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

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  • Berhe, Hailay Weldegiorgis
  • Makinde, Oluwole Daniel
  • Theuri, David Mwangi

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.

Suggested Citation

  • Berhe, Hailay Weldegiorgis & Makinde, Oluwole Daniel & Theuri, David Mwangi, 2019. "Co-dynamics of measles and dysentery diarrhea diseases with optimal control and cost-effectiveness analysis," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 903-921.
    • Handle: RePEc:eee:apmaco:v:347:y:2019:i:c:p:903-921
    DOI: 10.1016/j.amc.2018.11.049
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    References listed on IDEAS

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    1. Pang, Liuyong & Ruan, Shigui & Liu, Sanhong & Zhao, Zhong & Zhang, Xinan, 2015. "Transmission dynamics and optimal control of measles epidemics," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 131-147.
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    Cited by:

    1. Berhe, Hailay Weldegiorgis, 2020. "Optimal Control Strategies and Cost-effectiveness Analysis Applied to Real Data of Cholera Outbreak in Ethiopia’s Oromia Region," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Das, Dhiraj Kumar & Kar, T.K., 2021. "Global dynamics of a tuberculosis model with sensitivity of the smear microscopy," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Yuan, Yiran & Li, Ning, 2022. "Optimal control and cost-effectiveness analysis for a COVID-19 model with individual protection awareness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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