Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control.

Authors

  • Shaibu Osman Department of Mathematics, Pan African University, Institute for Basic Sciences, Technology and Innovations, Box 62000-00200, Nairobi-Kenya. https://orcid.org/0000-0003-3692-3846
  • Oluwole Daniel Makinde Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395.
  • David Mwangi Theuri Department of Mathematics, Jomo Kenyatta University of Agriculture and Technology, Nairo-Kenya, Box 62000-00200, Nairobi-Kenya.

DOI:

https://doi.org/10.5556/j.tkjm.51.2020.2860

Keywords:

Listeriosis, Backward bifurcation, endemic equilibrium, reproductive number, Pontryagin Maximum principle.

Abstract

Listeriosis is a serious disease caused by the germ Listeria monocytogenes. People usually become ill with listeriosis after eating contaminated food including meat. The disease primarily affects pregnant women, newborns, older adults, and people with weakened immune systems. In this paper, we propose and scrutinize a model problem describing the transmission dynamics of Listeriosis epidemic in animal and human population using the stability theory of differential equations. The model is qualitatively analysed for the basic reproduction number as well as possibility of forward and backward bifurcation with respect to the stability of disease free and endemic equilibria. The impact of the model parameters on the disease was evaluated via sensitivity analysis. An extension of the model to include time dependent control variables such as treatment, vaccination and education of susceptible (human) is carried out. Using Pontryagin’s Maximum Principle, we obtain the optimal control strategies needed for combating Listeriosis disease. Numerical simulation of the model is performed and pertinent results are displayed graphically and discussed quantitatively.

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Published

2020-11-01

How to Cite

Osman, S., Makinde, O. D., & Theuri, D. M. (2020). Mathematical Modelling of Listeriosis Epidemics in Animal and Human Population with Optimal Control. Tamkang Journal of Mathematics, 51(4), 261-287. https://doi.org/10.5556/j.tkjm.51.2020.2860

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