Study of COVID-19 cases with real data analysis

In this work, patients of corona virus disease 2019, known as COVID-19, have been studied in Pakistan and its neighboring countries Iran, India and Afghanistan through the mathematical model in the form of coupled system of five ordinary differential equations. Two types of equilibria, infection free and endemic, are obtained. After the calculation of reproduction number, global stability of disease free equilibrium is proved using Lyapunov function theory where as graph theoretic approach is utilized to discuss the ultimate behavior of infection present constant level. Moreover, robustness of the model has been verified by applying it on the real data of COVID-19. Parameter values are obtained through the model calibration with the actual data for each country. To recognize the crucial factors, in disseminating or controlling the disease, sensitivity analysis of the reproduction number is performed by calculating the ratios of relative change in the parameters and corresponding difference in the value of basic reproduction number. Statistical method, based on the development of Autoregressive Integrated Moving Average (ARIMA) models, has also been applied on the available data. After testing different ARIMA models, the best fitted ones are identified.