ORIGINAL ARTICLE • Rev. bras. epidemiol. 26 01 Dec 20232023 • https://doi.org/10.1590/1980-549720230054   copy

Preventable COVID-19 cases and deaths by alternative vaccination and non-pharmacological intervention policies in Brazil

Casos e mortes evitáveis de COVID-19 por políticas de vacinação alternativas e intervenções não farmacológicas no Brasil

Samantha Rodrigues de Araújo João Flávio de Freitas Almeida Lásara Fabrícia Rodrigues Elaine Leandro Machado About the authors

ABSTRACT

Objective:

This work aimed to estimate the avoidable COVID-19 cases and deaths with the anticipation of vaccination, additional doses, and effective non-pharmacological interventions in Brazil.

Methods:

We developed a susceptible-exposed-infectious-recovered-susceptible model based on epidemiological indicators of morbidity and mortality derived from data obtained from the Health Information System of the Ministry of Health of Brazil. The number of cases and deaths was estimated for different scenarios of vaccination programs and non-pharmacological interventions in the states of Brazil (from March 8, 2020, to June 5, 2022).

Results:

The model-based estimate showed that 40 days of vaccination anticipation, additional vaccine doses, and a higher level the nonpharmacological interventions would reduce and delay the pandemic peak. The country would have 17,121,749 fewer COVID-19 cases and 391,647 avoidable deaths

Conclusion:

The results suggest that if 80% of the Brazilian population had been vaccinated by May 2021, 59.83% of deaths would have been avoided in Brazil.

Keywords
Health planning; COVID-19; Vaccines; Program evaluation; Epidemiological model

RESUMO

Objetivo:

Este trabalho visou estimar os casos e óbitos evitáveis de COVID-19 com a antecipação da vacinação, doses adicionais de vacinas e intervenções não farmacológicas eficazes no Brasil.

Métodos:

Propôs-se um modelo suscetível-exposto-infectado-recuperado-suscetível baseado em indicadores epidemiológicos de morbidade e mortalidade obtidos de Sistemas de Informação em Saúde do Ministério da Saúde do Brasil. O número de casos e mortes evitáveis foi estimado para diferentes cenários de programas de vacinação e intervenções não farmacológicas nos estados do Brasil (de 8 de março de 2020 a 5 de junho de 2022).

Resultados:

A estimativa baseada no modelo mostrou que 40 dias de antecipação da vacinação, doses adicionais de vacina e um nível mais alto de intervenções não farmacológicas reduziriam e retardariam o pico da pandemia. Haveria 17.121.749 casos a menos de COVID-19 e 391.647 mortes evitáveis no país.

Conclusão:

Os resultados sugerem que, se 80% da população brasileira tivesse sido vacinada até maio de 2021, haveria 59,83% de mortes evitadas no Brasil.

Palavras-chave:
Planejamento em saúde; COVID-19; Vacinas; Avaliação de programa; Modelo epidemiológico

INTRODUCTION

Since February 2020, the world has been ravaged by the COVID-2019 pandemic, with over 635 million confirmed cases and 6.61 million confirmed deaths worldwide11. Brasil. Ministério da Saúde. Painel coronavírus [Internet]. [cited on Feb 15, 2023]. Available at: https://covid.saude.gov.br/
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Uncertainty surrounding COVID-19 and its treatment challenged healthcare professionals and policymakers55. Bertsimas D, Li ML, Soni S. THEMIS : a framework for cost-benefit analysis of COVID-19 non-pharmaceutical interventions. medRxiv 2022; 2020. https://doi.org/10.1101/2022.04.09.22273656
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https://doi.org/10.1007/s10729-020-09542... . Countries’ healthcare systems faced beds and ventilators shortages55. Bertsimas D, Li ML, Soni S. THEMIS : a framework for cost-benefit analysis of COVID-19 non-pharmaceutical interventions. medRxiv 2022; 2020. https://doi.org/10.1101/2022.04.09.22273656
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https://doi.org/10.1016/j.epidem.2022.10... . At the political level, countries implemented social distancing measures and other NPIs, such as lockdowns and distancing regulations (restricting travel, mass gatherings, closure of workplaces/schools), mandatory use of masks, and hand hygiene with alcohol to slow the spread of the pandemic44. Arachchilage KH, Hussaini MY. Ranking non-pharmaceutical interventions against Covid-19 global pandemic using global sensitivity analysis–effect on number of deaths. Chaos Solitons Fractals 2021; 152: 111458. https://doi.org/10.1016/j.chaos.2021.111458.
https://doi.org/10.1016/j.chaos.2021.111... ,55. Bertsimas D, Li ML, Soni S. THEMIS : a framework for cost-benefit analysis of COVID-19 non-pharmaceutical interventions. medRxiv 2022; 2020. https://doi.org/10.1101/2022.04.09.22273656
https://doi.org/10.1101/2022.04.09.22273... ,99. Fair KR, Karatayev VA, Anand M, Bauch CT. Estimating COVID-19 cases and deaths prevented by non-pharmaceutical interventions, and the impact of individual actions: a retrospective model-based analysis. Epidemics 2022; 39: 100557. https://doi.org/10.1016/j.epidem.2022.100557
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https://doi.org/10.1016/j.jtbi.2022.1111... . Despite their proven effectiveness in reducing virus transmission and deaths, oscillating strategies carried economic and humanitarian costs, ranging from unemployment to depression and anxiety55. Bertsimas D, Li ML, Soni S. THEMIS : a framework for cost-benefit analysis of COVID-19 non-pharmaceutical interventions. medRxiv 2022; 2020. https://doi.org/10.1101/2022.04.09.22273656
https://doi.org/10.1101/2022.04.09.22273... ,66. Bertsimas D, Boussioux L, Cory-Wright R, Delarue A, Digalakis V, Jacquillat A, et al. From predictions to prescriptions: a data-driven response to COVID-19. Health Care Manag Sci 2021; 24(2): 253-72. https://doi.org/10.1007/s10729-020-09542-0
https://doi.org/10.1007/s10729-020-09542... .

