Co-dynamics of measles and dysentery diarrhea diseases with optimal control and cost-effectiveness analysis

Hailay Weldegiorgis Berhe, Oluwole Daniel Makinde and David Mwangi Theuri

Applied Mathematics and Computation, 2019, vol. 347, issue C, 903-921

Abstract: In this paper we propose a co-dynamics deterministic system for measles and dysentery diarrhea diseases in a single host population. Using center manifold theory, we show that the co-dynamics model may exhibit a backward bifurcation for some parameter values. Numerical simulations of the system show that the two diseases always coexist if R0 > 1. The system is extended to include time-dependent control-variables: vaccination, treatment and sanitation of the environment, to minimize the number of infected humans and the cost of implementation of the controls. The Pontryagin Maximum Principle was employed to find the necessary conditions for the existence of the optimal controls. The numerical simulations show that the effective controls could reduce the diseases in the community. The incremental cost-effectiveness ratio was used to quantify the cost-effectiveness analysis. It is found that the control strategy which implements vaccination, treatment of dysentery diarrhea and sanitation of the environment is the most cost-effective.

Keywords: Co-dynamics; Backward bifurcation; Optimal control; Numerical simulation; Cost-effectiveness (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:903-921

DOI: 10.1016/j.amc.2018.11.049

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