IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i2p322-d1571239.html
   My bibliography  Save this article

Seasonal Mathematical Model of Salmonellosis Transmission and the Role of Contaminated Environments and Food Products

Author

Listed:
  • Mohammed H. Alharbi

    (Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Fawaz K. Alalhareth

    (Department of Mathematics, College of Arts and Sciences, Najran University, Najran 55461, Saudi Arabia
    These authors contributed equally to this work.)

  • Mahmoud A. Ibrahim

    (Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., 6720 Szeged, Hungary
    National Laboratory for Health Security, University of Szeged, Aradi vértanúk tere 1., 6720 Szeged, Hungary
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
    These authors contributed equally to this work.)

Abstract

Salmonellosis continues to be a global public health priority in which humans, livestock, and the contaminated environment interact with food to create complex interactions. Here, a new non-autonomous model is proposed to capture seasonal dynamics of Salmonella typhimurium transmission with key compartments that include humans, cattle, and bacteria in environmental and food sources. The model explores how bacterial growth, shedding, and ingestion rates, along with contamination pathways, determine disease dynamics. Some analytical derivations of the basic reproduction number ( R 0 ) and threshold conditions for disease persistence or extinction are derived by using the spectral radius of a linear operator associated with the monodromy matrix. Parameter estimation for the model was accomplished with the aid of Latin hypercube sampling and least squares methods on Salmonella outbreak data from Saudi Arabia ranging from 2018 to 2021. The model was able to conduct an analysis based on the estimated 0.606 value of R 0 , and this meant that the model was able to fit reasonably well for both the cumulative and the new individual case data, which in turn, suggests the disease is curable. Predictions indicate a gradual decline in the number of new cases, with stabilization anticipated at approximately 40,000 cumulative cases. Further simulations examined the dynamics of disease extinction and persistence based on R 0 . When R 0 is less than 1, the disease-free equilibrium is stable, resulting in the extinction of the disease. Conversely, when R 0 exceeds 1, the disease persists, exhibiting endemic characteristics with recurrent outbreaks. Sensitivity analysis identified several parameters as having a significant impact on the model’s outcomes, specifically mortality and infection rates, along with decay rates. These findings highlight the critical importance of precise parameter estimation in understanding and controlling the transmission dynamics of Salmonella. Sensitivity indices and contour plots were employed to assess the impact of various parameters on the basic reproduction number and provide insights into the factors most influencing disease transmission.

