Mathematical Biosciences and Engineering, 2010, 7(2): 313-345. doi: 10.3934/mbe.2010.7.313.

Primary: 92-08, 92D30, 37M05; Secondary: 65L12, 92C60.

Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Vector control for the Chikungunya disease

1. CIRAD, Umr AMAP, Montpellier, F-34000
2. CIRAD, Umr PVBMT, Saint-Pierre, F-97410

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.
  Article Metrics

Keywords Chikungunya; numerical simulation.; differential equation; vector control; equilibrium; vector-borne disease; nonstandard finite difference method; basic reproduction number; global stability

Citation: Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences and Engineering, 2010, 7(2): 313-345. doi: 10.3934/mbe.2010.7.313


This article has been cited by

  • 1. Martial L. Ndeffo-Mbah, David P. Durham, Laura A. Skrip, Elaine O. Nsoesie, John S. Brownstein, Durland Fish, Alison P. Galvani, Evaluating the effectiveness of localized control strategies to curtail chikungunya, Scientific Reports, 2016, 6, 1, 10.1038/srep23997
  • 2. K. C. Patidar, Nonstandard finite difference methods: recent trends and further developments, Journal of Difference Equations and Applications, 2016, 22, 6, 817, 10.1080/10236198.2016.1144748
  • 3. Helena Sofia Rodrigues, M. Teresa T. Monteiro, Delfim F. M. Torres, Sensitivity Analysis in a Dengue Epidemiological Model, Conference Papers in Mathematics, 2013, 2013, 1, 10.1155/2013/721406
  • 4. Hammami Pachka, Tran Annelise, Kemp Alan, Tshikae Power, Kgori Patrick, Chevalier Véronique, Paweska Janusz, Jori Ferran, Rift Valley fever vector diversity and impact of meteorological and environmental factors on Culex pipiens dynamics in the Okavango Delta, Botswana, Parasites & Vectors, 2016, 9, 1, 10.1186/s13071-016-1712-1
  • 5. Yan Wang, Xianning Liu, Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays, Mathematics and Computers in Simulation, 2017, 138, 31, 10.1016/j.matcom.2016.12.011
  • 6. Alessandra Lo Presti, Eleonora Cella, Silvia Angeletti, Massimo Ciccozzi, Molecular epidemiology, evolution and phylogeny of Chikungunya virus: An updating review, Infection, Genetics and Evolution, 2016, 41, 270, 10.1016/j.meegid.2016.04.006
  • 7. Helena Sofia Rodrigues, M. Teresa T. Monteiro, Delfim F. M. Torres, Alan Zinober, Dengue disease, basic reproduction number and control, International Journal of Computer Mathematics, 2012, 89, 3, 334, 10.1080/00207160.2011.554540
  • 8. Louis Clément Gouagna, Jean-Sébastien Dehecq, Didier Fontenille, Yves Dumont, Sébastien Boyer, Seasonal variation in size estimates of Aedes albopictus population based on standard mark–release–recapture experiments in an urban area on Reunion Island, Acta Tropica, 2015, 143, 89, 10.1016/j.actatropica.2014.12.011
  • 9. Eminugroho Ratna Sari, Nur Insani, Dwi Lestari, The Preventive Control of a Dengue Disease Using Pontryagin Minimum Principal, Journal of Physics: Conference Series, 2017, 855, 012045, 10.1088/1742-6596/855/1/012045
  • 10. Carrie A. Manore, Richard S. Ostfeld, Folashade B. Agusto, Holly Gaff, Shannon L. LaDeau, Samuel V. Scarpino, Defining the Risk of Zika and Chikungunya Virus Transmission in Human Population Centers of the Eastern United States, PLOS Neglected Tropical Diseases, 2017, 11, 1, e0005255, 10.1371/journal.pntd.0005255
  • 11. Shangbing Ai, Jia Li, Junliang Lu, Mosquito-Stage-Structured Malaria Models and Their Global Dynamics, SIAM Journal on Applied Mathematics, 2012, 72, 4, 1213, 10.1137/110860318
