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Analysis of a Comprehensive Mathematical Model for Leptospirosis Dynamics: An Optimal Control Application

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  • Habtamu Ayalew Engida

Abstract

The emergence and re‐emergence of infectious diseases present a major challenge to global public health. Leptospirosis is one of the significant public health issues in tropical regions worldwide; nevertheless, insufficient awareness has resulted in the under‐reporting of its actual incidence and mortality rates. This study presents a comprehensive mathematical model for leptospirosis to analyze the transmission dynamics of the disease. We further explored the model to assess the effectiveness and cost‐effectiveness of different intervention strategies to combat the epidemic. The next‐generation matrix approach is applied to derive the basic reproduction number (R0) of the formulated model. The model has a disease‐free equilibrium, which is globally asymptotically stable when R0

Suggested Citation

  • Habtamu Ayalew Engida, 2025. "Analysis of a Comprehensive Mathematical Model for Leptospirosis Dynamics: An Optimal Control Application," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:7338974
    DOI: 10.1155/jom/7338974
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    References listed on IDEAS

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    1. Muhammad Altaf Khan & Saeed Islam & Sher Afzal Khan & Ilyas Khan & Sharidan Shafie & Taza Gul, 2014. "Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, November.
    2. Gallego, María Alejandra & Simoy, María Verónica, 2021. "Mathematical modeling of leptospirosis: A dynamic regulated by environmental carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Malede Atnaw Belay & Jeconia Abonyo Okelo & David Mwangi Theuri & Haileyesus Tessema Alemneh & Negesse Yizengaw Alemu, 2025. "A Coinfection Model of Bacterial Meningitis and Hepatitis B Diseases With Optimal Control and Cost-Effectiveness Analysis," Journal of Applied Mathematics, Hindawi, vol. 2025, pages 1-32, January.
    4. Abboubakar, Hamadjam & Kouchéré Guidzavaï, Albert & Yangla, Joseph & Damakoa, Irépran & Mouangue, Ruben, 2021. "Mathematical modeling and projections of a vector-borne disease with optimal control strategies: A case study of the Chikungunya in Chad," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
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    6. Ebrima Kanyi & Ayodeji Sunday Afolabi & Nelson Owuor Onyango, 2021. "Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2021(1).
    7. Muhammad Altaf Khan & Saeed Islam & Sher Afzal Khan & Ilyas Khan & Sharidan Shafie & Taza Gul, 2014. "Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Malede Atnaw Belay & Jeconia Abonyo Okelo & David Mwangi Theuri & Haileyesus Tessema Alemneh & Negesse Yizengaw Alemu, 2025. "A Coinfection Model of Bacterial Meningitis and Hepatitis B Diseases With Optimal Control and Cost‐Effectiveness Analysis," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    9. Ebrima Kanyi & Ayodeji Sunday Afolabi & Nelson Owuor Onyango, 2021. "Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis," Journal of Applied Mathematics, Hindawi, vol. 2021, pages 1-20, May.
    10. Habtamu Ayalew Engida & David Mwangi Theuri & Duncan Kioi Gathungu & John Gachohi & Haileyesus Tessema Alemneh, 2025. "A Coinfection Model of Leptospirosis and Melioidosis With Optimal Control," Journal of Applied Mathematics, Hindawi, vol. 2025, pages 1-25, May.
    11. Andrea Di Liddo, 2016. "Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs," Mathematics, MDPI, vol. 4(2), pages 1-27, April.
    12. Habtamu Ayalew Engida & David Mwangi Theuri & Duncan Kioi Gathungu & John Gachohi & Haileyesus Tessema Alemneh, 2025. "A Coinfection Model of Leptospirosis and Melioidosis With Optimal Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    13. Kouidere, Abdelfatah & Balatif, Omar & Rachik, Mostafa, 2021. "Analysis and optimal control of a mathematical modeling of the spread of African swine fever virus with a case study of South Korea and cost-effectiveness," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
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