Optimal Intervention Strategies for Transmission Dynamics of Cholera Disease

Peter James Olumuyiwa; Ayoade Ayotunde Abayomi; Ayoola Tawakalt Abosede; Oguntolu Festus Abiodun; Amadiegwu Sylvanus; Abioye Adesoye Idowu

Peter James Olumuyiwa Department of Mathematics, University of Ilorin, PMB 1515, Ilorin, Kwara State, Nigeria.
Ayoade Ayotunde Abayomi Department of Mathematical and Computing Sciences, Kola Daisi University, Ibadan, Oyo State, Nigeria
Ayoola Tawakalt Abosede Department of Mathematical Sciences,Osun State University, PMB 4494, Oshogbo, Osun State, Nigeria.
Oguntolu Festus Abiodun Department of Mathematics, Federal University of Technology, PMB 65, Minna,Niger State, Nigeria.
Amadiegwu Sylvanus Department of Mathematics, School of General Studies, Maritime Academy of Nigeria , PMB 1089,AkwaIbom State, Nigeria.
Abioye Adesoye Idowu Department of Mathematics, University of Ilorin, PMB 1515, Ilorin, Kwara State, Nigeria.

Abstract

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.

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