Countries such as Taiwan and South Korea extensively tested and isolated the infected, and European countries, such as Spain, France, the United Kingdom, Germany, and Italy, imposed restrictive lockdowns to avoid the virus’ spread77. Biswas D, Alfandari L. Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19. Eur J Oper Res 2022; 303(3): 1372-91. https://doi.org/10.1016/j.ejor.2022.03.052
https://doi.org/10.1016/j.ejor.2022.03.0... . On the other hand, Brazil, Sweden, and the United States adopted a less comprehensive approach reacting late to the epidemic and allowing infections to increase rapidly55. Bertsimas D, Li ML, Soni S. THEMIS : a framework for cost-benefit analysis of COVID-19 non-pharmaceutical interventions. medRxiv 2022; 2020. https://doi.org/10.1101/2022.04.09.22273656
https://doi.org/10.1101/2022.04.09.22273... ,77. Biswas D, Alfandari L. Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19. Eur J Oper Res 2022; 303(3): 1372-91. https://doi.org/10.1016/j.ejor.2022.03.052
https://doi.org/10.1016/j.ejor.2022.03.0... , which might have resulted in an excess of cases and deaths1212. Hasan U, Al Jassmi H, Tridane A, Stanciole A, Al-Hosani F, Aden B. Modelling the effect of non-pharmaceutical interventions on COVID-19 transmission from mobility maps. Infect Dis Model 2022; 7(3): 400-18. https://doi.org/10.1016/j.idm.2022.07.004
https://doi.org/10.1016/j.idm.2022.07.00... ,1414. Zhao S, Wang K, Chong MKC, Musa SS, He M, Han L, et al. The non-pharmaceutical interventions may affect the advantage in transmission of mutated variants during epidemics: a conceptual model for COVID-19. J Theor Biol. 2022; 542: 111105. https://doi.org/10.1016/j.jtbi.2022.111105
https://doi.org/10.1016/j.jtbi.2022.1111... .

In December 2020, Regulatory Agencies approved COVID-19 vaccines, and vaccination started in many countries22. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level [Internet]. [cited on Mar 17, 2023]. Available at: https://preprints.scielo.org/index.php/scielo/preprint/view/362/444
https://preprints.scielo.org/index.php/s... ,33. Cota W. Número de casos confirmados de COVID-19 no Brasil [Internet]. [cited on Mar 17, 2023]. Available at: https://covid19br.wcota.me/
https://covid19br.wcota.me/... ,1515. University of Oxford. Coronavirus (COVID-19) vaccinations [Internet]. 2023 [cited on Feb 16, 2023]. Available at: https://ourworldindata.org/covid-vaccinations?country=BRA
https://ourworldindata.org/covid-vaccina... . Russia started its vaccination programs on December 5th, 2020, and the United Kingdom, the United States, and the United Arab Emirates on December 14th, 2020. Latin American countries such as Chile, Argentina, and Mexico started vaccination on December 24th, 2020. On the other hand, in the American continent, Brazil was one of the nations that postponed the beginning of the vaccination program, starting only on January 18th, 202111. Brasil. Ministério da Saúde. Painel coronavírus [Internet]. [cited on Feb 15, 2023]. Available at: https://covid.saude.gov.br/
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https://legis.senado.leg.br/comissoes/mn... .

Despite having one of the world’s most successful immunization programs through the National Immunization Program (PNI) of the Ministry of Health, the vaccination strategy and the campaign against COVID-19 in Brazil were implemented slowly and not timely, in contrast to previous successful vaccination campaigns, such as the 2009 H1N1 influenza pandemic, in which 89 million doses of influenza vaccine were administered in three months1717. Centro de Estudos Estratégicos da Fiocruz. Antonio Ivo de Carvalho. Combate à epidemia de H1N1: um histórico de sucesso [Internet]. 2021 [cited on May 5, 2022]. Available at: https://cee.fiocruz.br/?q=node/1314
https://cee.fiocruz.br/?q=node/1314... . Aspects such as the lack of coordination and support for scientific research from the federal government and the oscillating and relaxed application of NPIs1818. Aquino EML, Silveira IH, Pescarini JM, Aquino R, Souza-Filho JA, Rocha AS, et al. Social distancing measures to control the COVID-19 pandemic: potential impacts and challenges in Brazil. Cien Saude Colet 2020; 25(suppl 1): 2423-46. https://doi.org/10.1590/1413-81232020256.1.10502020
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www.oxfam.org.br/download/12262/... resulted in 655,000 deaths from COVID-19 by June 202211. Brasil. Ministério da Saúde. Painel coronavírus [Internet]. [cited on Feb 15, 2023]. Available at: https://covid.saude.gov.br/
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https://legis.senado.leg.br/comissoes/mn... . To improve future NPI policies and vaccination, we need to estimate the number of SARS-CoV-2 virus cases and deaths that could have been avoided if the NPIs strategy and the COVID-19 vaccination had been effectively implemented. Therefore, we simulated the dynamics of the COVID-19 pandemic in Brazil, using the susceptible-exposed-infected-recovered-susceptible (SEIRS) model for different vaccination and NPIs strategies.

