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Vaccination models and optimal control strategies to dengue. (English) Zbl 1282.92022
Summary: As the development of a dengue vaccine is ongoing, we simulate an hypothetical vaccine as an extra protection to the population. In a first phase, the vaccination process is studied as a new compartment in the model, and different ways of distributing the vaccines are investigated: pediatric and random mass vaccines, with distinct levels of efficacy and durability. In a second step, the vaccination is seen as a control variable in the epidemiological process. In both cases, epidemic and endemic scenarios are included in order to analyze distinct outbreak realities.

92C60 Medical epidemiology
49N90 Applications of optimal control and differential games
92-08 Computational methods for problems pertaining to biology
vaccines; SVIR model
Full Text: DOI arXiv
[1] Scherer, A.; McLean, A., Mathematical models of vaccination, British Med. Bull., 62, 1, 187, (2002)
[2] Farrington, C., On vaccine efficacy and reproduction numbers, Math. Biosci., 185, 1, 89, (2003) · Zbl 1021.92034
[3] Otero, M.; Schweigmann, N.; Solari, H. G., A stochastic spatial dynamical model for aedes aegypti, Bull. Math. Biol., 70, 5, 1297, (2008) · Zbl 1142.92028
[4] Cattand, P., Disease Control Priorities in Developing Countries, (2006), DCPP Publications, Ch. Tropical diseases lacking adequate control measures: dengue, leishmaniasis, and African trypanosomiasis, pp. 451-466
[5] Keeling, M. J.; Rohani, P., Modeling infectious diseases in humans and animals, (2008), Princeton University Press Princeton, NJ · Zbl 1279.92038
[6] Murrell, S.; Wu, S. C.; Butler, M., Review of dengue virus and the development of a vaccine, Biotechnol. Adv., 29, 2, 239, (2011)
[7] Clark, D. V., Economic impact of dengue fever/ dengue hemorrhagic fever in Thailand at the family and population levels, Am. J. Trop. Med. Hyg., 72, 6, 786, (2005)
[8] Shepard, D. S., Cost-effectiveness of a pediatric dengue vaccine, Vaccine, 22, 9-10, 1275, (2004)
[9] Suaya, J. A., Cost of dengue cases in eight countries in the americas and Asia: a prospective study, Am. J. Trop. Med. Hyg., 80, 5, 846, (2009)
[10] Supriatna, A. K.; Soewono, E.; Van Gils, S. A., A two-age-classes dengue transmission model, Math. Biosci., 216, 1, 114, (2008) · Zbl 1151.92019
[11] H.S. Rodrigues, M.T.T. Monteiro, D.F.M. Torres, Modeling and optimal control applied to a vector borne disease, in: J. Vigo-Aguiar (Ed.), Proceedings of the 2012 International Conference on Computational and Mathematical Methods in Science and Engineering, vol. III, 2012, pp. 1063-1070.
[12] Dumont, Y.; Chiroleu, F., Vector control for the chikungunya disease, Math. Biosci. Eng., 7, 2, 313, (2010) · Zbl 1259.92071
[13] Rodrigues, H. S.; Monteiro, M. T.T.; Torres, D. F.M.; Zinober, A., Dengue disease, basic reproduction number and control, Int. J. Comput. Math., 89, 3, 334, (2012) · Zbl 1237.92042
[14] de Castro Medeiros, L. C.; Castilho, C. A.R.; Braga, C.; de Souza, W. V.; Regis, L.; Monteiro, A. M.V., Modeling the dynamic transmission of dengue fever: investigating disease persistence, PLoS Negl. Trop. Dis., 5, 1, e942, (2011), pp. 14
[15] Zhou, Y.; Liu, H., Stability of periodic solutions for an SIS model with pulse vaccination, Math. Comput. Modell., 38, 299, (2003) · Zbl 1045.92042
[16] S. Gandon, M. Mackinnon, S. Nee, A. Read, Imperfect vaccination: some epidemiological and evolutionary consequences, in: Proceedings of Biological Sciences, vol. 270, 2003, pp. 1129.
[17] Liu, X.; Takeuchib, Y.; Iwami, S., SVIR epidemic models with vaccination strategies, J. Theoret. Biol., 253, 1, (2008) · Zbl 1398.92243
[18] DeRoeck, D.; Deen, J.; Clemens, J. D., Policymakers’ views on dengue fever/dengue haemorrhagic fever and the need for dengue vaccines in four southeast Asian countries, Vaccine, 22, 121, (2003)
[19] P. Stechlinski, A study of infectious disease models with switching, Ph.D. thesis, University of Waterloo, 2009.
[20] Cesari, L., Optimization — theory and applications, Problems with ordinary differential equations, Applications of Mathematics, vol. 17, (1983), Springer-Verlag New York, Heidelberg-Berlin
[21] Silva, C. J.; Torres, D. F.M., Optimal control strategies for tuberculosis treatment: a case study in angola, Numer. Algebra Control Optim., 2, 3, 601, (2012) · Zbl 1253.92035
[22] Pontryagin, L. S.; Boltyanskii, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F.; Neustadt, L. W., The mathematical theory of optimal processes, (1962), Interscience Publishers John Wiley & Sons, Inc. New York-London, Translated from the Russian by K.N. Trirogoff · Zbl 0102.32001
[23] Betts, J., Practical methods for optimal control using nonlinear programming, Advances in Design and Control, (2001), SIAM · Zbl 0995.49017
[24] Trélat, E., Contrôle optimal: théorie & applications, Collection Mathématiques Concrètes, (2005), Vuibert · Zbl 1112.49001
[25] Lenhart, S.; Workman, J. T., Optimal control applied to biological models, Chapman & Hall/CRC mathematical and computational biology series, (2007), Chapman & Hall/CRC Boca Raton, FL
[26] Hirmajer, T.; Balsa-Canto, E.; Banga, J. R., Dotcvpsb, a software toolbox for dynamic optimization in systems biology, Bioinformatics, 10, 199, (2009)
[27] H.S. Rodrigues, M.T.T. Monteiro, D.F.M. Torres, Insecticide control in a dengue epidemics model, in: T.E. Simos, et al. (Eds.), Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Rhodes, Greece. American Institute of Physics Conf. Proc., no. 1281 in American Institute of Physics Conf. Proc., 2010, pp. 979-982.
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