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

Mohammed H. Alharbi (), Fawaz K. Alalhareth and Mahmoud A. Ibrahim ()
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Mohammed H. Alharbi: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
Fawaz K. Alalhareth: Department of Mathematics, College of Arts and Sciences, Najran University, Najran 55461, Saudi Arabia
Mahmoud A. Ibrahim: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., 6720 Szeged, Hungary

Mathematics, 2025, vol. 13, issue 2, 1-26

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.

Keywords: Salmonella typhimurium; non-autonomous model; basic reproduction number (? 0 ); seasonal dynamics; sensitivity analysis; global stability; periodic solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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