Analysis of Listeriosis Transmission Dynamics with Optimal Control - Applied Mathematics

AM > Vol.11 No.7, July 2020

Applied Mathematics

Volume 11, Issue 7 (July 2020)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

Analysis of Listeriosis Transmission Dynamics with Optimal Control ()

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DOI: 10.4236/am.2020.117048 524 Downloads 1,851 Views Citations

Author(s)

Shaibu Osman¹, Dominic Otoo², Charles Sebil^3*

Affiliation(s)

¹Department of Basic Sciences, School of Basic and Biomedical Sciences, University of Health and Allied Sciences, Ho, Ghana.
²Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, Ghana.
³Department of Mathematics, Kwame Nkrumah University of Science and Technology, Private Mail Bag, Kumasi, Ghana.

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.

KEYWORDS

Listeriosis Model, Basic Reproductive Number, Optimal Control, Pontryagin’s Maximum Principle, Cost Effectiveness

Share and Cite:

Osman, S. , Otoo, D. and Sebil, C. (2020) Analysis of Listeriosis Transmission Dynamics with Optimal Control. Applied Mathematics, 11, 712-737. doi: 10.4236/am.2020.117048.

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