American Institute of Mathematical Sciences

Advanced
2010, 7(2): 313-345. doi: 10.3934/mbe.2010.7.313

Vector control for the Chikungunya disease

Yves Dumont 1, and  Frederic Chiroleu 2,

1. 

CIRAD, Umr AMAP, Montpellier, F-34000, France
2. 

CIRAD, Umr PVBMT, Saint-Pierre, F-97410, France

Received  June 2009 Revised  January 2010 Published  April 2010

We previously proposed a compartmental model to explain the outbreak of Chikungunya disease in Réunion Island, a French territory in Indian Ocean, and other countries in 2005 and possible links with the explosive epidemic of 2006. In the present paper, we asked whether it would have been possible to contain or stop the epidemic of 2006 through appropriate mosquito control tools. Based on new results on the Chikungunya virus, its impact on mosquito life-span, and several experiments done by health authorities, we studied several types of control tools used in 2006 to contain the epidemic. We present an analysis of the model, and we develop a new nonstandard finite difference scheme to provide several simulations with and without mosquito control. Our preliminary study shows that an early use of a combination of massive spraying and mechanical control (like the destruction of breeding sites) can be efficient, to stop or contain the propagation of Chikungunya infection, with a low impact on the environment.
Keywords: Chikungunya, numerical simulation., differential equation, vector control, equilibrium, vector-borne disease, nonstandard finite difference method, basic reproduction number, global stability.
Mathematics Subject Classification: Primary: 92-08, 92D30, 37M05; Secondary: 65L12, 92C6.
Citation: Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313-345. doi: 10.3934/mbe.2010.7.313
[1]

Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565
[2]

Kbenesh Blayneh, Yanzhao Cao, Hee-Dae Kwon. Optimal control of vector-borne diseases: Treatment and prevention. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 587-611. doi: 10.3934/dcdsb.2009.11.587
[3]

Xia Wang, Yuming Chen. An age-structured vector-borne disease model with horizontal transmission in the host. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1099-1116. doi: 10.3934/mbe.2018049
[4]

Xinli Hu, Yansheng Liu, Jianhong Wu. Culling structured hosts to eradicate vector-borne diseases. Mathematical Biosciences & Engineering, 2009, 6 (2) : 301-319. doi: 10.3934/mbe.2009.6.301
[5]

Derdei Mahamat Bichara. Effects of migration on vector-borne diseases with forward and backward stage progression. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 6297-6323. doi: 10.3934/dcdsb.2019140
[6]

A. K. Misra, Anupama Sharma, Jia Li. A mathematical model for control of vector borne diseases through media campaigns. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1909-1927. doi: 10.3934/dcdsb.2013.18.1909
[7]

Shangbing Ai. Global stability of equilibria in a tick-borne disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 567-572. doi: 10.3934/mbe.2007.4.567
[8]

Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37
[9]

Harald Fripertinger. The number of invariant subspaces under a linear operator on finite vector spaces. Advances in Mathematics of Communications, 2011, 5 (2) : 407-416. doi: 10.3934/amc.2011.5.407
[10]

Xiao-Bing Li, Xian-Jun Long, Zhi Lin. Stability of solution mapping for parametric symmetric vector equilibrium problems. Journal of Industrial & Management Optimization, 2015, 11 (2) : 661-671. doi: 10.3934/jimo.2015.11.661
[11]

Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6771-6782. doi: 10.3934/dcdsb.2019166
[12]

Djamila Moulay, M. A. Aziz-Alaoui, Hee-Dae Kwon. Optimal control of chikungunya disease: Larvae reduction, treatment and prevention. Mathematical Biosciences & Engineering, 2012, 9 (2) : 369-392. doi: 10.3934/mbe.2012.9.369
[13]

Anatoli F. Ivanov, Sergei Trofimchuk. Periodic solutions and their stability of a differential-difference equation. Conference Publications, 2009, 2009 (Special) : 385-393. doi: 10.3934/proc.2009.2009.385
[14]

Kenji Kimura, Yeong-Cheng Liou, David S. Shyu, Jen-Chih Yao. Simultaneous system of vector equilibrium problems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 161-174. doi: 10.3934/jimo.2009.5.161
[15]

Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595
[16]

Mary P. Hebert, Linda J. S. Allen. Disease outbreaks in plant-vector-virus models with vector aggregation and dispersal. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2169-2191. doi: 10.3934/dcdsb.2016042
[17]

Ronald E. Mickens. A nonstandard finite difference scheme for the drift-diffusion system. Conference Publications, 2009, 2009 (Special) : 558-563. doi: 10.3934/proc.2009.2009.558
[18]

Roumen Anguelov, Jean M.-S. Lubuma, Meir Shillor. Dynamically consistent nonstandard finite difference schemes for continuous dynamical systems. Conference Publications, 2009, 2009 (Special) : 34-43. doi: 10.3934/proc.2009.2009.34
[19]

Luciano Abadías, Carlos Lizama, Pedro J. Miana, M. Pilar Velasco. On well-posedness of vector-valued fractional differential-difference equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2679-2708. doi: 10.3934/dcds.2019112
[20]

Gerardo 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. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1455-1474. doi: 10.3934/mbe.2013.10.1455

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (24)
  • HTML views (0)
  • Cited by (41)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences