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Mathematical model on the transmission dynamics of leptospirosis in human and animal population with optimal control strategies using real statistical data

Author

Listed:
  • Festus Abiodun Oguntolu

    (Federal University of Technology)

  • Olumuyiwa James Peter

    (University of Medical Sciences
    University of Medical Sciences)

  • Benjamin Idoko Omede

    (Prince Abubakar Audu (Formerly Kogi State) University)

  • Ghaniyyat Bolanle Balogun

    (University of Ilorin)

  • Tawakalt Abosede Ayoola

    (Osun State University)

Abstract

Leptospirosis poses a significant public health challenge, with a growing incidence in both human and animal populations. The complex interplay between reservoir hosts, environmental factors, and human activities complicates efforts to curb the spread of the disease. Consequently, this paper presents a deterministic mathematical model for the transmission dynamics of leptospirosis within the intertwined human and animal populations. A comprehensive examination of the model revealed that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is below one. Utilizing center manifold theory, we demonstrated that the Leptospirosis model displays forward bifurcation. Consequently, the epidemiological significance of this forward bifurcation suggests that eradicating leptospirosis from the community is feasible, provided the reproduction number remains below one. We conducted a sensitivity analysis on the basic reproduction number of Leptospirosis to identify parameters that contribute positively to the disease’s spread. Furthermore, We validated our Leptospirosis model by fitting it with confirmed cases reported in Kerala State, India, covering the period from January 2021 to December 2022. This calibration process ensures the model’s accuracy and reliability in reflecting real-world epidemiological dynamics within the specified region and timeframe. In addition, we enhanced the Leptospirosis model by incorporating three time-dependent control measures. These controls encompass the vaccination of animals, environmental sanitation, and preventive actions such as using hand gloves and goggles when handling animals, as well as wearing rubber boots during periods of flooding or heavy rainfall. Results obtained from numerical simulations indicate that implementing the vaccination of animals as a standalone control strategy has no discernible effect on the number of infected humans or the bacteria population. However, when the three time-dependent control measures are combined, there is a substantial and meaningful impact on reducing the number of infected humans, infected animals, and the overall bacteria population within a relatively short timeframe. This underscores the effectiveness of the integrated approach in mitigating the spread of leptospirosis across both human and animal populations.

Suggested Citation

  • Festus Abiodun Oguntolu & Olumuyiwa James Peter & Benjamin Idoko Omede & Ghaniyyat Bolanle Balogun & Tawakalt Abosede Ayoola, 2025. "Mathematical model on the transmission dynamics of leptospirosis in human and animal population with optimal control strategies using real statistical data," Quality & Quantity: International Journal of Methodology, Springer, vol. 59(2), pages 1405-1444, April.
    • Handle: RePEc:spr:qualqt:v:59:y:2025:i:2:d:10.1007_s11135-024-02016-3
    DOI: 10.1007/s11135-024-02016-3
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    References listed on IDEAS

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    1. Sarah Tubiana & Marc Mikulski & Jérôme Becam & Flore Lacassin & Patrick Lefèvre & Ann-Claire Gourinat & Cyrille Goarant & Eric D'Ortenzio, 2013. "Risk Factors and Predictors of Severe Leptospirosis in New Caledonia," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 7(1), pages 1-8, January.
    2. Ojo, Mayowa M. & Benson, Temitope O. & Peter, Olumuyiwa James & Goufo, Emile Franc Doungmo, 2022. "Nonlinear optimal control strategies for a mathematical model of COVID-19 and influenza co-infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    3. Za'er Abo-Hammour & Othman Alsmadi & Shaher Momani & Omar Abu Arqub, 2013. "A Genetic Algorithm Approach for Prediction of Linear Dynamical Systems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-12, December.
    4. Taher S. Hassan & E. M. Elabbasy & A.E. Matouk & Rabie A. Ramadan & Alanazi T. Abdulrahman & Ismoil Odinaev & Binxiang Dai, 2022. "Routh–Hurwitz Stability and Quasiperiodic Attractors in a Fractional-Order Model for Awareness Programs: Applications to COVID-19 Pandemic," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-15, April.
    5. repec:plo:pntd00:0003898 is not listed on IDEAS
    6. Asmalia Md-Lasim & Farah Shafawati Mohd-Taib & Mardani Abdul-Halim & Ahmad Mohiddin Mohd-Ngesom & Sheila Nathan & Shukor Md-Nor, 2021. "Leptospirosis and Coinfection: Should We Be Concerned?," IJERPH, MDPI, vol. 18(17), pages 1-17, September.
    7. Mas Harithulfadhli Agus Ab Rahman & Suhaily Mohd Hairon & Rukman Awang Hamat & Tengku Zetty Maztura Tengku Jamaluddin & Mohd Nazri Shafei & Norazlin Idris & Malina Osman & Surianti Sukeri & Zainudin A, 2018. "Leptospirosis Health Intervention Module Effect on Knowledge, Attitude, Belief, and Practice among Wet Market Workers in Northeastern Malaysia: An Intervention Study," IJERPH, MDPI, vol. 15(7), pages 1-12, July.
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