Title: A mathematical model and optimal control for Listeriosis disease from ready-to-eat food products

Authors: C.W. Chukwu; F. Nyabadza; J.K.K. Asamoah

Addresses: Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, Kingsway Campus, P.O. Box 524, 2006, Johannesburg, South Africa ' Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, Kingsway Campus, P.O. Box 524, 2006, Johannesburg, South Africa ' Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

Abstract: Ready-to-eat food (RTE) are foods that are intended by the producers for direct human consumption without the need for further preparation. In the present study, a deterministic model of Listeriosis disease transmission dynamics with control measures is analysed. Equilibrium points of the model in the absence of control measures were determined, and their local stabilities established. We formulate an optimal control problem and analytically give sufficient conditions for the optimality. The transversality conditions for the model with controls are also given. Numerical simulations of the optimal control strategies were performed to illustrate the results. The numerical findings suggest that the constant implementation of 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 from RTE food products.

Keywords: Listeria; contaminated food products; food contamination threshold; optimal control interventions; numerical simulations.

DOI: 10.1504/IJCSM.2023.130421

International Journal of Computing Science and Mathematics, 2023 Vol.17 No.1, pp.39 - 49

Received: 17 Aug 2020
Accepted: 19 Oct 2020
Published online: 20 Apr 2023 *