The SEIR modelling approach was used to estimate the progression of the COVID-19 pandemic and to discuss the control strategies when implementing social distancing, periods of school closures, and human mobility patterns measures2020. Prem K, Liu Y, Russell TW, Kucharski AJ, Eggo RM, Davies N, et al. The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. Lancet Public Health 2020; 5(5): e261-70. https://doi.org/10.1016/S2468-2667(20)30073-6
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21. Yang Z, Zeng Z, Wang K, Wong SS, Liang W, Zanin M, et al. Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions. J Thorac Dis 2020; 12(3): 165-74. https://doi.org/10.21037/jtd.2020.02.64
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22. Tang B, Wang X, Li Q, Bragazzi NL, Tang S, Xiao Y, et al. Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions. J Clin Med 2020; 9(2): 462. https://doi.org/10.3390/jcm9020462
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23. Gatto M, Bertuzzo E, Mari L, Miccoli S, Carraro L, Casagrandi R, et al. Spread and dynamics of the COVID-19 epidemic in Italy: effects of emergency containment measures. Proc Natl Acad Sci U S A 2020; 117(19): 10484-91. https://doi.org/10.1073/pnas.2004978117
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24. Chang S, Pierson E, Koh PW, Gerardin J, Redbird B, Grusky D, et al. Mobility network models of COVID-19 explain inequities and inform reopening. Nature 2021; 589(7840): 82-7. https://doi.org/10.1038/s41586-020-2923-3
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25. Roda WC, Varughese MB, Han D, Li MY. Why is it difficult to accurately predict the COVID-19 epidemic? Infect Dis Model 2020; 5: 271-81. https://doi.org/10.1016/j.idm.2020.03.001
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26. He S, Peng Y, Sun K. SEIR modeling of the COVID-19 and its dynamics. Nonlinear Dyn 2020; 101(3): 1667-80. https://doi.org/10.1007/s11071-020-05743-y
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27. Wang H, Wang Z, Dong Y, Chang R, Xu C, Yu X, et al. Phase-adjusted estimation of the number of Coronavirus Disease 2019 cases in Wuhan, China. Cell Discov 2020; 6:10. https://doi.org/10.1038/s41421-020-0148-0
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28. IHME COVID-19 Forecasting Team. Modeling COVID-19 scenarios for the United States. Nat Med 2021; 27(1): 94-105. https://doi.org/10.1038/s41591-020-1132-9
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29. Borges ME, Ferreira LS, Poloni S, Bagattini AM, Franco C, Rosa MQM, et al. Modelling the impact of school reopening and contact tracing strategies on Covid-19 dynamics in different epidemiologic settings in Brazil. Glob Epidemiol 2022; 4; 100094. https://doi.org/10.1016/j.gloepi.2022.100094
https://doi.org/10.1016/j.gloepi.2022.10... -3030. Jorge DCP, Rodrigues MS, Silva MS, Cardim LL, Silva NB, Silveira IH, et al. Assessing the nationwide impact of COVID-19 mitigation policies on the transmission rate of SARS-CoV-2 in Brazil. Epidemics 2021; 35: 100465. https://doi.org/10.1016/j.epidem.2021.100465
https://doi.org/10.1016/j.epidem.2021.10... . The studies proposed measures to reduce the height of the peak to allow more time for health systems to expand and respond. The present study contributes to evaluate the impact of NPIs on the progress of the pandemic. This work’s scientific contribution reveals the potential of an earlier vaccination program to prevent cases and deaths.

This work aims to estimate the number of preventable cases and deaths from COVID-19 upon vaccination programs and non-pharmacological interventions in Brazil.

METHODS

Data sources and measurements

This work uses daily historical data from each state for the number of cases (infections), deaths (absolute number of deaths), and number of vaccinated individuals available at https://github.com/wcota/covid19br3131. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level. https://doi.org/10.1590/SciELOPreprints.362
https://doi.org/10.1590/SciELOPreprints.... which aggregates data from at least two main sources22. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level [Internet]. [cited on Mar 17, 2023]. Available at: https://preprints.scielo.org/index.php/scielo/preprint/view/362/444
https://preprints.scielo.org/index.php/s... : the Ministry of Health11. Brasil. Ministério da Saúde. Painel coronavírus [Internet]. [cited on Feb 15, 2023]. Available at: https://covid.saude.gov.br/
https://covid.saude.gov.br/... and Brasil.IO3232. Brasil.io. COVID-19. Boletins informativos e casos do coronavírus por município por dia [Internet]. 2022 [cited on Apr 4, 2023]. Available at: https://brasil.io/dataset/covid19/caso/
https://brasil.io/dataset/covid19/caso/... . Previous works use the same data source in their analysis (see, for example, Araújo et al.3333. Araújo JLB, Oliveira EA, Lima Neto AS, Andrade Jr JS, Furtado V. Unveiling the paths of COVID-19 in a large city based on public transportation data. Sci Rep 2023; 13(1): 5761. https://doi.org/10.1038/s41598-023-32786-z
https://doi.org/10.1038/s41598-023-32786... , Badr et al.3434. Badr HS, Zaitchik BF, Kerr GH, Nguyen NLH, Chen YT, Hinson P, et al. Unified real-time environmental-epidemiological data for multiscale modeling of the COVID-19 pandemic. Sci Data 2023; 10(1): 367. https://doi.org/10.1038/s41597-023-02276-y
https://doi.org/10.1038/s41597-023-02276... , Cassão et al.3535. Cassão V, Alves D, Mioto ACA, Mozini MT, Segamarchi RB, Miyoshi NSB. Unsupervised analysis of COVID-19 pandemic evolution in brazilian states: Vaccination Scenario. Procedia Comput Sci 2023; 219: 1453-61. https://doi.org/10.1016/j.procs.2023.01.435
https://doi.org/10.1016/j.procs.2023.01.... , Aragão et al.3636. Aragão DP, Oliveira EV, Bezerra AA, Santos DH, Silva Junior AG, Pereira IG, et al. Multivariate data driven prediction of COVID-19 dynamics: towards new results with temperature, humidity and air quality data. Environ Res 2022; 204(Pt D): 112348. https://doi.org/10.1016/j.envres.2021.112348
https://doi.org/10.1016/j.envres.2021.11... , and Almeida et al.3737. Almeida L, Carelli PV, Cavalcanti NG, Nascimento Jr JD, Felinto D. Quantifying political influence on COVID-19 fatality in Brazil. PLoS One 2022; 17(7: e0264293. https://doi.org/10.1371/journal.pone.0264293
https://doi.org/10.1371/journal.pone.026... ).

