### Mathematical Biosciences and Engineering

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

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

• 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.

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

### Related Papers:

• 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.

 [1] [ D. L. Chao,D. T. Dimitrov, Seasonality and the effectiveness of mass vaccination, Math Biosci Eng, 13 (2016): 249-259. [2] [ G. Chowell,R. Fuentes,A. Olea,X. Aguilera,H. Nesse,J. M. Hyman, The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile, Math Biosci Eng, 10 (2013): 1455-1474. [3] [ L. Esteva,H. M. Yang, Mathematical model to acess the control of aedes aegypti mosquitoes by sterile insect technique, Math. Biosci, 198 (2005): 132-147. [4] [ T. P. O. Evans,S. R. Bishop, A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito aedes aegypti, Math. Biosci, 254 (2014): 6-27. [5] [ Z. Feng,J. X. Velasco-Hernandez, Competitive exclusion in a vector-host model for the dengue fever, J. Math. Biol, 35 (1997): 523-544. [6] [ D. J. Gubler, Dengue and dengue hemorrhagic fever: Its history and resurgence as a global public health problem, (eds. D. J. Gubler, G. Kuno), Dengue and Dengue Hemorrhagic Fever, New York: CAB International, null (1997): 1-22. [7] [ D. J. Gubler, Epidemic dengue/dengue hemorrhagic fever as a public health, social and economic problem in the 21st century, Trends Microbiol, 10 (2002): 100-103. [8] [ R.-W. S. Hendron,M. B. Bonsall, The interplay of vaccination and vector control on small dengue networks, J. Theor. Biol, 407 (2016): 349-361. [9] [ H. Hughes,N. F. Britton, Modelling the use of wolbachia to control dengue fever transmission, Bull Math Biol, 75 (2013): 796-818. [10] [ https://www.theguardian.com/world/2015/may/24/sterile-mosquitoes-released-in/chinato-fight-dengue-fever. [11] [ http://www.iflscience.com/health-and-medicine/gm-mosquitoes-set-be-released-brazil-combat-dengue-0/. [12] [ J. H. Jones, Notes on $R_{0}$ Department of Anthropological Sciences, Stanford University, 2007. [13] [ G. Knerer,C. S. M. Currie,S. C. Brailsford, Impact of combined vector-control and vaccination strategies on transmission dynamics of dengue fever: A model-based analysis, Health Care Manag Sci, 18 (2015): 205-217. [14] [ E. F. Knipling, Possibilities of insect control or eradication through the use of sexually sterile males, J. Econ. Entomol, 48 (1955): 459-462. [15] [ E. F. Knipling, The Basic Principles of Insect Population and Suppression and Management USDA handbook. Washington, D. C. , USDA, 1979. [16] [ E. F. Knipling, Sterile insect technique as a screwworm control measure: The concept and its development, Misc. Pub. Entomol. Soc. Am, 62 (1985): 4-7. [17] [ J. P. LaSalle, The Stability of Dynamical Systems Regional Conf. Series Appl. Math. , 25, SIAM, Philadelphia, 1976. [18] [ A. Mishra,S. Gakkhar, The effects of awareness and vector control on two strains dengue dynamics, Appl. Math. Comput, 246 (2014): 159-167. [19] [ A. M. P. Montoya,A. M. Loaiza,O. T. Gerard, Simulation model for dengue fever transmission with integrated control, Appl. Math. Sci, 10 (2016): 175-185. [20] [ D. Moulay,M. A. Aziz-Alaoui,Hee-Dae Kwon, Optimal control of chikungunya disease: Larvae reduction, treatment and prevention, Math Biosci Eng, 9 (2012): 369-392. [21] [ D. Moulay,M. A. Aziz-Alaoui,M. Cadivel, The chikungunya disease: Modeling, vector and transmission global dynamics, Math. Biosci, 229 (2011): 50-63. [22] [ L. Perko, Differential Equations and Dynamical Systems Texts in Applied Mathematics, 7. Springer-Verlag, New York, 1991. [23] [ H. S. Rodrigues,M. T. T. Monteiro,D. F. M. Torres, Vaccination models and optimal control strategies to dengue, Math. Biosci, 247 (2014): 1-12. [24] [ S. Syafruddin,M. S. M. Noorani, SEIR model for transmission of dengue fever in Selangor Malaysia, International Journal of Modern Physics: Conference Series, 9 (2012): 380-389. [25] [ R. C. A. Thomé,H. M. Yang,L. Esteva, Optimal control of aedes aegypti mosquitoes by the sterile insect technique and insecticide, Math. Biosci, 223 (2010): 12-23. [26] [ World Health Organization, Dengue: Guidelines for Diagnosis, Treatment, Prevention and Control, Geneva: World Health Organization and the Special Programme for Research and Training in Tropical Diseases, 2009. [27] [ http://www.cdc.gov/dengue/epidemiology.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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