Suggested Citation

  • Mohammed H. Alharbi & Fawaz K. Alalhareth & Mahmoud A. Ibrahim, 2025. "Seasonal Mathematical Model of Salmonellosis Transmission and the Role of Contaminated Environments and Food Products," Mathematics, MDPI, vol. 13(2), pages 1-26, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:322-:d:1571239
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/2/322/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/2/322/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrea Saltelli, 2002. "Sensitivity Analysis for Importance Assessment," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 579-590, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Makam, Vaishno Devi & Millossovich, Pietro & Tsanakas, Andreas, 2021. "Sensitivity analysis with χ2-divergences," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 372-383.
    2. S. Cucurachi & E. Borgonovo & R. Heijungs, 2016. "A Protocol for the Global Sensitivity Analysis of Impact Assessment Models in Life Cycle Assessment," Risk Analysis, John Wiley & Sons, vol. 36(2), pages 357-377, February.
    3. Kunz, Nathan & Chesney, Thomas & Trautrims, Alexander & Gold, Stefan, 2023. "Adoption and transferability of joint interventions to fight modern slavery in food supply chains," International Journal of Production Economics, Elsevier, vol. 258(C).
    4. Yun, Wanying & Lu, Zhenzhou & Feng, Kaixuan & Li, Luyi, 2019. "An elaborate algorithm for analyzing the Borgonovo moment-independent sensitivity by replacing the probability density function estimation with the probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 99-108.
    5. Gonnet, Gaston H. & Stewart, John & Lafleur, Joseph & Keith, Stephen & McLellan, Mark & Jiang-Gorsline, David & Snider, Tim, 2021. "Analysis of feature influence on Covid-19 Death Rate Per Country Using a Novel Orthogonalization Technique," MetaArXiv 4kw2n, Center for Open Science.
    6. Abdur Rahim Hamidi & Jiangwei Wang & Shiyao Guo & Zhongping Zeng, 2020. "Flood vulnerability assessment using MOVE framework: a case study of the northern part of district Peshawar, Pakistan," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 101(2), pages 385-408, March.
    7. Kamoonpuri, Sana Zehra & Sengar, Anita, 2023. "Hi, May AI help you? An analysis of the barriers impeding the implementation and use of artificial intelligence-enabled virtual assistants in retail," Journal of Retailing and Consumer Services, Elsevier, vol. 72(C).
    8. Chen, Yaqian & Nakao, Hiroya & Kang, Yanmei, 2024. "Emergence of pathological beta oscillation and its uncertainty quantification in a time-delayed feedback Parkinsonian model," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    9. Li, Haihe & Wang, Pan & Huang, Xiaoyu & Zhang, Zheng & Zhou, Changcong & Yue, Zhufeng, 2021. "Vine copula-based parametric sensitivity analysis of failure probability-based importance measure in the presence of multidimensional dependencies," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    10. Emanuele Borgonovo, 2006. "Measuring Uncertainty Importance: Investigation and Comparison of Alternative Approaches," Risk Analysis, John Wiley & Sons, vol. 26(5), pages 1349-1361, October.
    11. Jung, WoongHee & Taflanidis, Alexandros A., 2023. "Efficient global sensitivity analysis for high-dimensional outputs combining data-driven probability models and dimensionality reduction," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    12. Paleari, Livia & Movedi, Ermes & Zoli, Michele & Burato, Andrea & Cecconi, Irene & Errahouly, Jabir & Pecollo, Eleonora & Sorvillo, Carla & Confalonieri, Roberto, 2021. "Sensitivity analysis using Morris: Just screening or an effective ranking method?," Ecological Modelling, Elsevier, vol. 455(C).
    13. Aguirre-Zapata, Estefania & Alvarez, Hernan & Lema-Perez, Laura & di Sciascio, Fernando & Amicarelli, Adriana N., 2024. "Interpretability in the modeling spectrum: A conceptual framework and a quantification index," Ecological Modelling, Elsevier, vol. 498(C).
    14. Mohammed H. Alharbi & Fawaz K. Alalhareth & Mahmoud A. Ibrahim, 2023. "Analyzing the Dynamics of a Periodic Typhoid Fever Transmission Model with Imperfect Vaccination," Mathematics, MDPI, vol. 11(15), pages 1-26, July.
    15. Liu, Xing & Ferrario, Elisa & Zio, Enrico, 2019. "Identifying resilient-important elements in interdependent critical infrastructures by sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 423-434.
    16. WoongHee Jung & Aikaterini P. Kyprioti & Ehsan Adeli & Alexandros A. Taflanidis, 2023. "Exploring the sensitivity of probabilistic surge estimates to forecast errors," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 115(2), pages 1371-1409, January.
    17. Hanthanan Arachchilage, Kalpana & Hussaini, Mohammed Yousuff, 2021. "Ranking non-pharmaceutical interventions against Covid-19 global pandemic using global sensitivity analysis—Effect on number of deaths," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    18. Mariem Ellouze & Jean‐Pierre Gauchi & Jean‐Christophe Augustin, 2010. "Global Sensitivity Analysis Applied to a Contamination Assessment Model of Listeria monocytogenes in Cold Smoked Salmon at Consumption," Risk Analysis, John Wiley & Sons, vol. 30(5), pages 841-852, May.
    19. Ma, Yuan-Zhuo & Jin, Xiang-Xiang & Zhao, Xiang & Li, Hong-Shuang & Zhao, Zhen-Zhou & Xu, Chang, 2024. "Reliability-oriented global sensitivity analysis using subset simulation and space partition," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    20. Francesco Polese & Carmen Gallucci & Luca Carrubbo & Rosalia Santulli, 2021. "Predictive Maintenance as a Driver for Corporate Sustainability: Evidence from a Public-Private Co-Financed R&D Project," Sustainability, MDPI, vol. 13(11), pages 1-21, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:322-:d:1571239. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.