The study used data from March 2020 to June 2022 from the 26 Brazilian states and the Federal District (DF) to develop the SEIRS model. First, we estimated the parameters of the SEIRS model for each state. Then, we used this parameter to estimate the cases of infection in Brazil (Figure 1).

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Figura 1.
Estimated cases of infections in Brazil using the susceptible-exposed-infected-recovered-susceptible model.

The COVID-19 Pandemic Parliamentary Commission of Inquiry (CPI COVID-19)(1616. Brasil. Senado Federal. Atividade Legislativa. Relatório final CPI da pandemia [Internet]. 2021 [cited on May 5, 2022]. Available at: https://legis.senado.leg.br/comissoes/mnas?codcol=2441&tp=4
https://legis.senado.leg.br/comissoes/mn... ) addressed the delay in the Brazilian vaccination program, stating that Brazil could have started the vaccination program in the first half of December 2020, like most Latin American countries (see page 239 of the report). Therefore, as indicated in the CPI report, we anticipated the vaccination schedule in Brazil to December 8th, 2020 (a possible date).

We estimated the number of cases and deaths for three possible scenarios of vaccination programs and NPI strategies in 819 days of the pandemic: from March 8th, 2020, to June 5th, 2022.

Scenario 1 [Vaccination anticipation]: Vaccination from the first possible day in Brazil (2020, December 8th) without adding doses.

Scenario 2 [Vaccination anticipation and additional doses of vaccines]: This scenario assumes the anticipation of the vaccination program to December 8th, 2020, and the availability of vaccine doses to vaccinate 80% of the Brazilian population (delivered in early December 2020 until May 31, 2021; see Annexes in the Supplementary Material).

Scenario 3 [Vaccination anticipation, additional doses of vaccines, and effective NPIs]: Besides anticipating the vaccination program to 2020 December 8th and the additional vaccine doses, we propose Scenario 3 by changing the NPIs to a 34.22% higher effectiveness. We assume that a higher NPI effectiveness is a 34.22% lower number of deaths obtained by the city of Belo Horizonte compared to other Brazilian capitals with more than one million inhabitants3838. Prefeitura de Belo Horizonte. BH é a capital com mais de 1 milhão de pessoas com menor risco de morte de Covid [Internet]. 2022 [cited on Feb 16, 2023]. Available at: https://prefeitura.pbh.gov.br/noticias/bh-e-capital-com-mais-de-1-milhao-de-pessoas-com-menor-risco-de-morte-de-covid
https://prefeitura.pbh.gov.br/noticias/b... .

Susceptible-exposed-infected-recovered-susceptible model: capturing the effects of vaccination and non-pharmaceutical interventions

The epidemiological SEIRS model (Figure 2) predicts infectious disease dynamics by compartmentalizing the population. The model is governed by a system of ordinary differential equations (1–7)3939. McGee RS. SEIRS model description [Internet]. 2020 [cited Feb 16, 2023]. Available at: https://github.com/ryansmcgee/seirsplus/wiki/SEIRS-Model-Description
https://github.com/ryansmcgee/seirsplus/... , where S, E, I, R, and F are the amount of susceptible, exposed, infectious, recovered, and deceased individuals, respectively; N is the total number of individuals in the populations; QE are the exposed quarantined individuals ; QI are the infectious quarantined individuals; β is the rate of transmission (exposure); βQ is the rate of transmissibility of quarantined individuals; σ is the rate of infection (upon exposure); σQ is the rate of progression to infectiousness for quarantined individuals (inverse of the latent period); γ is the rate of recovery (upon infection); γQ is the rate of recovery for quarantined individuals (inverse of the infectious period); γI is the rate of recovery for infected individuals; ξ is the rate of re-susceptibility (inverse of temporary immunity period; 0 if permanent immunity period) (upon recovery); μI is the rate of infection-related death; μQ is the rate of death for quarantined individuals; ω is the rate of infection by new variants; and q is the weight of intensity of global interactions for individuals in quarantine.

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Figura 2.
Susceptible-exposed-infected-recovered-susceptible diagram.

