Analysis and application of some mathematical models with numerical methods

In this study, we investigated Covid-19 in Turkey epidemic and made predictions about its spread. Applying Covid-19 data to the logistic growth model and SIR model, we have tried to estimate the parameters that can be used to quantify the temporal evolution of Covid-19 in the country using Taylor matrix and collocation method. Moreover, we thought that modeling the epidemic with fixed parameters was not very accurate, considering the change in the number of cases as a result of the government interventions and that more accurate predictions could be made when the parameters were calculated dynamically instead. We focused on a dynamic SIR model in which the recovery rate is fixed at 1/15, but the spread rate is dependent on the interventions made rather than being constant. While developing the model, we first determined the change points according to the number of cases with CPA, then considering that the frequency of cases is greatly affected by the timing of action and that symptoms of Covid-19 infection, such as mild respiratory symptoms and fever, begin to appear 5-6 days after infection, we matched the change points with the times of the intervations. We estimated the spread rates for each range of change points within the scope of these interventions. With the results of the Kruskall Wallis test, we determined that the reason for the difference in the model's spread rates were these intervations made with %95 confidence. Moreover, with the Non-parametric Dunn's test, it was obtained that there were significant differences between full closure and partial closure, as well as between full closure and gradual normalization, with %99 confidence. This also shows that there is a significant difference in the number of cases that may occur with full closure compared to the number of cases after partial closure and gradual normalization.