Oseloka Okey (Professor)Zewdie Esayas2018-06-182023-11-182018-06-182023-11-182015-04http://etd.aau.edu.et/handle/12345678/1204Epidemiological 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.enComputationalThesis