The proposed model distinguishes the individuals into two groups throughout the pandemic: in quarantine, i.e., a group created from the tested population; and out of quarantine. Exposed and infectious individuals are tested at rates θE and θI, that test positively for infection with probabilities ψE and ψI, respectively (the false positive rate is assumed to be zero). A positive test result moves an individual into the appropriate quarantine state and the individuals remain in isolation until their designated isolation time has been reached or until they recover. In addition to addressing quarantine, the model introduces elements such as social distancing and the transmissibility rate. There are groups at higher risk of death, such as the elderly and individuals with comorbidities and social vulnerabilities(4040. Lapo-Talledo GJ, Talledo-Delgado JA, Fernández-Aballí LS. A competing risk survival analysis of the sociodemographic factors of COVID-19 in-hospital mortality in Ecuador. Cad Saude Publica 2023; 39(1): e00294721. https://doi.org/10.1590/0102-311XEN294721
https://doi.org/10.1590/0102-311XEN29472... ,4141. Leveau CM, Bastos LS. Socio-spatial inequalities in COVID-19 mortality in the three waves: an intraurban analysis in Argentina. Cad Saude Publica 2022; 38(5): e00163921.). We adopted an average rate of deaths per infected population.

(1)S·=−βSIN−qβQSQIN
(2)E·=−βSIN+qβQSQIN−σE−θEψEE
(3)I·=(σ+ω)E−γI−μII−θIψI
(4)Q·E=θEψEE−σQQE
(5)Q·I=θIψII−σQQE−γQQI−μQQI
(6)R·=γI+γQQI
(7)F·=μII+μQQI
(8)N=S+E+I+QE+QI+R

We propose an extended version of the SEIRS model by incorporating the virus transmission rate varying in time (β), the vaccination program, and the effect of NPIs in the number of cases and deaths on the curve of COVID-19 for all Brazilian states. Hence, the curve of the cases estimated by the SEIRS model is modeled according to the five parameters that vary in time: β, ω, Edist, Evac, and Pvac. In this work, we modeled these parameters varying over time to address the different stages of the pandemic. The parameters β, ω, Edist, and Evac were adjusted using historical data of reported infections referring to two and a half years of the pandemic in Brazil. On the other hand, the Pvac is a parameter obtained directly from the data collected3131. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level. https://doi.org/10.1590/SciELOPreprints.362
https://doi.org/10.1590/SciELOPreprints.... .

The rate of transmission (β) is a key parameter in determining how fast COVID-19 can spread through the population during the early stages of the disease. Its estimation is inherently challenging since the reported cases are likely to be a smaller fraction of real cases4242. Paes NA, Ferreira AMS, Moura LA. Proposta metodológica para avaliação de registros de óbitos por COVID-19. Cad Saúde Pública 2023; 39(1): e00096722. https://doi.org/10.1590/0102-311XPT096722
https://doi.org/10.1590/0102-311XPT09672... and the real number of cases and their changes over time is unknown.

We also incorporate the effect of NPIs into the SEIRS model by introducing PE as the percentage of the exposed population in Equation 9. In this case, the effect of the NPIs is represented by ,Edist the effectiveness of social distancing.

(9)PE=1−Edist

Moreover, the effect of the vaccine is included in Equation 10, where Ps is the percentage of the susceptible population; Pvac is the percentage of the vaccinated population22. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level [Internet]. [cited on Mar 17, 2023]. Available at: https://preprints.scielo.org/index.php/scielo/preprint/view/362/444
https://preprints.scielo.org/index.php/s... ,33. Cota W. Número de casos confirmados de COVID-19 no Brasil [Internet]. [cited on Mar 17, 2023]. Available at: https://covid19br.wcota.me/
https://covid19br.wcota.me/... , and Evac is the vaccine effectiveness. We also assume that vaccinated and unvaccinated individuals are susceptible to the virus with different probabilities.

(10)PS=PE∗(1−Pvac∗Evac)

The estimated number of deaths (M) is presented in Equation 11, in which λ is the death rate of vaccinated individuals22. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level [Internet]. [cited on Mar 17, 2023]. Available at: https://preprints.scielo.org/index.php/scielo/preprint/view/362/444
https://preprints.scielo.org/index.php/s... ,33. Cota W. Número de casos confirmados de COVID-19 no Brasil [Internet]. [cited on Mar 17, 2023]. Available at: https://covid19br.wcota.me/
https://covid19br.wcota.me/... ,4343. Fundação Oswaldo Cruz. Boletim especial: balanço de dois anos da pandemia Covid-19 [Internet]. 2022 [cited Apr 5, 2023]. Available at: https://portal.fiocruz.br/sites/portal.fiocruz.br/files/documentos_2/boletim_covid_2022-balanco_2_anos_pandemia-redb.pdf
https://portal.fiocruz.br/sites/portal.f... , ρ is the death rate of unvaccinated individuals22. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level [Internet]. [cited on Mar 17, 2023]. Available at: https://preprints.scielo.org/index.php/scielo/preprint/view/362/444
https://preprints.scielo.org/index.php/s... ,33. Cota W. Número de casos confirmados de COVID-19 no Brasil [Internet]. [cited on Mar 17, 2023]. Available at: https://covid19br.wcota.me/
https://covid19br.wcota.me/... ,4343. Fundação Oswaldo Cruz. Boletim especial: balanço de dois anos da pandemia Covid-19 [Internet]. 2022 [cited Apr 5, 2023]. Available at: https://portal.fiocruz.br/sites/portal.fiocruz.br/files/documentos_2/boletim_covid_2022-balanco_2_anos_pandemia-redb.pdf
https://portal.fiocruz.br/sites/portal.f... , and CP is the number of predicted cases.

