A Theoretical Model of Listeriosis Driven by Cross Contamination of Ready-to-Eat Food Products

Abstract

Cross contamination that results in food-borne disease outbreaks remains a major problem in processed foods globally. In this paper, a mathematical model that takes into consideration cross contamination of Listeria monocytogenes from a food processing plant environment is formulated using a system of ordinary differential equations. The model has three equilibria: the disease-free equilibrium, Listeria-free equilibrium, and endemic equilibrium points. A contamination threshold ℛwf is determined. Analysis of the model shows that the disease-free equilibrium point is locally stable for ℛwf<1 while the Listeria-free and endemic equilibria are locally stable for ℛwf>1. The time-dependent sensitivity analysis is performed using Latin hypercube sampling to determine model input parameters that significantly affect the severity of the listeriosis. Numerical simulations are carried out, and the results are discussed. The results show that a reduction in the number of contaminated workers and removal of contaminated food products are essential in eliminating the disease in the human population and vice versa. The results have significant public health implications in the management and containment of any listeriosis disease outbreak.

A Mathematical Model and Optimal Control for Listeriosis Disease from Ready-to-Eat Food Products

“…But before the sensitivity analysis, we explain how the parameter values were obtained. There are very limited resources of mathematical models and in literature based on Listeriosis disease epidemics, as a result most of the parameters values used in this work given in Table 1 were estimated except for the food product removal rate μ f = 0.0099 which is from Chukwu and Nyabadza (2020). We used the fourth order Runge-Kutta numerical scheme in Matlab with a unit time step one (1) to carry out the simulations with the following initial conditions; s (0) = 0.6, i (0) = 0.3, l m (0) = 0.1, f u = 0.7, f c = 0.3, which initial conditions are chosen hypothetically for illustrative purposes and do not reflect real-life applications.…”

“…Recently, mathematical models have been used to study the transmission dynamics of Listeriosis (see for example Stout et al (2020); Otoo et al (2020); Osman et al (2018); Witbooi etal. (2020); Chukwu and Nyabadza (2020)). In particular, Otoo et al (2020) studied the optimal control of Listriosis with system of equations describing the disease transmission in both human and animal populations.…”

Modelling the Potential Role of Media Campaigns on the Control of Listeriosis

“…Similarly, substituting all the expressions from equations (14) into the first equation of (7), and after some algebraic manipulations we obtain the following quadratic equation in terms…”

“…To date, there are very few mathematical models on the dynamics of Listeriosis (see, for instance, [11][12][13][14]), let alone those investigating the potential role of media awareness campaigns on the dynam ics of Listeriosis. This paper is motivated by the work done in [17].…”

“…Human beings contract Listeriosis through the ingestion of contaminated RTE food products such as cantaloupes, meat, Ricotta Salata cheese, vegetables, polony, bean sprouts, ham, or directly from the environment [3, 4]. The epidemiology of Listeriosis is clearly articulated in [1, 4, 14].…”