Successive pandemic waves with more virulent strains, and the effects of vaccination for SARS-CoV-2

Castro e Silva, A.; Bernardes, A. T.; Barbosa, E.; Dattilo, W.; Ribeiro, S. P.

Hundred years after the flu pandemic of 1918, the world faces an outbreak of a new severe acute respiratory syndrome, caused by a novel coronavirus. With a high transmissibility, the pandemic spreads worldwide, creating a scenario of devastation in many countries. By middle of 2021, about $3%$ of the world population has been infected and more than 4 million people have died. Different from the $H_1N_1$ pandemic, which had a deadly wave and cessed, the new disease is maintained by successive waves, mainly produced by new virus variants, and the small number of vaccinated people. In the present work, we create a version of the SIR model with spatial localization of persons, their movements, and taking into account social isolation probabilities. We discuss the effects of virus variants, and the role of vaccination rate in the pandemic dynamics. We show that, unless a global vaccination is implemented, we will have continuous waves of infections.