(11)M=[ρ∗CP∗(1−Pvac)]+[λ∗CP∗Pvac]

Due to the lack of detailed data, we assume four simplifying assumptions. First, the population is homogeneous, i.e., all individuals have the same infection rate and parameters. Second, all individuals are equally likely to interact with all other individuals. Third, this model assumes that individuals are tested randomly at exponentially distributed intervals corresponding to mean testing rates. Finally, the model assumes a population uniformly dispersed in a geographical area, despite the fact that urban centers with a greater concentration of population can present a higher probability of infection than areas with a smaller number of people.

The model was implemented in Python software (Python Language Reference, version 3.10.4). The code is available in Supplementary Materials.

The criterion used to evaluate the predictive performance of the SEIRS model was the mean absolute percentage error (MAPE). MAPE was calculated using Equation 12, in which Pt is the predicted value at time t, Zt is the observed value at time t and T is the number of predictions.

(12)MAPE=1T∑t=1T|(Pt−Zt)Zt|

RESULTS

Brazil had a cumulative infection quantity of 30,733,955 cases and 654,572 deaths by June 202211. Brasil. Ministério da Saúde. Painel coronavírus [Internet]. [cited on Feb 15, 2023]. Available at: https://covid.saude.gov.br/
https://covid.saude.gov.br/...

2. Cota W. Monitoring the number of COVID-19 cases and deaths in Brazil at municipal and federative units level [Internet]. [cited on Mar 17, 2023]. Available at: https://preprints.scielo.org/index.php/scielo/preprint/view/362/444
https://preprints.scielo.org/index.php/s... -33. Cota W. Número de casos confirmados de COVID-19 no Brasil [Internet]. [cited on Mar 17, 2023]. Available at: https://covid19br.wcota.me/
https://covid19br.wcota.me/... , with 2.57% deaths per infected person (lethality rate)4343. Fundação Oswaldo Cruz. Boletim especial: balanço de dois anos da pandemia Covid-19 [Internet]. 2022 [cited Apr 5, 2023]. Available at: https://portal.fiocruz.br/sites/portal.fiocruz.br/files/documentos_2/boletim_covid_2022-balanco_2_anos_pandemia-redb.pdf
https://portal.fiocruz.br/sites/portal.f... . The model presented a MAPE of 5.12% for all of Brazil, suggesting good accuracy in predicting epidemic diseases based on the results of Zhang et al.4444. Zhang X, Zhang T, Young AA, Li X. Applications and comparisons of four time series models in epidemiological surveillance data. PLoS One 2014; 9(2): e88075. https://doi.org/10.1371/journal.pone.0088075
https://doi.org/10.1371/journal.pone.008... We present the results for the three scenarios using a 30-day moving average to plot the curve of the cases for better curve smoothing.

  1. -

    Scenario 1 [Vaccination anticipation]: The model estimates that 3,517,329 cases and 86,639 deaths could have been avoided (Figure 3).

  2. -

    Scenario 2 [Vaccination anticipation and additional doses of vaccines]: As a result, the model estimates that 11,697,890 cases and 266,953 deaths would be avoided during the analyzed period (Figure 4).

  3. -

    Scenario 3 [Vaccination anticipation, additional doses, and effective NPIs]: The result of this scenario estimates the prevention of 17,121,749 cases and 391,647 deaths. The estimated infection curve to Scenario 3 is presented in Figure 5.

Thumbnail
Figura 3.
Estimated infection curve of Scenario 1.
Thumbnail
Figura 4.
Estimated infection curve of Scenario 2.
Thumbnail
Figura 5.
Estimated infection curve of Scenario 3.

Table 1 summarizes the SEIRS model estimates for the three scenarios considering all Brazilian states. In this sense, our simulations show that control measures aimed at timely vaccination (early), availability of additional doses, and more robust NPIs could have significantly prevented the number of cases and deaths from COVID-19 in Brazil.

Thumbnail
Table 1.
Simulated scenarios

DISCUSSION

COVID-19, a contact-transmissible infectious disease, spreads through a population via direct contact between individuals99. Fair KR, Karatayev VA, Anand M, Bauch CT. Estimating COVID-19 cases and deaths prevented by non-pharmaceutical interventions, and the impact of individual actions: a retrospective model-based analysis. Epidemics 2022; 39: 100557. https://doi.org/10.1016/j.epidem.2022.100557
https://doi.org/10.1016/j.epidem.2022.10... ,2020. Prem K, Liu Y, Russell TW, Kucharski AJ, Eggo RM, Davies N, et al. The effect of control strategies to reduce social mixing on outcomes of the COVID-19 epidemic in Wuhan, China: a modelling study. Lancet Public Health 2020; 5(5): e261-70. https://doi.org/10.1016/S2468-2667(20)30073-6
https://doi.org/10.1016/S2468-2667(20)30... . Control measures are applied to avoid cases and deaths from the disease. This work aims to estimate the number of preventable cases and deaths from COVID-19 upon alternative control measures of vaccination and NPIs in Brazil. Therefore, we modelled the real curve of cases and deaths and evaluated the effect of different vaccination strategies and NPIs measures. To this end, we used the SEIRS epidemiological model by estimating pandemic parameters. The simulation shows that intense control measures of NPIs and anticipation of vaccination would have reduced cumulative infections by the end of 2020 while also delaying the peak of the disease.

Scenario 1 shows the avoidable number of cases and deaths if the vaccination program had been implemented with no additional doses of vaccine, i.e., if the country had implemented all the previous strategies in addition to anticipating the start of vaccination. In this scenario, we observe that 86,639 (13.23%) deaths could have been avoided, showing the importance of timely time vaccination strategies.

