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

Festus Abiodun Oguntolu, Olumuyiwa James Peter (), Benjamin Idoko Omede, Ghaniyyat Bolanle Balogun and Tawakalt Abosede Ayoola
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Festus Abiodun Oguntolu: Federal University of Technology
Olumuyiwa James Peter: 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

Quality & Quantity: International Journal of Methodology, 2025, vol. 59, issue 2, No 17, 1405-1444

Abstract: 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.

Keywords: Leptospirosis; Basic reproduction number; Stability; Sensitivity analysis; Bifurcation; 92B05; 92D30; 92-10; 34D20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11135-024-02016-3

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