Mathematical Model on Optimal Combination of Vaccination and Antiviral Therapy to Curb In uenza in Kenya

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.