Mathematical Biosciences and Engineering (MBE)

Optimal control of chikungunya disease: Larvae reduction, treatment and prevention
Pages: 369 - 392, Issue 2, April 2012

doi:10.3934/mbe.2012.9.369      Abstract        References        Full text (499.3K)           Related Articles

Djamila Moulay - LMAH, Université du Havre, 25 rue Philippe Lebon, BP540, 76058 Le Havre Cedex, France (email)
M. A. Aziz-Alaoui - LMAH, Université du Havre, 25 rue Philippe Lebon, BP540, 76058 Le Havre Cedex, France (email)
Hee-Dae Kwon - Department of Mathematics, Inha University, Incheon, 402-751, South Korea (email)

1 B. M. Adams, H. T. Banks, M. Davidian, H.-D. Kwon, H. T. Tran, S. N. Wynne and E. S. Rosenberg, HIV dynamics: Modeling, data analysis, and optimal treatment protocols, J. Comput. Appl. Math., 184 (2005), 10-49.       
2 B. M. Adams, H. T. Banks, H.-D. Kwon and H. T. Tran, Dynamic multidrug therapies for HIV: Optimal and STI control approaches, Mathematical Biosciences and Engineering, 1 (2004), 223-241.       
3 J. Adhami and P. Reiter, Introduction and establishment of Aedes (Stegomyia) albopictus skuse (diptera : Culicidae) in Albania, American Mosquito Control Association, 14 (1998), 340-343.
4 N. Alphey, M. B. Bonsall and L. Alphey, Modeling resistance to genetic control of insects, Journal of Theoretical Biology, 270 (2011), 42-55.
5 Be dry with mosquitoes, 2011. Available from: http://www.albopictus.eid-med.org/.
6 N. Bacaër, Approximation of the basic reproduction number $R_0$ for vector-borne diseases with a periodic vector population, Bulletin of Mathematical Biology, 69 (2007), 1067-1091.       
7 M. Q. Benedict, R. S. Levine, W. A. Hawley and L. P. Lounibos, Spread of the tiger: Global risk of invasion by the mosquito Aedes albopictus, Vector Borne and Zoonotic Diseases, 7 (2007), 76-85.
8 K. Blayneh, Y. Cao and H.-D. Kwon, Optimal control of vector-borne disease: Treatment and prevention, Discrete and Continuous Dynamical Systems Series B, 11 (2009), 587-611.       
9 C. Cosner, J. Beier, R. Cantrell, D. Impoinvil, L. Kapitanski, M. Potts, A. Troyo and S. Ruan, The effects of human movement on the persistence of vector-borne diseases, Journal of Theoretical Biology, 258 (2009), 550-560.
10 N. Curcó, N. Gimènez, M. Serra, A. Ripoll, M. García and P. Vives, Asian tiger mosquito bites: Perception of the affected population after Aedes albopictus became established in Spain, Actas Dermo-Sifiliogràficas (English Edition), 99 (2008), 708-713.
11 T. Das, M. C. Jaffar-Bandjee, J. J. Hoarau, P. K. Trotot, M. Denizot, G. Lee-Pat-Yuen, R. Sahoo, P. Guiraud, D. Ramful, S. Robin, J. L. Alessandri, B. A. Gauzere and P. Gasque, Chikungunya fever: CNS infection and pathologies of a re-emerging arbovirus, Progress in Neurobiology, 91 (2010), 121-129,
12 H. Delatte, G. Gimonneau, A. Triboire and D.Fontenille, Influence of temperature on immature development, survival, longevity, fecundity, and gonotrophic cycles of Aedes albopictus, vector of chikungunya and dengue in the Indian Ocean, Journal of Medical Entomology, 46 (2009), 33-41.
13 H. Delatte, C. Paupy, J. S. Dehecq, J. Thiria, A. B. Failloux and D. Fontenille, Aedes albopictus, vector of chikungunya and dengue viruses in reunion island: Biology and control, Parasite, 15 (2008), 3-13.
14 E. Depoortere, S. Salmaso, M. Pompa, P. Guglielmetti and D. Coulombier, Chikungunya in Europe, The Lancet, 371 (2008), 723-723.
15 M. Diallo, J. Thonnon, M. Traore-Lamizana and D. Fontenille, Vectors of chikungunya virus in Senegal: Current data and transmission cycles, The American Journal of Tropical Medicine and Hygiene, 60 (1999), 281-286.
16 O. Diekmann and J .A. P. Heesterbeek, "Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation," Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2000.       
17 P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.       
18 M. Dubrulle, L. Mousson, S. Moutailler, M. Vazeille and A. B. Failloux, Chikungunya virus and Aedes mosquitoes: Saliva is infectious as soon as two days after oral infection, PLoS ONE, 4 (2009), e5895.
19 Y. Dumont and F. Chiroleu, Vector control for the chikungunya disease, Mathematical Biosciences and Engineering, 7 (2010), 313-345.       
20 Y. Dumont, F. Chiroleu and C. Domerg, On a temporal model for the chikungunya disease: Modeling, theory and numerics, Mathematical Biosciences, 213 (2008), 80-91.       
21 M. Enserink, Epidemiology: Tropical disease follows mosquitoes to Europe, Science, 317 (2007), 1485a.
22 L. Esteva and C. Vargas, A model for dengue disease with variable human population, Journal of Mathematical Biology, 38 (1999), 220-240.       
23 W. H. Fleming and R. W. Rishel, "Deterministic and Stochastic Optimal Control," Applications of Mathematics, No. 1, Springer-Verlag, Berlin-New York, 1975.       