Comparing the strategy adopted in Brazil with the results obtained in Scenario 2, 38.06% of cases and 40.78% of deaths could be avoided by anticipating vaccination and purchasing additional vaccine doses. Our projections show that the deaths could be substantially decreased if the population’s vaccination coverage was higher until May 2021.

Similar works by Ferreira et al.4545. Ferreira LS, Marquitti FMD, Silva RLP, Borges ME, Gomes MFC, Cruz OG, et al. Estimating the impact of implementation and timing of the COVID-19 vaccination programme in Brazil: a counterfactual analysis. Lancet Reg Health Am 2023; 17: 100397. https://doi.org/10.1016/j.lana.2022.100397
https://doi.org/10.1016/j.lana.2022.1003... , Santos et al.4646. Santos CVB, Noronha TG, Werneck GL, Struchiner CJ, Villela DAM. Estimated COVID-19 severe cases and deaths averted in the first year of the vaccination campaign in Brazil: a retrospective observational study. Lancet Reg Health Am 2023; 17: 100418. https://doi.org/10.1016/j.lana.2022.100418
https://doi.org/10.1016/j.lana.2022.1004... , Santos et al.4747. Santos CVB, Valiati NCM, Noronha TG, Porto VBG, Pacheco AG, Freitas LP, et al. The effectiveness of COVID-19 vaccines against severe cases and deaths in Brazil from 2021 to 2022: a registry-based study. Lancet Reg Health Am 2023; 20: 100465. https://doi.org/10.1016/j.lana.2023.100465
https://doi.org/10.1016/j.lana.2023.1004... , and Orellana et al.4848. Orellana JDY, Cunha GM, Marrero L, Leite IC, Domingues CMAS, Horta BL. Changes in the pattern of COVID-19 hospitalizations and deaths after substantial vaccination of the elderly in Manaus, Amazonas State, Brazil. Cad Saude Publica 2022; 38(5): PT192321. https://doi.org/10.1590/0102-311XPT192321
https://doi.org/10.1590/0102-311XPT19232... demonstrate the direct impact of COVID-19 vaccination in reducing the number of deaths. Ferreira et al.4545. Ferreira LS, Marquitti FMD, Silva RLP, Borges ME, Gomes MFC, Cruz OG, et al. Estimating the impact of implementation and timing of the COVID-19 vaccination programme in Brazil: a counterfactual analysis. Lancet Reg Health Am 2023; 17: 100397. https://doi.org/10.1016/j.lana.2022.100397
https://doi.org/10.1016/j.lana.2022.1003... and Orellana et al.4848. Orellana JDY, Cunha GM, Marrero L, Leite IC, Domingues CMAS, Horta BL. Changes in the pattern of COVID-19 hospitalizations and deaths after substantial vaccination of the elderly in Manaus, Amazonas State, Brazil. Cad Saude Publica 2022; 38(5): PT192321. https://doi.org/10.1590/0102-311XPT192321
https://doi.org/10.1590/0102-311XPT19232... also evaluate changes in hospitalization patterns, and Santos et al.4646. Santos CVB, Noronha TG, Werneck GL, Struchiner CJ, Villela DAM. Estimated COVID-19 severe cases and deaths averted in the first year of the vaccination campaign in Brazil: a retrospective observational study. Lancet Reg Health Am 2023; 17: 100418. https://doi.org/10.1016/j.lana.2022.100418
https://doi.org/10.1016/j.lana.2022.1004... and Santos et al.4747. Santos CVB, Valiati NCM, Noronha TG, Porto VBG, Pacheco AG, Freitas LP, et al. The effectiveness of COVID-19 vaccines against severe cases and deaths in Brazil from 2021 to 2022: a registry-based study. Lancet Reg Health Am 2023; 20: 100465. https://doi.org/10.1016/j.lana.2023.100465
https://doi.org/10.1016/j.lana.2023.1004... analyze the reduction in severe cases, both associated with vaccination.

The vaccination against COVID-19 in Brazil started almost one year after the beginning of the pandemic. During this period, control of the infection was carried out only by the NPIs. Brazil reacted ineffectively to the pandemic compared to most countries through oscillating NPIs77. Biswas D, Alfandari L. Designing an optimal sequence of non-pharmaceutical interventions for controlling COVID-19. Eur J Oper Res 2022; 303(3): 1372-91. https://doi.org/10.1016/j.ejor.2022.03.052
https://doi.org/10.1016/j.ejor.2022.03.0... ,1616. Brasil. Senado Federal. Atividade Legislativa. Relatório final CPI da pandemia [Internet]. 2021 [cited on May 5, 2022]. Available at: https://legis.senado.leg.br/comissoes/mnas?codcol=2441&tp=4
https://legis.senado.leg.br/comissoes/mn... . Strategies considered “flexible or relaxed” did not prevent increasing cases and deaths55. Bertsimas D, Li ML, Soni S. THEMIS : a framework for cost-benefit analysis of COVID-19 non-pharmaceutical interventions. medRxiv 2022; 2020. https://doi.org/10.1101/2022.04.09.22273656
https://doi.org/10.1101/2022.04.09.22273... . In this sense, we observed that if the municipalities had adopted effective NPIs combined with a timely vaccination program and additional doses of vaccines, 17,121,749 cases of COVID-19 would have been avoided and 391,647 deaths would have been avoided, i.e., the country would have avoided 55.70% of cases and 59.83% of deaths by adopting Scenario 3 compared to the baseline one. Scenario 3 also highlights the importance of implementing NPI strategies. Comparing its results with Scenario 2, 17.64% of cases and 19.04% of deaths could have been avoided by implementing these strategies.

