OPTIMAL CONTROL ANALYSIS OF A SEIV EPIDEMIC MODEL WITH VACCINATION AND EDUCATION

Abstract

This paper discusses optimal control of a mathematical epidemic model governed by an ODE system with saturated incidence rate.  An epidemic model is developed using optimal control theory by dividing the population into Susceptible, Exposed, Infected, and Vaccinated (SEIV) sub populations.  In the model we assume that half of new born individual have been vaccinated. Optimal control is conducted by adding two control variables namely vaccination and education. The aim of optimal control is to minimize the density of exposed subpopulation, infected subpopulation, and the cost of control. Optimal control is obtained by applying Pontryagin minimum principle. Furthermore, the optimal control problem is solved numerically by using Forward-Backward Sweep method. Three approaches were used to conduct numerical simulations, applying vaccination control without education, applying education control without vaccination, and using both vaccination and education control. There are Numerical simulations show that vaccination and education are effective in reducing exposed and infected subpopulation.