Abstract
Listeriosis is a food-borne disease that mainly affects pregnant women and newborns. We propose and analyze a deterministic model of Listeriosis by considering three groups of individuals: newborns, pregnant women, and others. Mathematical analysis of the model is performed, and equilibrium points are determined. The model has three equilibria, namely, the disease-free equilibrium, the bacteria-free equilibrium, and the endemic equilibrium. We use Castillo-Chavez theorem to establish the global stability of the disease-free equilibrium when the basic reproduction number is less than 1. The local asymptotic stability of the bacteria-free, and endemic equilibria are also established using the sign of the eigenvalues of the Jacobian matrix. We use the non-standard finite difference scheme and carried numerical simulations to confirm the theoretical results. We further show the impact of specific parameters on the dynamics of infectious individuals and observe that intervention is required in all the sub-populations by reducing the contact rate and vertical transmission to mininmize the number of infectious.
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