Modeling and controlling Leptospirosis transmission in humans and rodents

Volume 39, Issue 1, pp 30--49 https://dx.doi.org/10.22436/jmcs.039.01.03

Publication Date: March 06, 2025 Submission Date: October 06, 2024 Revision Date: November 11, 2024 Accteptance Date: December 10, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 93 Downloads
• 337 Views

Authors

V. Saravanan - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamilnadu-600 127, India. R. Chinnathambi - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamilnadu-600 127, India. F. A. Rihan - Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain, 15551, UAE.

Abstract

Leptospirosis is a commonly undiagnosed and under-reported bacterial disease that affects both animals and humans. Studies suggest that the risk of infection varies based on individuals' occupations and living environments. This study employs a mathematical model that assesses the impact of rodent-borne diseases on human populations. A disease-causing agent in the environment can lead to human infection. Additionally, humans can become infected by interacting with infected rodents. The purpose of this paper is to construct a SIR (human)-SI (rodent) model of bacterial populations with Holling type II functional responses, as well as chemical disinfectants. Infection-free and endemic steady states are examined for positivity, boundedness of solutions, and stability. The disease transmission is reduced through non-pharmaceutical interventions as well as the infected rodent populations are controlled by integrated pest management. Using sensitivity analysis, we evaluate the effect of parameters' uncertainty. We study the optimal conditions to reduce bacterial density in the environment by considering control variables as chemical disinfectants and treatment functions. Numerical simulations confirm the theoretical findings.

Share and Cite

Keywords

• Integrated pest management
• leptospirosis
• non-pharmaceutical intervention
• optimal control
• sensitivity analysis
• stability

MSC

•  34D20
•  37N35
•  65P40
•  90C31
•  92B05

References

• [1] H. T. Alemneh, A co-infection model of dengue and leptospirosis diseases, Adv. Difference Equ., 2020 (2020), 23 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [2] Antima, S. Banerjee, Modeling the dynamics of leptospirosis in India, Sci. Rep., 13 (2023), 15 pages
  • View Article
  • Google Scholar


• [3] G. P. Balakrishnan, R. Chinnathambi, F. A. Rihan, A fractional-order control model for diabetes with restraining and time-delay, J. Appl. Math. Comput., 69 (2023), 3403–3420
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] C. Benjamín, P. Luis, C.-L. Fernando, Modeling the effects of pH variation and bacteriocin synthesis on bacterial growth, Appl. Math. Model., 110 (2022), 285–297
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] A. Bhalraj, A. Azmi, M. H. Mohd, Analytical and numerical solutions of Leptospirosis model, Int. J. Math. Comput. Sci., 16 (2021), 949–961
  • View Article
  • Google Scholar
  • MATH


• [6] S. Chadsuthi, C. Modchang, Y. Lenbury, S. Iamsirithaworn, W. Triampo, Modeling seasonal leptospirosis transmission and its association with rainfall and temperature in Thailand using time-series and ARIMAX analyses, Asian Pac. J. Trop. Med., 5 (2012), 539–546
  • View Article
  • Google Scholar


• [7] J. Croda, A. N. D. Neto, R. A. Brasil, C. Pagliari, A. C. Nicodemo, M. I. S. Duarte, Leptospirosis pulmonary haemorrhage syndrome is associated with linear deposition of immunoglobulin and complement on the alveolar surface, Clin. Microbiol. Infect., 16 (2010), 593–599
  • View Article
  • Google Scholar


• [8] K. Das, R. Chinnathambi, M. N. Srinivas, F. A. Rihan, An analysis of time-delay epidemic model for TB, HIV, and AIDS co-infections, Results Control Optim., 12 (2023), 13 pages
  • View Article
  • Google Scholar


• [9] O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365–382
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] L. Douchet, C. Goarant, M. Mangeas, C. Menkes, S. Hinjoy, V. Herbreteau, Unraveling the invisible leptospirosis in mainland Southeast Asia and its fate under climate change, Sci. Total Environ., 832 (2022), 12 pages
  • View Article
  • Google Scholar


• [11] H. A. Engida, D. M. Theuri, D. K. Gathungu, J. Gachohi, Optimal control and cost-effectiveness analysis for leptospirosis epidemic, J. Biol. Dyn., 17 (2023), 20 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] H. A. Engida, D. M. Theuri, D. Gathungu, J. Gachohi, H. T. Alemneh, A mathematical model analysis for the transmission dynamics of leptospirosis disease in human and rodent populations, Comput. Math. Methods Med., 2022 (2022), 23 pages
  • View Article
  • Google Scholar


• [13] M. Farman, A. Akgül, M. Sultan, S. Riaz, H. Asif, P. Agarwal, M. K. Hassani, Numerical study and dynamics analysis of diabetes mellitus with co-infection of COVID-19 virus by using fractal fractional operator, Sci. Rep., 14 (2024), 19 pages
  • View Article
  • Google Scholar


• [14] M. Farman, N. Gokbulut, U. Hurdoganoglu, E. Hincal, K. Suer, Fractional order model of MRSA bacterial infection with real data fitting: Computational Analysis and Modeling, Comput. Biol. Med., 173 (2024),
  • View Article
  • Google Scholar


• [15] M. Farman, A. Shehzad, K. S. Nisar, E. Hincal, A. Akgul, A mathematical fractal-fractional model to control tuberculosis prevalence with sensitivity, stability, and simulation under feasible circumstances, Comput. Biol. Med., 178 (2024),
  • View Article
  • Google Scholar


• [16] D. I. Galan, A. A. Roess, S. V. C. Pereira, M. C. Schneider, Epidemiology of human leptospirosis in urban and rural areas of Brazil, 2000–2015, PLoS ONE, 16 (2021), 20 pages
  • View Article
  • Google Scholar


• [17] M. A. Gallega, M. V. Simoy, Mathematical modeling of leptospirosis: A dynamic regulated by environmental carrying capacity, Chaos Solitons Fractals, 152 (2021), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [18] R. K. Gupta, R. K. Rai, P. K. Tiwari, A. K. Misra, M. Martcheva, A mathematical model for the impact of disinfectants on the control of bacterial diseases, J. Biol. Dyn., 17 (2023), 28 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] M. A. Khan, S. F. Saddiq, S. Islam, I. Khan, S. Shafie, Dynamic Behavior of Leptospirosis Disease with Saturated Incidence Rate, Int. J. Appl. Comput. Math., 2 (2016), 435–452
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] S. Kundu, H. J. Alsakaji, F. A. Rihan, S. Maitra, R. K. Upadhyay, Investigating the dynamics of a delayed stagestructured epidemic model with saturated incidence and treatment functions, Eur. Phys. J. Plus, 137 (2022),
  • View Article
  • Google Scholar


• [21] S. Lenhart, J. T. Workman, Optimal control applied to biological models, Chapman & Hall/CRC, Boca Raton, FL (2007)
  • View Article
  • Google Scholar


• [22] Y.-H. Liu, Y.-H. Chen, C.-M. Chen, Fulminant Leptospirosis Presenting with Rapidly Developing Acute Renal Failure and Multiorgan Failure, Biomedicines, 12 (2024), 13 pages
  • View Article
  • Google Scholar


• [23] H. D. Ngoma, P. R. Kiogora, I. Chepkwony, A Fractional Order Model of Leptospirosis Transmission Dynamics with Environmental Compartment, Global J. Pure Appl. Math., 18 (2022), 81–110
  • View Article
  • Google Scholar


• [24] A. Ngwira, S. Manda, E. D. Karimuribo, S. I. Kimera, C. Stanley, Spatial analysis of livestock disease data in sub- Saharan Africa: A scoping review, Sci. Afr., 23 (2024), 14 pages
  • View Article
  • Google Scholar


• [25] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, E. F. Mishechenko, The mathematical theory of optimal processes, Interscience Publishers John Wiley & Sons, New York-London (1962)
  • View Article
  • Google Scholar


• [26] F. A. Rihan, Delay differential equations and applications to biology, Springer, Singapore (2021)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [27] U. A. M. Roslan, N. Y. Narayanan, Sensitivity analysis for the dynamics of Leptospirosis disease, Malays. J. Math. Sci., 13 (2019), 77–84
  • View Article
  • Google Scholar
  • MATH


• [28] S. Ullah, M. F. Khan, S. A. A. Shah, M. Farooq, M. A. Khan, M. B. Mamat, Optimal control analysis of vector-host model with saturated treatment, Eur. Phys. J. Plus, 135 (2020), 25 pages
  • View Article
  • Google Scholar
  • MATH


• [29] D. Vandroux, C. Chanareille, B. Delmas, B.-A. Gauzere, N. Allou, L. Raffray, M.-C. Jaffar-Bandjee, O. Martinet, C. Ferdynus, J. Jabot, Acute respiratory distress syndrome in leptospirosis, J. Crit. Care, 51 (2019), 165–169
  • View Article
  • Google Scholar


• [30] World Health Organization, Human leptospirosis: Guidance for diagnosis, Surveillance and control, , (2003),
  • View Article
  • Google Scholar


• [31] Y. Xu, Q. Ye, Human leptospirosis vaccines in China, Hum. Vaccines Immunother., 14 (2018), 984–993
  • View Article
  • Google Scholar