Epidemiological Modeling of Measles Infection with Optimal Control of Vaccination and Supportive Treatment

Abstract

We consider an SEIR model with constant population size and formulate an optimal control problem subject to vaccination and supportive treatment as controls. Our aim is to find the optimal combination of vaccination and supportive treatment strategies that will minimize the cost of the two control measures as well as the number of infectives while efficiently balancing vaccination and management of measles applied to the models with various cost scenarios. We used Pontryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal combination of the strategies required to achieve the set objective will depend on the relative cost of each of the control measures and the resulting optimality system showed that, the use of vaccinating and supportive treating at the same time at the highest possible rate to the population as early as possible is essential for controlling measles epidemic. The results from our simulation are discussed.