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

Arti Mishra; Benjamin Ambrosio; Sunita Gakkhar; M. A. Aziz-Alaoui; Arti Mishra; Benjamin Ambrosio; Sunita Gakkhar; M. A. Aziz-Alaoui

doi:10.3934/mbe.2018020

Mathematical Biosciences and Engineering

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

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

1.
Department of Mathematics, Indian Institute of Technology Roorkee, Uttarakhand 247667, India
2.
Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France

Received: 15 December 2016 Accepted: 31 March 2017 Published: 01 April 2018
MSC : Primary: 97M10, 37C75

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.
- Dengue,
- network model,
- basic reproduction number,
- stability,
- sterile insect technique
Citation: Arti Mishra, Benjamin Ambrosio, Sunita Gakkhar, M. A. Aziz-Alaoui. A network model for control of dengue epidemic using sterile insect technique[J]. Mathematical Biosciences and Engineering, 2018, 15(2): 441-460. doi: 10.3934/mbe.2018020

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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.

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