Effects of Isoperimetric Constraint for Reducing HSV-2 Infection Using Optimal Control Strategy
Keywords:Herpes Simplex Virus Type-2 (HSV-2), Mathematical model, Optimal control, Characterization of the objective functional, Pontryagin’s Maximunm Principle, Optimality system, Hamiltonian (H), Isoperimetric constraint
Optimal control is helpful for testing and comparing different vaccination strategies of a certain disease. Genital herpes is one of the most prevalent sexually-transmitted diseases globally. In this paper, we have proposed an optimal control problem applied to HSV-2 model after introducing the constraint and state variables. Optimal control problem is formulated based on ordinary differential equation and isoperimetric constraint in the vaccine supply is also included. Mathematical analysis such as the characterization of optimal control using Pontryagin’s maximum principle is studied. Generally optimal control theory is used for finding the optimal way for implementing the strategies, minimizing the number of infectious and latent individuals and keeping the cost of implementation as low as possible. Here the optimality system is derived and solved numerically using a Runge-Kutta fourth order method and this is an iterative method. Using numerical simulation we observe that how the optimal vaccination schedule is altered by imposing isoperimetric constraint. Finally, on applying the isoperimetric constraint on the optimal control problem of HSV-2 epidemic model, we observe that optimal vaccination schedule with isoperimetric constraint indicates successful short-term control of the disease.
GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 62-68
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