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

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.