Optimal Control Analysis of an Age-Structured Malaria Model Incorporating Children under Five Years and Pregnant Women
George Theodore Azu-Tungmah *
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Francis T. Oduro
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Gabriel A. Okyere
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
In this article, we apply the optimal control theory to a new age-structured malaria model with three infectious compartments for people under five years, over five years and pregnant women. The model is formulated for malaria endemic areas in the world and the following malaria control strategies ITN, IRS, Chemoprophylaxis and Improved Clinical Treatment were examined and analysed on the mode. The Cost-effectiveness Analysis points out that more attention should be given Insecticide -Treated bed nets (ITNs) in order to eliminate the malaria disease globally because the female Anopheles mosquitoes need human blood to lay their eggs. The expression for the effective reproduction number has been derived by using the next-generation method. The impact of the controls on the was studied and it came out that all the four controls have a positive impact such that the ITNs can reduce to zero as the value of ITNs approaches one. Pontryagin’s Maximum Principle was applied to analyse the optimal control model theoretically and the optimality system was solved numerically through an iterative scheme.
The optimal plots (Figs. 4-8) reveal that best control strategies for malaria elimination is the combination of ITN, Chemoprophylaxis and Improved Clinical Treatment. However, the Cost-effectiveness Analysis points out that ITN is economically best solution for fighting malaria in poor malaria endemic areas.
Keywords: Insecticide Treated bed nets (ITNs), Indoor Residual Spraying (IRS), chemoprophylaxis, improved clinical treatment, effective reproduction number