Mathematical modelling of epidemic diseases

Various epidemics, which started in certain parts of the world from time to time due to many reasons such as earthquakes, floods, wars and environmental pollution, have caused great losses for human beings. Mathematical models were used to visualize the progress of infectious diseases. First of all, with the SIR model as a first mathematical model, other mathematical models which is obtained by adding different categories to this model were examined. Numerical methods were used in the solution of these models which include differential equations expressing the change with respect to time. In addition, Covid-19 disease, which causes pandemics all over the world, is highly contagious and can result in death, has been modelled by including vaccine parameters in the mathematical models in the literature. The numerical solutions of this model was compared with real data in the framework of Türkiye during a determined period. The effect of the vaccine on the process of Covid-19 disease, which is easily and highly contagious in both urban and social life, was investigated in the SVIR model, which was obtained by adding the vaccine as a new category.