TITLE:
Analysis of Listeriosis Transmission Dynamics with Optimal Control
AUTHORS:
Shaibu Osman, Dominic Otoo, Charles Sebil
KEYWORDS:
Listeriosis Model, Basic Reproductive Number, Optimal Control, Pontryagin’s Maximum Principle, Cost Effectiveness
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.7,
July
30,
2020
ABSTRACT: Listeriosis is an illness caused by the germ Listeria monocytogenes.
Generally, humans are infected with listeriosis after eating contaminated food.
Listeriosis mostly affects people with weakened immune systems, pregnant women
and newborns. In this paper, a model describing the dynamics of Listeriosis is developed and analysed using ordinary differential
equations. The model was analysed both quantitatively and qualitatively for its
local and global stability, basic reproductive number and parameter
contributions to the basic reproductive number to understand the impact of each
parameter on the disease spread. The Listeriosis model has been extended to
include time dependent control variables such as treatment of both humans and
animals, vaccination and education of humans. Pontryagin’s
Maximum Principle was introduced to obtain the best optimal control strategies
required for curbing Listeriosis infections. Numerical simulation was performed
and the results displayed graphically and discussed. Cost effectiveness
analysis was conducted using the intervention averted ratio (IAR) concepts and
it was revealed that the most effective intervention strategy is the treatment
of infected humans and animals.