24 P. J. Gullan and P. Cranston, "The Insects: An Outline of Entomology," 4th edition, Wiley-Blackwell, 2010.
25 M. G. Guzman and G. Kouri, Dengue and dengue hemorrhagic fever in the Americas: Lessons and challenges, Journal of Clinical Virology, 27 (2003), 1-13.
26 W. A. Hawley, The biology of Aedes albopictus, J. Am. Mosq. Control Assoc. Suppl., 1 (1988), 1-39.
27 H. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653.       
28 E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems Series B, 2 (2002), 473-482.       
29 K. Laras, N. C. Sukri, R. P. Larasati, M. J. Bangs, R. Kosim, Djauzi, T. Wandra, J. Master, H. Kosasih, S. Hartati, C. Beckett, E. R. Sedyaningsih, H. J. Beecham III and A. L. Corwin, Tracking the re-emergence of epidemic chikungunya virus in Indonesia, Transactions of the Royal Society of Tropical Medicine and Hygiene, 99 (2005), 128-141.
30 D. L. Lukes, "Differential Equations. Classical to Controlled," Mathematics in Science and Engineering, 162, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1982.       
31 W. H. R. Lumdsen, An epidemic of virus disease in Southern Province, Tanganyika territory, in 1952-1953. II. General description and epidemiology, Transactions of the Royal Society of Tropical Medicine and Hygiene, 49 (1955), 23-57.
32 C. J. Mitchell, Geographic spread of Aedes albopictus and potential for involvement in arbovirus cycles in the Mediterranean basin, Journal of Vector Ecology, 20 (1995), 44-58.
33 D. Moulay, M. A. Aziz-Alaoui and M. Cadivel, The chikungunya disease: Modeling, vector and transmission global dynamics, Mathematical Biosciences, 229 (2011), 50-63.       
34 C. Paupy, H. Delatte, L. Bagny, V. Corbel and D. Fontenille, Aedes albopictus, an arbovirus vector: From the darkness to the light, Microbes and Infection, 11 (2009), 1177-1185.
35 G. Pialoux, B. A. Gaüzère and M. Strobel, Infection à virus chikungunya: Revue générale par temps d'épidémie, Médecine et Maladies Infectieuses, 36 (2006), 253-263.
36 L. Pontryagin, V. Boltyanskii, R. Gamkrelidze and E. Mishchenko, "The Mathematical Theory of Optimal Processes," A Pergamon Press Book, The Macmillan Co., New York, 1964.       
37 S. Rajapakse, C. Rodrigo and A. Rajapakse, Atypical manifestations of chikungunya infection, Transactions of the Royal Society of Tropical Medicine and Hygiene, 104 (2010), 89-96.
38 G. Rezza, L. Nicoletti, R. Angelini, R. Romi, A. Finarelli, M. Panning, P. Cordioli, C. Fortuna, S. Boros, F. Magurano, G. Silvi, P. Angelini, M. Dottori, M. Ciufolini, G. Majori and A. Cassone, Infection with chikungunya virus in Italy: An outbreak in a temperate region, The Lancet, 370 (2007), 1840-1846.
39 M. C. Robinson, An epidemic of virus disease in Southern Province, Tanganyika territory, in 1952-53. I. Clinical features, Transactions of the Royal Society of Tropical Medicine and Hygiene, 49 (1955), 28-32.
40 R. W. Ross, The newala epidemic. III. The virus: Isolation, pathogenic properties and relationship to the epidemic, Epidemiology and Infection, 54 (1956), 177-191.
41 T. Seyler, Y. Hutin, V. Ramanchandran, R. Ramakrishnan, P. Manickam and M. Murhekar, Estimating the burden of disease and the economic cost attributable to chikungunya, Andhra Pradesh, India, 2005-2006, Transactions of the Royal Society of Tropical Medicine and Hygiene, 104 (2010), 133-138.
42 D. Sissoko, D. Malvy, C. Giry, G. Delmas, C. Paquet, P. Gabrie, F. Pettinelli, M. A. Sanquer and V. Pierre, Outbreak of chikungunya fever in Mayotte, Comoros Archipelago, 2005-2006, Transactions of the Royal Society of Tropical Medicine and Hygiene, 102 (2008), 780-786.
43 A. B. Sudeep and D. Parashar, Chikungunya: An overview, Journal of Biosciences, 33 (2008), 443-449.
44 B. V. Tandale, P. S. Sathe, V. A. Arankalle, R. Wadia, R. Kulkarni, S. V. Shah, S. K. Shah, J. K. Sheth, A. Sudeep, A. S. Tripathy and A. C. Mishra, Systemic involvements and fatalities during chikungunya epidemic in India, 2006, Journal of Clinical Virology, 46 (2009), 145-149.
45 R. C. Thomé, H. M. Yang and L. Esteva, Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide, Mathematical Biosciences, 223 (2010), 12-23.       
46 M. Vazeille, C. Jeannin, E. Martin, F. Schaffner and A. B. Failloux, Chikungunya: A risk for Mediterranean countries, Acta Tropica, 105 (2008), 200-202.
47 World-Health-Organization, Dengue and severe dengue, factsheet no. 117, revised may 2008, Geneva, World Health Organization, 2008. Available from: http://www.who.int/mediacentre/factsheets/fs117/en/.
48 H. M. Yang and C. P. Ferreira, Assessing the effects of vector control on dengue transmission, Applied Mathematics and Computation, 198 (2008), 401-413.       

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