  • 12. Annelise Tran, Grégory L'Ambert, Guillaume Lacour, Romain Benoît, Marie Demarchi, Myriam Cros, Priscilla Cailly, Mélaine Aubry-Kientz, Thomas Balenghien, Pauline Ezanno, A Rainfall- and Temperature-Driven Abundance Model for Aedes albopictus Populations, International Journal of Environmental Research and Public Health, 2013, 10, 5, 1698, 10.3390/ijerph10051698
  • 13. Derdei Bichara, Carlos Castillo-Chavez, Vector-borne diseases models with residence times – A Lagrangian perspective, Mathematical Biosciences, 2016, 281, 128, 10.1016/j.mbs.2016.09.006
  • 14. Helena Sofia Rodrigues, M. Teresa T. Monteiro, Delfim F.M. Torres, Vaccination models and optimal control strategies to dengue, Mathematical Biosciences, 2014, 247, 1, 10.1016/j.mbs.2013.10.006
  • 15. Lin Ling, Guirong Jiang, Tengfei Long, The dynamics of an SIS epidemic model with fixed-time birth pulses and state feedback pulse treatments, Applied Mathematical Modelling, 2015, 39, 18, 5579, 10.1016/j.apm.2015.01.022
  • 16. Claire Dufourd, Yves Dumont, Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control, Computers & Mathematics with Applications, 2013, 66, 9, 1695, 10.1016/j.camwa.2013.03.024
  • 17. Y. Dumont, J. Thuilliez, Human behaviors: A threat to mosquito control?, Mathematical Biosciences, 2016, 281, 9, 10.1016/j.mbs.2016.08.011
  • 18. Xinzhi Liu, Peter Stechlinski, , Infectious Disease Modeling, 2017, Chapter 6, 179, 10.1007/978-3-319-53208-0_6
  • 19. Joanna Waldock, Nastassya L. Chandra, Jos Lelieveld, Yiannis Proestos, Edwin Michael, George Christophides, Paul E. Parham, The role of environmental variables onAedes albopictusbiology and chikungunya epidemiology, Pathogens and Global Health, 2013, 107, 5, 224, 10.1179/2047773213Y.0000000100
  • 20. Folashade B. Agusto, Optimal control and cost-effectiveness analysis of a three age-structured transmission dynamics of chikungunya virus, Discrete and Continuous Dynamical Systems - Series B, 2016, 22, 3, 687, 10.3934/dcdsb.2017034
  • 21. Helena Sofia Rodrigues, M. Teresa T. Monteiro, Delfim F. M. Torres, Seasonality effects on dengue: basic reproduction number, sensitivity analysis and optimal control, Mathematical Methods in the Applied Sciences, 2016, 39, 16, 4671, 10.1002/mma.3319
  • 22. Irfan A. Rather, Hilal A. Parray, Jameel B. Lone, Woon K. Paek, Jeongheui Lim, Vivek K. Bajpai, Yong-Ha Park, Prevention and Control Strategies to Counter Dengue Virus Infection, Frontiers in Cellular and Infection Microbiology, 2017, 7, 10.3389/fcimb.2017.00336
  • 23. K.F. Gurski, A simple construction of nonstandard finite-difference schemes for small nonlinear systems applied to SIR models, Computers & Mathematics with Applications, 2013, 66, 11, 2165, 10.1016/j.camwa.2013.06.034
  • 24. Grant D. Brown, Aaron T. Porter, Jacob J. Oleson, Jessica A. Hinman, Approximate Bayesian computation for spatial SEIR(S) epidemic models, Spatial and Spatio-temporal Epidemiology, 2018, 24, 27, 10.1016/j.sste.2017.11.001
  • 25. Yu-Han Kao, Marisa C. Eisenberg, Practical unidentifiability of a simple vector-borne disease model: Implications for parameter estimation and intervention assessment, Epidemics, 2018, 10.1016/j.epidem.2018.05.010
