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In this paper, we present a new method for successfully simulating the dynamics of COVID-19, experimentally focusing on the third wave. This method, namely, the Method of Parallel Trajectories (MPT), is based on the recently introduced self-organized diffusion model. According to this method, accurate simulation of the dynamics of the COVID-19 infected population evolution is accomplished by considering not the total data for the infected population, but successive segments of it. By changing the initial conditions with which each segment of the simulation is produced, we achieve close and detailed monitoring of the evolution of the pandemic, providing a tool for evaluating the overall situation and the fine-tuning of the restrictive measures. Finally, the application of the proposed MPT on simulating the pandemic's third wave dynamics in Greece and Italy is presented, verifying the method's effectiveness. [ABSTRACT FROM AUTHOR]