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

Abstract Ready-to-eat food (RTE) are foods that are intended by the producers for direct human consumption without the need for further preparation. The primary source of human Listeriosis is mainly through ingestion of contaminated RTE food products. Thus, implementing control strategies for Listeriosis infectious disease is vital for its management and eradication. In the present study, a deterministic model of Listeriosis disease transmission dynamics with control measures was analyzed. We assumed that humans are infected with Listeriosis either through ingestion of contaminated food products or directly with Listeria Monocytogenes in their environment. Equilibrium points of the model in the absence of control measures were determined, and their local asymptotic stability established. We formulate an optimal control problem and analytically give sufficient conditions for the optimality and the transversality conditions for the model with controls. Numerical simulations of the optimal control strategies were performed to illustrate the results. The numerical findings suggest that constant implementation of the joint optimal control measures throughout the modelling time will be more efficacious in controlling or reducing the Listeriosis disease. The results of this study can be used as baseline measures in controlling Listeriosis disease from ready-to-eat food products.