  • 26. Marguerite Robinson, Anne Conan, Veasna Duong, Sowath Ly, Chantha Ngan, Philippe Buchy, Arnaud Tarantola, Xavier Rodó, Michael J. Turell, A Model for a Chikungunya Outbreak in a Rural Cambodian Setting: Implications for Disease Control in Uninfected Areas, PLoS Neglected Tropical Diseases, 2014, 8, 9, e3120, 10.1371/journal.pntd.0003120
  • 27. Laith Yakob, Archie C. A. Clements, Michael George Roberts, A Mathematical Model of Chikungunya Dynamics and Control: The Major Epidemic on Réunion Island, PLoS ONE, 2013, 8, 3, e57448, 10.1371/journal.pone.0057448
  • 28. D. Moulay, M.A. Aziz-Alaoui, M. Cadivel, The chikungunya disease: Modeling, vector and transmission global dynamics, Mathematical Biosciences, 2011, 229, 1, 50, 10.1016/j.mbs.2010.10.008
  • 29. Clelia F. Oliva, Maxime Jacquet, Jeremie Gilles, Guy Lemperiere, Pierre-Olivier Maquart, Serge Quilici, François Schooneman, Marc J. B. Vreysen, Sebastien Boyer, Basil Brooke, The Sterile Insect Technique for Controlling Populations of Aedes albopictus (Diptera: Culicidae) on Reunion Island: Mating Vigour of Sterilized Males, PLoS ONE, 2012, 7, 11, e49414, 10.1371/journal.pone.0049414
  • 30. HELENA SOFIA RODRIGUES, M. TERESA T. MONTEIRO, DELFIM F. M. TORRES, Dengue in Cape Verde: Vector Control and Vaccination, Mathematical Population Studies, 2013, 20, 4, 208, 10.1080/08898480.2013.831711
  • 31. Xinzhi Liu, Peter Stechlinski, , Infectious Disease Modeling, 2017, Chapter 4, 83, 10.1007/978-3-319-53208-0_4
  • 32. Rebecca C. Christofferson, Daniel M. Chisenhall, Helen J. Wearing, Christopher N. Mores, Lisa FP. Ng, Chikungunya Viral Fitness Measures within the Vector and Subsequent Transmission Potential, PLoS ONE, 2014, 9, 10, e110538, 10.1371/journal.pone.0110538
  • 33. Folashade B. Agusto, Shamise Easley, Kenneth Freeman, Madison Thomas, Mathematical Model of Three Age-Structured Transmission Dynamics of Chikungunya Virus, Computational and Mathematical Methods in Medicine, 2016, 2016, 1, 10.1155/2016/4320514
  • 34. Djamila Moulay, Yoann Pigné, A metapopulation model for chikungunya including populations mobility on a large-scale network, Journal of Theoretical Biology, 2013, 318, 129, 10.1016/j.jtbi.2012.11.008
  • 35. Shousheng Zhu, Nathalie Verdière, Lilianne Denis-Vidal, Djalil Kateb, Identifiability analysis and parameter estimation of a chikungunya model in a spatially continuous domain, Ecological Complexity, 2018, 34, 80, 10.1016/j.ecocom.2017.12.004
  • 36. Djamila Moulay, M. A. Aziz-Alaoui, Hee-Dae Kwon, Optimal control of chikungunya disease: Larvae reduction, treatment and prevention, Mathematical Biosciences and Engineering, 2012, 9, 2, 369, 10.3934/mbe.2012.9.369
  • 37. Thomas Sochacki, Frédéric Jourdain, Yvon Perrin, Harold Noel, Marie-Claire Paty, Henriette de Valk, Alexandra Septfons, Frédéric Simard, Didier Fontenille, Benjamin Roche, Imported chikungunya cases in an area newly colonised byAedes albopictus: mathematical assessment of the best public health strategy, Eurosurveillance, 2016, 21, 18, 10.2807/1560-7917.ES.2016.21.18.30221
  • 38. Hamadjam Abboubakar, Jean Claude Kamgang, Leontine Nkague Nkamba, Daniel Tieudjo, Bifurcation thresholds and optimal control in transmission dynamics of arboviral diseases, Journal of Mathematical Biology, 2018, 76, 1-2, 379, 10.1007/s00285-017-1146-1
  • 39. Xinzhi Liu, Peter Stechlinski, Application of control strategies to a seasonal model of chikungunya disease, Applied Mathematical Modelling, 2015, 39, 12, 3194, 10.1016/j.apm.2014.10.035
