Dynamics of Salmonellosis and the impacts of contaminated dairy products and environments: Mathematical modeling perspective and parameter estimation

This study proposes a system of non-linear ordinary differential equations (ODEs) based on a SIR-type epidemic model to explore the role that humans and dairy cattle play in the contamination process and the effects of contaminated dairy products and environments in salmonellosis dynamics. The driving force behind using a system of non-linear ODEs lies in their ability to accurately capture biological complexity, such as population interactions, which are inherently non-linear. The positivity of model solutions is checked to ensure their mathematical and biological compatibility. The Lyapunov stability theorem is used to examine the global stability of the equilibria states based on the value of a threshold parameter $R_0$, also known as the basic reproduction number, which is formulated using the next generation matrix approach. Parameter estimation and model fitting are done using the least squares method along with the salmonellosis incidence data from 1990 to 2020. The uncertainty and global sensitivity analysis are performed using the Latin hypercube sampling and partial rank correlation coefficients methods. The dynamics of $R_0$ along with model parameters responsible for contamination are explored using contour plots. The proposed model is simulated with a statistical range of 95% confidence interval to assess the reliability and precision of the estimates derived from the real data. The simulations are performed to explore the complex scenarios and forecast the dynamics of salmonellosis. The results show that the bacteria growth rate, ingestion rates of Salmonella typhimurium bacteria in contaminated dairy products and environments, shedding rates of Salmonella typhimurium into the environments by the infected humans and dairy cattle, and the harvesting rate of contaminated dairy products are directly proportional to $R_0$, meaning that they are responsible for increasing the severity of salmonellosis whenever they are increased, while the decay rates of Salmonella typhimurium bacteria are inversely proportional to $R_0$. Control measures such as hand hygiene, food preparation cleanliness, cooking food thoroughly, isolating sick and new animals, and training farmers on symptom recognition and reporting cases to medical staff are recommended to mitigate the severity of salmonellosis.