Investigation of the effect of vaccination on pneumonia cases caused by COVID-19 in Turkey with mathematical models

In this study, the effect of vaccination on the evolution of the disease to pneumonia in the COVID-19 outbreak was investigated with a developed SEIR-type compartmental disease model. For the developed model, equilibrium points were determined, its stability was examined and the basic reproduction number was calculated. To reach the numerical solutions of the model, two periods of 62 days each were taken with the data obtained from the website of the T.C. Ministry of Health. Thus, the effectiveness of the vaccine was examined by comparing these two periods. Then, the graphs of the numerical solutions were created and their compatibility with the real data was examined. Afterwards, the model was transformed into a model with general fractional derivatives. Then the equilibrium points of the fractional model and the basic reproduction number were determined and also stability analysis was carried out. Finally, numerical solutions of this model were obtained separately for the fractional derivatives of Caputo, Caputo-Fabrizio and Atangana-Baleanu using the same data, and the solutions for different fractional orders were compared with each other.