Mathematical Model on Optimal Combination of Vaccination and Antiviral Therapy to Curb Inuenza in Kenya
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Date
2020
Authors
Nzioki, Derrick M.
Gatoto, James K.
Journal Title
Journal ISSN
Volume Title
Publisher
jamcs
Abstract
Human influenza is a contagious disease which, if proper precautions are not taken to control the
disease, can lead to massive mortality rates and high costs will be incurred to control the disease
in case of an outbreak. As a result, we investigate how the cost of implementing both vaccination
and antiviral therapy can be minimized and at the same time minimize the number of infected
individuals. We have developed a system of ordinary differential equations from our formulated
SVIR model and used vaccination and antiviral therapy to study influenza dynamics. We have
the basic reproductive number determined using the next generation matrix. The equilibria and
stability of the model has also been determined and analyzed. We have used the maximization
theory of Pontryagin to define the optimal control rates and then used MATLAB program to do
the numerical simulations. The numerical simulations done indicate that an ideal combination
of vaccination and antiviral therapy decreases the number of infected individuals which in turn
reduces the cost of applying the two control measures.
Description
article
Keywords
Influenza, antiviral therapy, vaccination, reproduction number, stability, optimal control, numerical simulation
Citation
Nzioki, D. M., & Gatoto, J. K. (2020). Mathematical Model on Optimal Combination of Vaccination and Antiviral Therapy to Curb In uenza in Kenya. Journal of Advances in Mathematics and Computer Science, 35(5), 134-147.