A fractional mathematical model for listeriosis infection using two kernels

Abstract

Listeriosis is a life-threatening illness that can be spread through contaminated food. The bacteria responsible for this disease is Listeria monocytogenes. The annual incidence rate ranges from less than one to more than ten per one million persons in different parts of the world. Despite the low incidence of listeriosis, the high mortality rate linked with the disease makes it a major public health problem. In this paper, we present an investigation of a nonlinear fractional mathematical model of listeriosis infection using two fractional kernels. To analyse the existence of the fractional model, we employ the fixed point technique, whereas stability is determined using the Hyers–Ulam analysis. The fractional model is numerically investigated using the Caputo–Fabrizio and Atangana-Baleanu-Caputo fractional kernels. The numerical results reveal that the Mittag- Leffler kernel captures fewer human infections than the exponential kernel. In other simulations, we presented the trajectory impacts of varying environmental transmission rates, the rate of infected human recovery, the rate at which uncontaminated food becomes contaminated, and the net growth rate of Listeria monocytogenes on all the affected compartments. We observed that these parameters in the model give distinct disease pathways (a unique rate of convergence), unlike the integer model. Furthermore, the exponential kernel shows more dynamics of contaminated foods than the Mittag-Leffler kernel, which indicates that an increase in contaminated food could lead to a high spread of listeriosis. Finally, we noticed the reduction in the rate of uncontaminated food becoming contaminated increases the number of recovered individuals.