MATHEMATICAL ANALYSIS OF A RISK STRUCTURED LISTERIOSIS DYNAMICS MODEL
Abstract
A foodborne disease called listeriosis is brought on by the bacteria Listeria monocytogenes which typically infects people after consuming contaminated food. Listeriosis mostly affects people with weakened immune systems, pregnant women and newborns. In this paper, we developed and analyzed a risk-structured mathematical model describing the dynamics of Listeriosis using ordinary differential equations. Three equilibrium points were obtained, viz; disease free equilibrium point, , bacteria free equilibrium point, , and endemic equilibrium point, . Contaminated food threshold was established as . The disease-free equilibrium and Bacteria-free equilibrium points are found to be locally asymptotically stable whenever the contaminated food threshold is less than unity (). Also, the endemic equilibrium point is found to be locally asymptotically stable using the Routh-Hurwitz criterion whenever the food safety index is less than unity (). Global stability analysis of the disease-free equilibrium point using Castillo-Chavez method revealed that the disease-free equilibrium point, is globally asymptotically stable.
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