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Free Terminal Time in Optimal Control approach of Chikungunya Model

by Meryem Alkama, Mostafa Rachik
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 140 - Number 13
Year of Publication: 2016
Authors: Meryem Alkama, Mostafa Rachik
10.5120/ijca2016909536

Meryem Alkama, Mostafa Rachik . Free Terminal Time in Optimal Control approach of Chikungunya Model. International Journal of Computer Applications. 140, 13 ( April 2016), 9-16. DOI=10.5120/ijca2016909536

@article{ 10.5120/ijca2016909536,
author = { Meryem Alkama, Mostafa Rachik },
title = { Free Terminal Time in Optimal Control approach of Chikungunya Model },
journal = { International Journal of Computer Applications },
issue_date = { April 2016 },
volume = { 140 },
number = { 13 },
month = { April },
year = { 2016 },
issn = { 0975-8887 },
pages = { 9-16 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume140/number13/24671-2016909536/ },
doi = { 10.5120/ijca2016909536 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T23:42:11.070763+05:30
%A Meryem Alkama
%A Mostafa Rachik
%T Free Terminal Time in Optimal Control approach of Chikungunya Model
%J International Journal of Computer Applications
%@ 0975-8887
%V 140
%N 13
%P 9-16
%D 2016
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Optimal control problems are an important mathematic tool used to reduce infectious diseases, most of works in this area considered time constant. In this paper, we present a free terminal optimal time control of Chikungunya epidemic model, which is an arthropod-borne virus (arbovirus) transmitted by mosquitoes of Aedes genus, with the order to give a minimum duration needed to reduce the infected group of both human and vector. We present a control simulating program using Matlab routines. The optimal control and the optimal final time are found using Pontryagin’s maximum principle and the additional transversality condition for the terminal time. We solved the optimality system by an iterative method, then we confirm the performance of the optimization strategy by numerical simulations.

References
  1. Rudolph KE, Lessler J, Moloney RM, Kmush B,Cummings DA. Incubation periods of mosquito-borne viral infections: a systematic review. Am J Trop Med Hyg. 2014 May;90(5):882-91
  2. Van Bortel W, Dorleans F, Rosine J, Blateau A, Rousset D, Matheus S, et al. Chikungunya outbreak in the Caribbean region, December 2013 to March 2014,and the signi.cance for Europe. Euro Surveill. 2014;19(13).
  3. European Centre for Disease Prevention and Control.Aedes albopictus factsheet [Internet]. Available from http://www.ecdc.europa.eu/en/healthtopics/vectors/mosquitoes/Pages/aedes-albopictus-factsheet.aspx.
  4. Alkama, M., et al. "Free terminal Time OptimalControlProblem of an SIR Epidemic Model with Vaccination."2014, International Journal of Science andResearch, ISSN 2319-7064.Research, ISSN 2319-7064.
  5. Moulay, D., M. A. Aziz-Alaoui, and M. Cadivel. "Thechikungunya disease: modeling, vector andtransmissionglobal dynamics." Mathematical biosciences229.1 (2011): 50-63.
  6. Moulay, Djamila, M. A. Aziz-Alaoui, and Hee-Dae Kwon. "Optimal control of chikungunya disease: larvaereduction, treatment and prevention." MathematicalBiosciences and Engineering 9.2 (2012): 369-392.
  7. M. Elhia , O. Balatif , J. Bouyaghroumni, E. Labriji, M. Rachik, Optimal Control Applied to the Spread of Inluenza A(H1N1), Applied Mathematical sciences, Vol.6, 2012, no. 82, 4057.4065
  8. 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), 473482.
  9. K. Blayneh, Y. Cao and H.D. Kwon, Optimal control of vector-borne disease: Treatment and prevention, Discreteand Continuous Dynamical Systems Series B, 11 (2009), 587.611.
  10. L. S. Pontryagin, V. G. Boltyanskii, R. V. GamkrelidzeE. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, 1962.
  11. H. Delatte, G. Gimonneau, A. Triboire, D. Fontenille,Influence of temperature on immature development, survival, longevity, fecundity, and gonotrophic cycles ofAedes albopictus, vector of chikungunya and dengue in the Indian Ocean, J. Med. Entomol. 46 (2009) 33.41.
  12. M. Dubrulle, L. Mousson, S. Moutailler, M. Vazeille, A.Failloux, Chikungunya virus and Aedes mosquitoes:saliva is infectious as soon as two days after oral infection, PLoS ONE 4 (6) (2009) e5895.
  13. J.X. Velasco-Hernàndez, A model for chagas disease involving transmission by vectors and blood transfusion, Theor. Popul. Biol. 46 (1) (1994) 1.
  14. Noël, H., and C. Rizzo. "Spread of chikungunya from the Caribbean to mainland Central and South America: a greater risk of spillover in Europe." Euro surveillance: bulletin Européen sur les maladies transmissibles European communicable diseasebulletin 19.28 (2014).
  15. Be dry with mosquitoes. Http://www.albopictus.eid med.org/index.htm, (2011).
  16. Outbreaks, Recent Chikungunya. "Chikungunya: nolonger a third world disease." (2007).
  17. Charrel, Rémi N., Xavier de Lamballerie, and DidierRaoult. "Chikungunya outbreaks-the globalization ofvectorborne diseases." New England Journal ofMedicine 356.8 (2007): 769.
Index Terms

Computer Science
Information Sciences

Keywords

Opimal control problems numerical simulations chikungunya

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