@article {Castro-e-Silva2021.09.21.21263901,
	title = {Successive pandemic waves with more virulent strains, and the effects of vaccination for SARS-CoV-2},
	journal = {medRxiv},
	year = {2021},
	publisher = {Cold Spring Harbor Laboratory Press},
	abstract = {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 the middle of 2021, about 3\% of the world population has been infected and more than 4 million people have died. Different from the H1N1 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.HighlightsThe COVID-19 has infected more than 200 millions and has killed more than 4 million persons.WHO has not been successful in defining a global vaccination policy.Many epidemic scenarios arise when different countries apply different vaccination strategies.Present model can show some insights on how vaccination programs can be managed.Competing Interest StatementThe authors have declared no competing interest.Funding StatementThis research did not receive any specific grant from funding agencies in the commercial, or non-profit sectors. SPR acknowledges grant from Conselho Nacional de Desenvolvimento Cientifico e Tecnologico - CNPq, through proccess 306572/2019-2.Author DeclarationsI confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.YesThe details of the IRB/oversight body that provided approval or exemption for the research described are given below:The manuscript is a modeling paper, there was no clinical trial of any kind.All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived.YesI understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).YesI have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable.YesThe code of model is included in manuscript files.},
	doi = {10.1101/2021.09.21.21263901},
	url = {https://www.medrxiv.org/content/early/2021/09/24/2021.09.21.21263901},
	author = {Castro-e-Silva, Alcides and Bernardes, Am{\'e}rico T and Gon\c calves Barbosa, Eduardo Augusto and D{\'a}ttilo, Wesley and S{\'E}RVIO P. RIBEIRO}
}
