Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Optimal control and cost-effectiveness analysis of a three age-structured transmission dynamics of chikungunya virus
Pages: 687 - 715, Issue 3, May 2017

doi:10.3934/dcdsb.2017034      Abstract        References        Full text (1294.4K)           Related Articles

Folashade B. Agusto - Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence KS 66045, United States (email)

1 F. B. Agusto, S. Easley, K. Freeman and M. Thomas, Mathematical model of a three age-structured transmission dynamics of Chikungunya Virus, Comput. Math. Methods Med., (2016), Art. ID 4320514, 31 pp.       
2 F. B. Agusto, Optimal isolation control strategies and cost-effectiveness analysis of a two-strain avian influenza model, BioSystems, 113 (2013), 155-164.
3 F. B. Agusto and S. Lenhart, Optimal Control of the spread of malaria super-infectivity, Journal of Biological Systems Special issue on Infectious Disease Modeling, 21 (2013), 1340002, 26pp.       
4 F. B. Agusto, N. Marcus and K. O. Okosun, Application of optimal control to the epidemiology of malaria disease, Electronic Journal of Differential Equations, 2012 (2012), 1-22.       
5 R. M. Anderson and R. May, Infectious Diseases of Humans, Oxford University Press, New York, 1991.
6 S. M. Blower and H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example, Int. Stat. Rev., 62 (1994), 229-243.
7 S. B. Cantor and T. G. Ganiats, Incremental cost-effectiveness analysis: The optimal strategy depends on the strategy set, Journal of Clinical Epidemiology, 52 (1999), 517-522.
8 Centers for Disease Control and Prevention. Chikungunya virus, Available from: http://www.cdc.gov/Chikungunya/symptoms/index.html.
9 L. J. Chang, K. A. Dowd, F. H. Mendoza, J. G. Saunders and S. Sitar, et al., Safety and tolerability of Chikungunya virus-like particle vaccine in healthy adults: A phase 1 dose-escalation trial, Lancet, 384 (2014), 2046-2052.
10 N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of Mathematical Biology, 70 (2008), 1272-1296.       
11 A. Costero, K. Mormann and S. A. Juliano, Asymmetrical competition and patterns of abundance of Aedes albopictus and Culex pipiens (Diptera: Culicidae), Journal of Medical Entomology, 42 (2005), 559-570.
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 O. Diekmann, J. A. P. Heesterbeek and J. A. P. Metz, On the definition and computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.       
14 M. Doucleff, Trouble In Paradise: Chikungunya outbreak grows in caribbean, Health News, 2013. Available from: http://www.npr.org/sections/health-shots/2013/12/18/255216192/trouble-in-paradise-Chikungunya-outbreak-grows-in-caribbean.
15 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.
16 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.       
17 Y. Dumont and F. Chiroleu, Vector control for the Chikungunya disease, Mathematical Biosciences and Engineering, 7 (2010), 313-345.       
18 M. Enserink, Epidemiology: Tropical disease follows mosquitoes to Europe, Science, 317 (2007), 1485a.
19 K. Fiscella and P. Franks, Cost-effectiveness of the transdermal nicotine patch as an adjunct to physicians smoking cessation counseling, JAMA, 276 (1996), 1247-1251.
20 W. H. Fleming and R. W. Rishel, Deterministic and Stochastic Optimal Control, Springer Verlag, New York, 1975.       
21 K. A. Freedberg, J. A. Scharfstein, G. R. Seage, E. Losina, M. C. Weinstein and D. E. Craven, et al., The cost-effectiveness of preventing AIDS-related opportunistic infections, JAMA, 279 (1998), 130-136.
22 H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev, 42 (2000), 599-653.       
23 H. R. Joshi, Optimal control of an HIV immunology model, Optim. Control Appl. Math, 23 (2002), 199-213.       
24 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.       
25 D. Kern, S. Lenhart, R. Miller and J. Yong, Optimal control applied to native-invasive population dynamics, J Biol Dyn., 1 (2007), 413-426.       
26 D. Kirschner, S. Lenhart and S. Serbin, Optimal control of the chemotherapy of HIV, J. Math. Biol., 35 (1997), 775-792.       
27 C. Lahariya and S. K. Pradhan, Emergence of Chikungunya virus in Indian subcontinent after 32 years: A review, Journal of Vector Borne Diseases, 43 (2006), 151-160.
28 S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, Chapman and Hall, 2007.       
29 S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178-196.       
30 C. Manore, J. Hickmann, S. Xu, H. Wearing and J. Hyman, Comparing Dengue and Chikungunya emergence and endemic Transmission in A. aegypti and A. albopictus, Journal of Theoretical Biology, 356 (2014), 174-191.       
