Effects of Isoperimetric Constraint for Reducing HSV-2 Infection Using Optimal Control Strategy

Abstract

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.