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Co-dynamics of Pneumonia and Typhoid fever diseases with cost effective optimal control analysis

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  • Tilahun, Getachew Teshome
  • Makinde, Oluwole Daniel
  • Malonza, David

Abstract

In this paper, we propose and analyze a mathematical model for Pneumonia–Typhoid co-infection to examine their characteristic relationship due to preventive and treatments strategies. Firstly, we qualitatively analyzed the model, and the basic reproduction number is determined with respect to the existence and stability of equilibria. The possibility of bifurcation is studied and also we investigated the sensitivity index of co-infection model reproduction number together with the local and global stability of the equilibra. Secondly, we extend the co-infection model by incorporating time dependent controls as intervention and we used Pontryagin’s maximum principle for derivation of necessary conditions for the optimal control and optimality system. Finally, the optimality system is numerically simulated by considering four strategies and also their cost effectiveness is analysed. We found that Pneumonia treatment with Typhoid fever prevention costs least. Therefore, for optimal cost effective control of both diseases, the policy makers must focus more on prevention strategy while treating the infected individual is not neglected.

Suggested Citation

  • Tilahun, Getachew Teshome & Makinde, Oluwole Daniel & Malonza, David, 2018. "Co-dynamics of Pneumonia and Typhoid fever diseases with cost effective optimal control analysis," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 438-459.
    • Handle: RePEc:eee:apmaco:v:316:y:2018:i:c:p:438-459
    DOI: 10.1016/j.amc.2017.07.063
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    Cited by:

    1. Abboubakar, Hamadjam & Kombou, Lausaire Kemayou & Koko, Adamou Dang & Fouda, Henri Paul Ekobena & Kumar, Anoop, 2021. "Projections and fractional dynamics of the typhoid fever: A case study of Mbandjock in the Centre Region of Cameroon," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. 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).
    3. Mohammed H. Alharbi & Fawaz K. Alalhareth & Mahmoud A. Ibrahim, 2023. "Analyzing the Dynamics of a Periodic Typhoid Fever Transmission Model with Imperfect Vaccination," Mathematics, MDPI, vol. 11(15), pages 1-26, July.
    4. Abboubakar, Hamadjam & Racke, Reinhard, 2021. "Mathematical modeling, forecasting, and optimal control of typhoid fever transmission dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    5. Fawaz K. Alalhareth & Mohammed H. Alharbi & Mahmoud A. Ibrahim, 2023. "Modeling Typhoid Fever Dynamics: Stability Analysis and Periodic Solutions in Epidemic Model with Partial Susceptibility," Mathematics, MDPI, vol. 11(17), pages 1-26, August.
    6. Khan, Tahir & Ullah, Zakir & Ali, Nigar & Zaman, Gul, 2019. "Modeling and control of the hepatitis B virus spreading using an epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 1-9.
    7. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
    8. Irena, Tsegaye Kebede & Gakkhar, Sunita, 2021. "Modelling the dynamics of antimicrobial-resistant typhoid infection with environmental transmission," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    9. Fatima, Bibi & Zaman, Gul, 2020. "Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Jorge E. Macías-Díaz & Nauman Ahmed & Muhammad Rafiq, 2019. "Analysis and Nonstandard Numerical Design of a Discrete Three-Dimensional Hepatitis B Epidemic Model," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    11. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    12. Sanubari Tansah Tresna & Subiyanto & Sudradjat Supian, 2022. "Mathematical Models for Typhoid Disease Transmission: A Systematic Literature Review," Mathematics, MDPI, vol. 10(14), pages 1-12, July.

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