Modelling and optimal control analysis of typhoid fever

Tawakalt Abosede Ayoola, Helen Olaronke Edogbanya, Olumuyiwa James Peter, Festus Abiodun Oguntolu, Kayode Oshinubi, Mutiu Lawal Olaosebikan

Abstract


In this paper, we formulate a deterministic mathematical model to describe the transmission dynamics of typhoid fever by incorporating some control strategies. In order to study the impact of these control strategies on the dynamics of typhoid fever, the model captures vaccination and educational campaign as control variables. We show that the model is mathematically and epidemiologically well positioned in a biologically feasible region in human populations. We carry out a detailed analysis to determine the basic reproduction number  necessary for the control of the disease. The optimal control strategies are used to minimize the infected carriers and infected individuals and the adverse side effects of one or more of the control strategies. We derive a control problem and the conditions for optimal control of the disease using Pontryagin’s Maximum Principle and it was shown that an optimal control exists for the proposed model. The optimality system is solved numerically, the numerical simulation of the model shows that possible optimal control strategies become more effective in the control and containment of typhoid fever when vaccination and educational campaign are combined optimally would reduce the spread of the disease.

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Published: 2021-08-19

How to Cite this Article:

Tawakalt Abosede Ayoola, Helen Olaronke Edogbanya, Olumuyiwa James Peter, Festus Abiodun Oguntolu, Kayode Oshinubi, Mutiu Lawal Olaosebikan, Modelling and optimal control analysis of typhoid fever, J. Math. Comput. Sci., 11 (2021), 6666-6682

Copyright © 2021 Tawakalt Abosede Ayoola, Helen Olaronke Edogbanya, Olumuyiwa James Peter, Festus Abiodun Oguntolu, Kayode Oshinubi, Mutiu Lawal Olaosebikan. 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.

 

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