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Analysis and Optimal Control Measures of a Typhoid Fever Mathematical Model for Two Socio-Economic Populations

Author

Listed:
  • Stephen Ekwueme Aniaku

    (Department of Mathematics, University of Nigeria, Nsukka 410105, Nigeria
    These authors contributed equally to this work.)

  • Obiora Cornelius Collins

    (Institute of Systems Science, Durban University of Technology, Durban 4000, South Africa
    These authors contributed equally to this work.)

  • Ifeanyi Sunday Onah

    (School of Mathematics and Statistics, Mathematics and Statistics Building, University of Glasgow, Glasgow G12 8QW, UK
    These authors contributed equally to this work.)

Abstract

Typhoid fever is an infectious disease that affects humanity worldwide; it is particularly dangerous in areas with communities of a lower socio-economic status, where many individuals are exposed to a dirty environment and unclean food. A mathematical model is formulated to analyze the impact of control measures such as vaccination of susceptible humans, treatment of infected humans and sanitation in different socio-economic communities. The model assumed that the population comprises of two socio-economic classes. The essential dynamical system analysis of our model was appropriately carried out. The impact of the control measures was analyzed, and the optimal control theory was applied on the control model to explore the impact of the different control measures. Numerical simulation of the models and the optimal controls were carried out and the obtained results indicate that the overall combination of the control measures eradicates typhoid fever in the population, but the controls are more optimal in higher socio-economic status communities.

Suggested Citation

  • Stephen Ekwueme Aniaku & Obiora Cornelius Collins & Ifeanyi Sunday Onah, 2023. "Analysis and Optimal Control Measures of a Typhoid Fever Mathematical Model for Two Socio-Economic Populations," Mathematics, MDPI, vol. 11(23), pages 1-24, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4722-:d:1285212
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    References listed on IDEAS

    as
    1. 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).
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    3. Aaron A. King & Edward L. Ionides & Mercedes Pascual & Menno J. Bouma, 2008. "Inapparent infections and cholera dynamics," Nature, Nature, vol. 454(7206), pages 877-880, August.
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