Title: Mathematical model of childhood diseases outbreak with optimal control and cost effectiveness strategy

Authors: Kazeem Oare Okosun; Oluwole Daniel Makinde

Addresses: Department of Mathematics, Vaal University of Technology, Vanderbijlpark, Gauteng, South Africa ' Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa

Abstract: In this paper, we derive and analyse a deterministic model for the transmission of childhood disease perform optimal control analysis of the model. The model is found to exhibit multiple equilibria. However, a unique endemic equilibrium exists when there is no disease induced death. We also derive and analyse the necessary conditions for the optimal control of the disease. In addition, we investigate the cost-effectiveness of the controls to determine the most effective strategy to control childhood disease with minimum costs. Finally, we present the numerical solutions.

Keywords: childhood coverage; sensitivity indices; Runge-Kutta integration scheme; diseases; epidemiological model; vaccination.

DOI: 10.1504/IJCSM.2019.098743

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.2, pp.115 - 128

Received: 02 Jun 2017
Accepted: 19 Jul 2017
Published online: 02 Apr 2019 *

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