# Optimal Control of Hand, Foot and Mouth Disease Model using Variational Iteration Method

Document Type : Full Length Article

Authors

1 Department of Mathematics, Stella Maris College, Chennai - 600 086

2 Department of Mathematics, Stella Maris College, chennai - 600086

Abstract

In this paper, the optimal control of transmission dynamics of hand, foot and mouth disease (HFMD), formulated by a compartmental deterministic SEIPR (Susceptible-Incubation (Exposed)- Infected - Post infection virus shedding - Recovered) model with vaccination and treatment as control parameters is considered. The objective function is based on the combination of minimizing the number of infected individuals and the cost involved in the interventions of vaccination given to the susceptible population and treatment given to the infected population. The existence for the optimal control pair is proved and the characterization of the optimal control pair is obtained by applying the Pontryagin's maximum principle.
The variational iteration method is adopted to solve the non-linear Hamilton equations derived from the Pontryagin's maximum principle theory. These equations constitute a two-point boundary value problem. By considering the correction functionals of the Hamilton equations, the Lagrange multipliers are easily identified and practical iteration formulas are derived. An algorithm is developed, based on this formulas,
to determine iteratively the solutions of the Hamilton equations with a desired accuracy. With the aid of solutions obtained, the optimal control law can be easily deduced. The results were analyzed and interpreted graphically using Maple.

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