  • 40. Tridip Sardar, Sourav Kumar Sasmal, Joydev Chattopadhyay, Estimating dengue type reproduction numbers for two provinces of Sri Lanka during the period 2013–14, Virulence, 2016, 7, 2, 187, 10.1080/21505594.2015.1096470
  • 41. Ahmed M. Elaiw, Taofeek O. Alade, Saud M. Alsulami, Analysis of within-host CHIKV dynamics models with general incidence rate, International Journal of Biomathematics, 2018, 1850062, 10.1142/S1793524518500626
  • 42. Marcos Amaku, Francisco Antonio Bezerra Coutinho, Silvia Martorano Raimundo, Luis Fernandez Lopez, Marcelo Nascimento Burattini, Eduardo Massad, A Comparative Analysis of the Relative Efficacy of Vector-Control Strategies Against Dengue Fever, Bulletin of Mathematical Biology, 2014, 76, 3, 697, 10.1007/s11538-014-9939-5
  • 44. M. Chapwanya, Y. Dumont, On crop vector-borne diseases. Impact of virus lifespan and contact rate on the traveling-wave speed of infective fronts, Ecological Complexity, 2018, 34, 119, 10.1016/j.ecocom.2017.08.002
  • 45. Hamadjam Abboubakar, Jean Claude Kamgang, Daniel Tieudjo, Backward bifurcation and control in transmission dynamics of arboviral diseases, Mathematical Biosciences, 2016, 278, 100, 10.1016/j.mbs.2016.06.002
  • 46. Xinzhi Liu, Peter Stechlinski, , Infectious Disease Modeling, 2017, Chapter 7, 227, 10.1007/978-3-319-53208-0_7
  • 47. Jing Chen, John C. Beier, Robert Stephen Cantrell, Chris Cosner, Douglas O. Fuller, Yongtao Guan, Guoyan Zhang, Shigui Ruan, Modeling the Importation and Local Transmission of Vector-Borne Diseases in Florida: The Case of Zika Outbreak in 2016, Journal of Theoretical Biology, 2018, 10.1016/j.jtbi.2018.07.026
  • 48. Ahmed M. Elaiw, Taofeek O. Alade, Saud M. Alsulami, Analysis of latent CHIKV dynamics models with general incidence rate and time delays, Journal of Biological Dynamics, 2018, 12, 1, 700, 10.1080/17513758.2018.1503349
  • 49. José V.J. Silva, Louisa F. Ludwig-Begall, Edmilson F. de Oliveira-Filho, Renato A.S. Oliveira, Ricardo Durães-Carvalho, Thaísa R.R. Lopes, Daisy E.A. Silva, Laura H.V.G. Gil, A scoping review of Chikungunya virus infection: epidemiology, clinical characteristics, viral co-circulation complications, and control, Acta Tropica, 2018, 10.1016/j.actatropica.2018.09.003
  • 50. Ahmed M. Elaiw, Taofeek O. Alade, Saud M. Alsulami, Global dynamics of delayed CHIKV infection model with multitarget cells, Journal of Applied Mathematics and Computing, 2018, 10.1007/s12190-018-1215-7
  • 51. Usman A. Danbaba, Salisu M. Garba, Modeling the transmission dynamics of Zika with sterile insect technique, Mathematical Methods in the Applied Sciences, 2018, 10.1002/mma.5336
  • 52. A. M. Elaiw, S. E. Almalki, A. D. Hobiny, Stability of CHIKV infection models with CHIKV-monocyte and infected-monocyte saturated incidences, AIP Advances, 2019, 9, 2, 025308, 10.1063/1.5085804
  • 53. Sylvestre Aureliano Carvalho, Stella Olivia da Silva, Iraziet da Cunha Charret, Mathematical modeling of dengue epidemic: control methods and vaccination strategies, Theory in Biosciences, 2019, 10.1007/s12064-019-00273-7
  • 54. Catherine Hierlihy, Lisa Waddell, Ian Young, Judy Greig, Tricia Corrin, Mariola Mascarenhas, Abdallah M. Samy, A systematic review of individual and community mitigation measures for prevention and control of chikungunya virus, PLOS ONE, 2019, 14, 2, e0212054, 10.1371/journal.pone.0212054
  • 55. Anne Fischer, Kurt Chudej, Hans Josef Pesch, Optimal vaccination and control strategies against dengue, Mathematical Methods in the Applied Sciences, 2019, 10.1002/mma.5594
