Epidemiological Modeling of Measles Disease with Optimal Control of Vaccination Strategy
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Date
2015-04
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Addis Ababa University
Abstract
Epidemiological models provide a powerful tool for investigating the dynamics and control of
infectious diseases, but quantifying the underlying epidemic structure can be challenging
especially for new and under-studied diseases. Measles is a highly infectious disease which has
a major impact on child survival, particularly in developing countries. The importance of
understanding the epidemiology of this disease is underlined by its ability to change rapidly in
the face of increasing immunization coverage with proper cost effectiveness. Much is still to be
learned about its epidemiology and the best strategies for administering measles vaccines.
However, it is clear that tremendous progress can be made in preventing death and disease
from measles with existing knowledge about the disease, and by using the presently available
vaccines and applying well-tried methods of treating cases. Since vaccination turned out to be
the most effective strategy against childhood disease, developing a framework that would
predict an optimal vaccine coverage level needed to control the spread of these diseases is
crucial. We consider an optimal control problem subject to an SEIR measles epidemic model
with vaccination controls. Our aim is find the best optimal control strategies to make the number
of infectious individuals as small as possible and to keep the vaccination ratio of measles as low
as possible during a certain vaccination period that will minimize the cost of control. We used
Pontryagin’s maximum principle to characterize the optimal levels of the controls. The resulting
optimality system is solved numerically by forward-backward sweep method. The results show
that the optimal vaccination policy differs according to the controlled and uncontrolled
individuals and has a very desirable effect upon the population for reducing the number of
infected individuals. The effect of vaccination on transmission dynamics of measles is studied.
The resulting optimality system also showed that, the use of vaccinating at the highest possible
rate to the population as early as possible is essential for controlling an epidemic of the measles
disease. Finally, we use our model to simulate the data of measles cases in the Ethiopia from
2004 to 2014 and design a control strategy (optimal vaccination policy) of the country to
eliminate the epidemic for the future course with optimal control theory. The results from our
simulation are discussed.
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Computational