Bifurcation, sensitivity and optimal control analysis of modelling Anthrax-Listeriosis co-dynamics

Shaibu Osman, Dominic Otoo, Charles Sebil, Oluwole Daniel Makinde

Abstract


In this paper, a deterministic model for the co-dynamics of Anthrax and Listerios diseases was formulated to investigate the qualitative and quantitative relationship of both diseases by incorporating prevention and treatment controls. The basic reproduction number, stability, existence and equilibria of each disease was investigated separately. The Anthrax-Listeriosis co-dynamics model was analysed and it the idea of backward bifurcation existed. The impact of Anthrax infection on the transmission of Listeriosis was determined. The Anthrax-Listeriosis co-dynamics model was extended and included time dependent control variables. Pontryagin’s Maximum Principle was used to obtain the optimal control strategies needed for eradication of Anthrax-Listeriosis infections. We performed the numerical simulation of the co-dynamics model in order to give the quantitative implications of the results. It was established that Anthrax infection can be attributed to increased risk of Listeriosis but Listeriosis infection is not associate with the risk of Anthrax. Effective control of Anthrax means incorporating both the intervention srategies of Anthrax and Listeriosis.

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Published: 2020-12-29

How to Cite this Article:

Shaibu Osman, Dominic Otoo, Charles Sebil, Oluwole Daniel Makinde, Bifurcation, sensitivity and optimal control analysis of modelling Anthrax-Listeriosis co-dynamics, Commun. Math. Biol. Neurosci., 2020 (2020), Article ID 98

Copyright © 2020 Shaibu Osman, Dominic Otoo, Charles Sebil, Oluwole Daniel Makinde. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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