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Mathematical Biosciences and Engineering (MBE)
 

A network model for control of dengue epidemic using sterile insect technique

Pages: 441 - 460, Volume 15, Issue 2, April 2018      doi:10.3934/mbe.2018020

 
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Arti Mishra - Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand 247667, India (email)
Benjamin Ambrosio - Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France (email)
Sunita Gakkhar - Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand 247667, India (email)
M. A. Aziz-Alaoui - Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France (email)

Abstract: In this paper, a network model has been proposed to control dengue disease transmission considering host-vector dynamics in $n$ patches. The control of mosquitoes is performed by SIT. In SIT, the male insects are sterilized in the laboratory and released into the environment to control the number of offsprings. The basic reproduction number has been computed. The existence and stability of various states have been discussed. The bifurcation diagram has been plotted to show the existence and stability regions of disease-free and endemic states for an isolated patch. The critical level of sterile male mosquitoes has been obtained for the control of disease. The basic reproduction number for $n$ patch network model has been computed. It is evident from numerical simulations that SIT control in one patch may control the disease in the network having two/three patches with suitable coupling among them.

Keywords:  Dengue, network model, basic reproduction number, stability, sterile insect technique.
Mathematics Subject Classification:  Primary: 97M10, 37C75.

Received: December 2016;      Accepted: March 2017;      Available Online: June 2017.

 References