjun Xu1Xiao Wang2Lizhi Cheng3College of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaXichang Satellite Launch Center, Xichang, Sichuan 615000, ChinaCollege of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaCollege of Science, National University of Defense Technology, Changsha, Hunan 410073, ChinaThe release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number R0 is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. By theoretical analysis of the dynamic behaviors of the models and numerical simulations, it is verified that malaria can be effectively controlled by the opportune release of transgenic mosquitoes; that is, when R0≤1, malaria will disappear; when R0>1, malaria will become an endemic disease in the target field.http://dx.doi.org/10.1155/2014/378968
spellingShingle Xiongwei Liu
Junjun Xu
Xiao Wang
Lizhi Cheng
Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes
Abstract and Applied Analysis
title Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes
title_full Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes
title_fullStr Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes
title_full_unstemmed Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes
title_short Behaviors and Numerical Simulations of Malaria Dynamic Models with Transgenic Mosquitoes
title_sort behaviors and numerical simulations of malaria dynamic models with transgenic mosquitoes
url http://dx.doi.org/10.1155/2014/378968
work_keys_str_mv AT xiongweiliu behaviorsandnumericalsimulationsofmalariadynamicmodelswithtransgenicmosquitoes
AT junjunxu behaviorsandnumericalsimulationsofmalariadynamicmodelswithtransgenicmosquitoes
AT xiaowang behaviorsandnumericalsimulationsofmalariadynamicmodelswithtransgenicmosquitoes
AT lizhicheng behaviorsandnumericalsimulationsofmalariadynamicmodelswithtransgenicmosquitoes