Optimal Intervention Strategies for Transmission Dynamics of Cholera Disease
In this paper, an optimal control model for cholera disease described by a system of first order ordinary differential equations was formulated and examined. The necessary conditions for the attainment of optimum level of control in the dynamical system were derived by employing the Pontryagin’s Maximum principle. Numerical studies of the analytical results were conducted to investigate the behaviour of the optimality system and the results were tabulated. The tabular results showed that the combination of the interventions up to 80% was capable of bringing cholera epidemic under control. As the rate of control was directly related to the cost of control, the result of the analysis revealed the control outlay that maintained the optimum balance of interventions with the lowest cost.
Agusto, F. B., Nizar, M., & Okosun, K. O. (2012). Application of optimal control to the epidemiology of malaria. Electronic Journal of Differential Equations, 81, 1-22.
Akande, K. A., & Ibrahim, M. O. (2017). Application of Differential Transformation Method in Solving Optimal Control of Terrorism Model. ABACUS. Journal of Mathematical Association of Nigeria (Mathematics Science Series), 44(1), 149 – 157.
Al-Arydah, M., Mwasa, A., Tchuenche, J. M., & Smith, R. J. (2013). Modeling cholera disease with education and chlorination. Journal of Biological systems, 21 (4), 3-8.
Edward, S., & Nyerere, N. (2015). A mathematical model for the dynamics of cholera with control measures. Applied and Computational Mathematics, 4(2), 53 - 63.
Isere, A. O., Osemwenkhae, J. E., & Okuonghae, D. (2014). Optimal control model for the outbreak of cholera in Nigeria. African Journal of Mathematics and Computer Science Research, 7(2), 24-30.
Kadaleka, S. (2011). Assessing the effects of nutrition and treatment in cholera dynamics: The case of Malawi. M. Sc. Dissertation, University of Der es Salaam.
Hassan, L., Abdelhadi, A., Mostafa, R., Jamal, B., & El Houssine, L. (2013). Stability Analysis and Optimal Vaccination Strategies for an SIR Epidemic Model. International Journal of Nonlinear Science, 16(4), 323 – 333.
Lashari, A. A., Hattaf, K., Zaman, G., & Li, X-z. (2013). Backward bifurcation and optimal control of a vector borne disease. Applied Mathematics & Information Sciences, 7(1), 301-309.
Nana-Kyere, S., HedeDoe, R., Boateng, F. A., Odum, J. K., Marmah, S., & Banon, D. T. (2017). Optimal Control Model of Malaria Disease with Standard Incidence Rate. Journal Advances in Mathematics and Computer Sciences, 23(5), 1-21.
Neilan, R. L. M., Schaefer, E., Gaff, H., Fister, K. R. & Lenhart, S. (2010). Modeling optimal intervention strategies for cholera. Bulletin of Mathematical Biology, 72, 2004-2018.
Oke, S. I., Matadi, M. B., & Zulu, S. S. (2018). Optimal control analysis of a mathematical model for breast cancer. Mathematical and Computational Applications, 23(21), 1-28.
Sule, A., & Lawal, J. (2018). Mathematical modelling and optimal control of Ebola virus disease (EVD). Annual Research & Review in Biology, 22(2), 1-11.
Wang, J., & Modnak, C. (2011). Modeling cholera dynamics with controls. Canadian Applied Mathematics Quarterly, 19(3), 11-17.