Ahmed Koura - Basic Science Department, Al-Safwa High Institute of Engineering, Egypt.
Kamal Raslsn - Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.
khalid k. Ali - Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt.
Mohamed Shaalan - Higher Technological Institute, Tenth of Ramadan City, Egypt.

The present article investigates a numerical analysis of COVID-۱۹ (temporal and spatio-tempora) lockdown-vaccination models. The proposed models consist of six nonlinear ordinary differential equations as a temporal model and six nonlinear partial differential equations as a spatio-temporal model. The evaluation of reproduction number is a forecast spread of the COVID-۱۹ pandemic. Sensitivity analysis is used to emphasize the importance of pandemic parameters. We show the stability regions of the disease-free equilibrium point and pandemic equilibrium point. We use effective methods such as central finite difference (CFD) and Runge-Kutta of fifth order (RK-۵). We apply Von-Neumann stability and consistency of the numerical scheme for the spatio-temporal model. We examine and compare the numerical results of the proposed models under various parameters.

COVID-۱۹ mathematical model, Reproduction number, Sensitivity analysis, Central finite method, Runge Kutta of fifth order method, Von-Neumann stability