31 E. Massad, S. Ma, M. N. Burattini, Y. Tun, F. A. B. Coutinho and W. Lang, The risk of Chikungunya fever in a dengue-endemic area, Journal of Travel Medicine, 15 (2008), 147-155.
32 R. G. McLeod, J. F. Brewster, A. B. Gumel and D. A. Slonowsky, Sensitivity and uncertainty analyses for a sars model with time-varying inputs and outputs, Math. Biosci. Eng., 3 (2006), 527-544.       
33 O. P. Misra and D. K. Mishra, Simultaneous effects of control Measures on the transmission dynamics of Chikungunya disease, Applied Mathematics, 2 (2012), 124-130.
34 D. Moulay, M. A. Aziz-Alaoui and M. Cadivel, The Chikungunya disease: Modeling, vector and transmission global dynamics, Mathematical Biosciences, 229 (2011), 50-63.       
35 H. Nur Aida, A. Abu Hassan, A. T. Nurita, M. R. Che Salmah and B. Norasmah, Population analysis of Aedes albopictus (Skuse)(Diptera: Culicidae) under uncontrolled laboratory conditions, Tropical Biomedicine, 25 (2008), 117-125.
36 K. O. Okosun, O. Rachid and N. Marcus, Optimal control strategies and cost-effectiveness analysis of a malaria model, Biosystems, 111 (2013), 83-101.
37 K. Pesko, C. J. Westbrook, C. N. Mores, L. P. Lounibos and M. H. Reiskind, Effects of infectious virus dose and bloodmeal delivery method on susceptibility of Aedes aegypti and Aedes albopictus to Chikungunya virus, Journal of Medical Entomology, 46 (2009), 395-399.
38 G. Pialoux, B. A. Gaüzère, S. Jauréguiberry and M. Strobel, Chikungunya, an epidemic arbovirosis, The Lancet Infectious Diseases, 7 (2007), 319-327.
39 S. D. Pinkerton, D. R. Holtgrave, W. J. DiFranceisco, L. Y. Stevenson and J. A. Kelly, Cost-effectiveness of a community-level HIV risk reduction intervention, Am J Public Health, 88 (1998), 1239-1242.
40 P. Poletti, G. Messeri, M. Ajelli, R. Vallorani, C. Rizzo and S. Merler, Transmission potential of Chikungunya virus and control measures: The case of Italy, PLoS ONE, 6 (2011), e18860.
41 P. Pongsumpun and S. Sangsawangl, Local stability analysis for age structural model of Chikungunya disease, Journal of Basic and Applied Scientific Research, 3 (2013), 302-312.
42 L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Wiley, New York, 1962.       
43 D. Ruiz-Moreno, I. S. Vargas, K. E. Olson and L. C. Harrington, Modeling dynamic introduction of Chikungunya virus in the United States, PLOS Neglected Tropical Disease, 6 (2012), e1918.
44 I. Schuffenecker, I. Iteman, A. Michault, S. Murri and L. Frangeul, et al., Genome microevolution of Chikungunya viruses causing the Indian Ocean outbreak, PLoS Med., 3 (2006), e263.
45 O. Schwartz and M. L. Albert, Biology and pathogenesis of Chikungunya virus, Nature Reviews Microbiology, 8 (2010), 491-500.
46 M. R. Sebastian, R. Lodha and S. K. Kabra, Chikungunya infection in children, Indian Journal of Pediatrics, 76 (2009), 185-189.
47 R. K. Singh, S. Tiwari, V. K. Mishra, R. Tiwari and T. N. Dhole, Molecular epidemiology of Chikungunya virus: Mutation in E1 gene region, Journal of Virological Methods, 185 (2012), 213-220.
48 J. E. Staples, S. L. Hills and A. M. Powers, Chikungunya. Centers for Disease Control and Prevention (CDC), 2014, http://wwwnc.cdc.gov/travel/yellowbook/2014/chapter-3-infectious-diseases-related-to-travel/Chikungunya. Accessed June 8, 2015.
49 K. A. Tsetsarkin, D. L. Vanlandingham, C. E. McGee and S. Higgs, A Single mutation in Chikungunya virus affects vector specificity and epidemic potential, PLoS Pathogens, 3 (2007), e201.
50 M. J. Turell, J. R. Beaman and R. F. Tammariello, Susceptibility of selected strains of Aedes aegypti and Aedes albopictus (Diptera: Culicidae) to Chikungunya virus, Journal of Medical Entomology, 29 (1992), 49-53.
51 P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48.       
52 M. Vazeille, S. Moutailler, D. Coudrier, C. Rousseaux and H. Khun, et al., Two Chikungunya isolates from the outbreak of La Reunion (Indian Ocean) exhibit different patterns of infection in the mosquito, Aedes albopictus, PLoS ONE, 2 (2007), e1168.
53 World Health Organization, Chikungunya, 2014, Available from: http://www.who.int/denguecontrol/arbo-viral/other_arboviral_Chikungunya/en/.
54 World Health Organization, Chikungunya, 2014, Available from: http://www.who.int/mediacentre/factsheets/fs327/en/.
55 X. Yan, Y. Zou and J. Li, Optimal quarantine and isolation strategies in epidemics control, World Journal of Modelling and Simulation, 3 (2007), 202-211.
56 X. Yan and Y. Zou, Optimal and sub-optimal quarantine and isolation control in SARS epidemics, Mathematical and Computer Modelling, 47 (2008), 235-245.       
57 L. Yakob and A. C. A. Clements, A Mathematical model of Chikungunya dynamics and control: The major epidemic on Réunion Island, PLoS ONE, 8 (2013), e57448.

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