  • 56. Helena Sofia Rodrigues, M. Teresa T. Monteiro, Delfim F. M. Torres, Ana Clara Silva, Carla Sousa, Cláudia Conceição, , Dynamics, Games and Science, 2015, Chapter 32, 593, 10.1007/978-3-319-16118-1_32
  • 57. A. M. Elaiw, S. E. Almalki, A. D. Hobiny, Global properties of saturated chikungunya virus dynamics models with cellular infection and delays, Advances in Difference Equations, 2019, 2019, 1, 10.1186/s13662-019-2409-5
  • 58. Xianning Liu, Yan Wang, Xiao-Qiang Zhao, Dynamics of a climate-based periodic Chikungunya model with incubation period, Applied Mathematical Modelling, 2019, 10.1016/j.apm.2019.11.038
  • 59. Ahmed M. Elaiw, Sami E. Almalki, A.D. Hobiny, Stability of delayed CHIKV dynamics model with cell-to-cell transmission, Journal of Intelligent & Fuzzy Systems, 2019, 1, 10.3233/JIFS-179531
  • 60. Ying Liu, Kate Lillepold, Jan C. Semenza, Yesim Tozan, Mikkel B.M. Quam, Joacim Rocklöv, Reviewing estimates of the basic reproduction number for dengue, Zika and chikungunya across global climate zones, Environmental Research, 2020, 182, 109114, 10.1016/j.envres.2020.109114
  • 61. Annelise Tran, Morgan Mangeas, Marie Demarchi, Emmanuel Roux, Pascal Degenne, Marion Haramboure, Gilbert Le Goff, David Damiens, Louis-Clément Gouagna, Vincent Herbreteau, Jean-Sébastien Dehecq, Suzanne Touzeau, Complementarity of empirical and process-based approaches to modelling mosquito population dynamics with Aedes albopictus as an example—Application to the development of an operational mapping tool of vector populations, PLOS ONE, 2020, 15, 1, e0227407, 10.1371/journal.pone.0227407
  • 62. Marion Haramboure, Pierrick Labbé, Thierry Baldet, David Damiens, Louis Clément Gouagna, Jérémy Bouyer, Annelise Tran, Modelling the control of Aedes albopictus mosquitoes based on sterile males release techniques in a tropical environment, Ecological Modelling, 2020, 424, 109002, 10.1016/j.ecolmodel.2020.109002
  • 63. Roumen Anguelov, Yves Dumont, Ivric Valaire Yatat Djeumen, Sustainable vector/pest control using the permanent sterile insect technique, Mathematical Methods in the Applied Sciences, 2020, 10.1002/mma.6385
  • 64. Yanyuan Xing, Zhiming Guo, Jian Liu, Backward bifurcation in a malaria transmission model, Journal of Biological Dynamics, 2020, 14, 1, 368, 10.1080/17513758.2020.1771443
  • 65. Xianning Liu, Yan Wang, Xiao-Qiang Zhao, Dynamics of a periodic Chikungunya model with temperature and rainfall effects, Communications in Nonlinear Science and Numerical Simulation, 2020, 105409, 10.1016/j.cnsns.2020.105409
  • 66. UA Danbaba, SM Garba, Stability Analysis and Optimal Control for Yellow Fever Model with Vertical Transmission, International Journal of Applied and Computational Mathematics, 2020, 6, 4, 10.1007/s40819-020-00860-z
  • 67. Taofeek O. Alade, Ahmed M. Elaiw, Saud M. Alsulami, Stability dynamics of a delayed generalized Chikungunya virus infection model, Journal of Applied Mathematics and Computing, 2020, 10.1007/s12190-020-01405-9
  • 68. Najmul Haider, Francesco Vairo, Giuseppe Ippolito, Alimuddin Zumla, Richard A. Kock, Basic Reproduction Number of Chikungunya Virus Transmitted by Aedes Mosquitoes, Emerging Infectious Diseases, 2020, 26, 10, 10.3201/eid2610.190957

Reader Comments

your name: *   your email: *  

Copyright Info: 2010, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved