MATHEMATICAL ANALYSIS OF A RISK STRUCTURED LISTERIOSIS DYNAMICS MODEL

Authors

  • M. Alkali
    Modibbo Adama University, Yola
  • Musa Abdullahi
    Modibbo Adama University, Yola
  • A. Alhassan
    Modibbo Adama University, Yola
  • S. Muhammad
    Modibbo Adama University, Yola
  • H. Zailani
    Modibbo Adama University, Yola

Keywords:

Listeria, Bacteria, Equilibria, Stability

Abstract

A foodborne disease called listeriosis is brought on by the bacteria Listeria monocytogenes which typically infects people after consuming contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, we developed and analyzed a risk-structured mathematical model describing the dynamics of Listeriosis using ordinary differential equations. Three equilibrium points were obtained, viz; disease free equilibrium point, , bacteria free equilibrium point, , and endemic equilibrium point, . Contaminated food threshold was established as . The disease-free equilibrium and Bacteria-free equilibrium points are found to be locally asymptotically stable whenever the contaminated food threshold is less than unity (). Also, the endemic equilibrium point is found to be locally asymptotically stable using the Routh-Hurwitz criterion whenever the food safety index is less than unity (). Global stability analysis of the disease-free equilibrium point using Castillo-Chavez method revealed that the disease-free equilibrium point,  is globally asymptotically stable.

Dimensions

Ajayeoba, T.A., Atanda, O.O., Obadina, A.O., Bankole, M.O., & Adelowo, O.O. (2016). The incidence and distribution of Listeria monocytogenes in ready- to-eat vegetables in South- Western Nigeria. Food Sci Nutr.4(1):5966.

Castillo-Chavez, C., Feng, Z. and Huang, W. (2002). On the Computation of RO and Its Role on Global Stability. In: Castillo-Chavez, P.C., Blower, S., Driessche, P., Kirschner, D. and Yakubu, A.-A., Eds., Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer, Berlin, 229. https://doi.org/10.1007/978-1-4757-3667-0_13

Chukwu, C.W., & Nyabadza, F. (2020). A theoretical model of listeriosis driven by cross contamination of ready-to-eat food products, Int. J. Math. Math. Sci. 14, http://dx.doi.org/10.1155/2020/9207403.

Cui, J., Sun, Y., & Zhu, H. (2007). The impact of media on the control of infectious diseases. Journal of Dynamics and Differential Equations, 20 (1), 31-53.

Danjuma R. U., Okolo P. N., & Dauda M. K. (2024). Mathematical Analysis of COVID-19 Infection model with demographic dynamics. FUDMA JOURNAL OF SCIENCES, 7(6), 92 - 103. https://doi.org/10.33003/fjs-2023-0706-2176

Ishola, O.O., Mosugu, J.I., & Adesokan, H.K. (2016). Prevalence and antibiotic susceptibility profiles of Listeria monocytogenes contamination of chicken flocks and meat in Oyo State, south-western Nigeria. J Prev Med Hyg.57(3):15763.

Iwu, C.D., & Okoh, I.A. (2020). Characterization of antibiogram fingerprints in Listeria monocytogenes recovered from irrigation water and agricultural soil samples. PLoS One. 10;15(2):e0228956. https://doi.org/10.1371/journal. pone.0228956.

Kunadu, A.P., Holmes, M., Miller, E.L., Grant, A.J. (2018). International Journal of Food Microbiology Microbiological quality and antimicrobial resistance characterization of Salmonella spp. in fresh milk value chains in Ghana. Int J Food Microbiol. 277(4):419. https://doi.org/10.1016/j.ijfoodmicro.201.8.04.025.

Ndahi, M.D., Kwaga, J.K.P., Bello, M., Kabir, J., Umoh, V.J., Yakubu, S.E., et al., (2014). Prevalence and antimicrobial susceptibility of Listeria monocytogenes and methicillin-resistant Staphylococcus aureus strains from raw meat and meat products in Zaria, Nigeria. Lett Appl Microbiol.58(3):2629. https://doi.org/10.1111/lam.12183.

Odu, N.N., & Okonko, I.O. (2017). Prevalence and antibiotic susceptibility of Listeria monocytogenes in retailed meats in Port Harcourt Metropolis. Nigeria Public Heal Res.7(4):919.

Osman, S., Makinde, O.D., & Theuri, D.M. (2018). Stability analysis and modelling of listeriosis dynamics in human and animal populations, Glob. J. Pure Appl. Math. 14 (1) (2018) 115137.

Osman, S., Otoo, D., Sebil, C.. & Makinde, O.D. (2020). Bifurcation, sensitivity and optimal control analysis of modelling anthrax-listeriosis co-dynamics, Commun. Math. Biol. Neurosci. http://dx.doi.org/10.28919/cmbn/5161.

Published

31-03-2025

How to Cite

MATHEMATICAL ANALYSIS OF A RISK STRUCTURED LISTERIOSIS DYNAMICS MODEL. (2025). FUDMA JOURNAL OF SCIENCES, 9(3), 302-308. https://doi.org/10.33003/fjs-2025-0903-3259

Issue

Vol. 9 No. 3 (2025): FUDMA Journal of Sciences - Vol. 9 No. 3

Section

Research Articles
Copyright & Licensing

FUDMA Journal of Sciences

How to Cite

MATHEMATICAL ANALYSIS OF A RISK STRUCTURED LISTERIOSIS DYNAMICS MODEL. (2025). FUDMA JOURNAL OF SCIENCES, 9(3), 302-308. https://doi.org/10.33003/fjs-2025-0903-3259

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