Optimal Control Strategy of a Dengue Epidemic Dynamics with Human-Mosquito Transmission
Abstract
In this paper, we presented a mathematical model of Dengue disease to understand its dynamics by using a set of differential equations to describe the effects between human and mosquito populations. The epidemic and endemic analyses have also presented along with numerical simulations to verify our model so that it can be further studied for public health interventions. Meanwhile, our optimal control problem has been investigated to explore control strategies to stop the Dengue disease outbreak. Our results show that strategically deployed control measures can reduced the numbers of infectious individuals. Keywords : Dengue fever, Mathematical model, equilibrium, Optimal control theoryReferences
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Asano, E., Gross, L.J., Lenhart, S. & Rea, L.A. (2008), Optimal control of vaccine distribution in rabies meta population model, Mathematical Biosciences and Engineering, 219-238.
Bowman, C., Gumel, A.B., Van den Driessche, P., Wu, J. & Zhu, H. (2005). A mathematical model for assessing control strategies against West Nile virus. Bull. Math. Biol., 67(5), 1107-1133.
Chavez, C.C, Feng, Z & Huang, W. (2001). On the Computation of R0 and its Role on Global Stability. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA, (Vol.125).
Esteva, L. & Vargas, C. (1998). Analysis of a dengue disease transmission model. Mathematical Biosciences an international journal, 131-151
Rodrigues, H.S., Monteiro, M.T.T., Torres, D.F.M. & Zinober, A. (2012). Dengue disease, basic reproduction number and control. Int. J. Comput. Math., 89(3), 334-346.
Singh, B., Jain, S., Khandelwal, R., Porwal, S. & Ujjainkar, G. (2014). Analysis of a dengue disease tramission model with vaccination. Advances in Applied Science Research., 5(3), 237-242
Pontryagin, L.S., Boltyanski, V.G., GamkreliZe, R.V. & Mishchenk, E.F. (1967). The Mathematical Theory of Optimal Process, Wiley, New York.
Van den Driessche, P. & Watmough, J. (2002). Reproduction numbers & sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci, 180, 29–48.
World Health Organization (WHO). Dengue. Retrieved July 2010, from http: www.who.int/topics/dengue/en.
Ali, T.M., Katim, F.A. & Kamil, A.A. (2015). Mathematical model of dengue fever and its sensitivity analysis. Pak. J. Statist., 31(6), 717-731.
Asano, E., Gross, L.J., Lenhart, S. & Rea, L.A. (2008), Optimal control of vaccine distribution in rabies meta population model, Mathematical Biosciences and Engineering, 219-238.
Bowman, C., Gumel, A.B., Van den Driessche, P., Wu, J. & Zhu, H. (2005). A mathematical model for assessing control strategies against West Nile virus. Bull. Math. Biol., 67(5), 1107-1133.
Chavez, C.C, Feng, Z & Huang, W. (2001). On the Computation of R0 and its Role on Global Stability. Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, IMA, (Vol.125).
Esteva, L. & Vargas, C. (1998). Analysis of a dengue disease transmission model. Mathematical Biosciences an international journal, 131-151
Rodrigues, H.S., Monteiro, M.T.T., Torres, D.F.M. & Zinober, A. (2012). Dengue disease, basic reproduction number and control. Int. J. Comput. Math., 89(3), 334-346.
Singh, B., Jain, S., Khandelwal, R., Porwal, S. & Ujjainkar, G. (2014). Analysis of a dengue disease tramission model with vaccination. Advances in Applied Science Research., 5(3), 237-242
Pontryagin, L.S., Boltyanski, V.G., GamkreliZe, R.V. & Mishchenk, E.F. (1967). The Mathematical Theory of Optimal Process, Wiley, New York.
Van den Driessche, P. & Watmough, J. (2002). Reproduction numbers & sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci, 180, 29–48.
World Health Organization (WHO). Dengue. Retrieved July 2010, from http: www.who.int/topics/dengue/en.
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2017-08-04
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บทความวิจัยจากการประชุมวิชาการระดับชาติ"วิทยาศาสตร์วิจัย"ครั้งที่ 9