In this context, Genari et al.4949. Genari J, Goedert GT, Lira SHA, Oliveira K, Barbosa A, Lima A, et al. Quantifying protocols for safe school activities. PLoS One 2022; 17(9): e0273425. https://doi.org/10.1371/journal.pone.0273425
https://doi.org/10.1371/journal.pone.027... address the safety of school activities considering the implementation of NPIs and vaccination, associating the adoption of effective NPI protocols with a reduction in the number of cases. On the other hand, Werneck et al.1919. Werneck GL, Bahia L, Moreira JPL, Scheffer M. Mortes evitáveis por COVID-19 no Brasil [Internet]. 2021 [cited on Aug 31, 2023]. Available at: www.oxfam.org.br/download/12262/
www.oxfam.org.br/download/12262/... and Silva et al.5050. Silva GA, Jardim BC, Santos CVB. Excess mortality in Brazil in times of Covid-19. Cien Saude Colet 2020; 25(9): 3345-54. https://doi.org/10.1590/1413-81232020259.23642020
https://doi.org/10.1590/1413-81232020259... estimate the number of cases and deaths that could be avoided in Brazil if only NPIs were used to control the pandemic.

In terms of the research method, the works that addressed this issue adopted methodologies such as the SEIR(4949. Genari J, Goedert GT, Lira SHA, Oliveira K, Barbosa A, Lima A, et al. Quantifying protocols for safe school activities. PLoS One 2022; 17(9): e0273425. https://doi.org/10.1371/journal.pone.0273425
https://doi.org/10.1371/journal.pone.027... ,5151. Silva PJS, Sagastizábal C, Nonato LG, Struchiner CJ, Pereira T. Optimized delay of the second COVID-19 vaccine dose reduces ICU admissions. Proc Natl Acad Sci U S A 2021; 118(35): e2104640118. https://doi.org/10.1073/pnas.2104640118
https://doi.org/10.1073/pnas.210464011... ), statistical methods(4545. Ferreira LS, Marquitti FMD, Silva RLP, Borges ME, Gomes MFC, Cruz OG, et al. Estimating the impact of implementation and timing of the COVID-19 vaccination programme in Brazil: a counterfactual analysis. Lancet Reg Health Am 2023; 17: 100397. https://doi.org/10.1016/j.lana.2022.100397
https://doi.org/10.1016/j.lana.2022.1003...

46. Santos CVB, Noronha TG, Werneck GL, Struchiner CJ, Villela DAM. Estimated COVID-19 severe cases and deaths averted in the first year of the vaccination campaign in Brazil: a retrospective observational study. Lancet Reg Health Am 2023; 17: 100418. https://doi.org/10.1016/j.lana.2022.100418
https://doi.org/10.1016/j.lana.2022.1004... -4747. Santos CVB, Valiati NCM, Noronha TG, Porto VBG, Pacheco AG, Freitas LP, et al. The effectiveness of COVID-19 vaccines against severe cases and deaths in Brazil from 2021 to 2022: a registry-based study. Lancet Reg Health Am 2023; 20: 100465. https://doi.org/10.1016/j.lana.2023.100465
https://doi.org/10.1016/j.lana.2023.1004... ), exploratory analysis(1919. Werneck GL, Bahia L, Moreira JPL, Scheffer M. Mortes evitáveis por COVID-19 no Brasil [Internet]. 2021 [cited on Aug 31, 2023]. Available at: www.oxfam.org.br/download/12262/
www.oxfam.org.br/download/12262/... ,5050. Silva GA, Jardim BC, Santos CVB. Excess mortality in Brazil in times of Covid-19. Cien Saude Colet 2020; 25(9): 3345-54. https://doi.org/10.1590/1413-81232020259.23642020
https://doi.org/10.1590/1413-81232020259... ), and ecological study(4848. Orellana JDY, Cunha GM, Marrero L, Leite IC, Domingues CMAS, Horta BL. Changes in the pattern of COVID-19 hospitalizations and deaths after substantial vaccination of the elderly in Manaus, Amazonas State, Brazil. Cad Saude Publica 2022; 38(5): PT192321. https://doi.org/10.1590/0102-311XPT192321
https://doi.org/10.1590/0102-311XPT19232... ). Genari et al.(4949. Genari J, Goedert GT, Lira SHA, Oliveira K, Barbosa A, Lima A, et al. Quantifying protocols for safe school activities. PLoS One 2022; 17(9): e0273425. https://doi.org/10.1371/journal.pone.0273425
https://doi.org/10.1371/journal.pone.027... ) use the SEIR method without assuming that individuals become susceptible again after recovery. On the other hand, based on Silva et al.(5151. Silva PJS, Sagastizábal C, Nonato LG, Struchiner CJ, Pereira T. Optimized delay of the second COVID-19 vaccine dose reduces ICU admissions. Proc Natl Acad Sci U S A 2021; 118(35): e2104640118. https://doi.org/10.1073/pnas.2104640118
https://doi.org/10.1073/pnas.210464011... ), we assume that vaccinated individuals can still become infected and in some cases even die.

Although the effects of interventions may vary among the countries, our approach is flexible enough to describe different pandemics or epidemics and to evaluate alternative scenarios in these situations. The proposed model provides better estimates of disease progression and highlights the usefulness of appropriate population vaccination programs and NPIs. Therefore, health planners can use it to manage future pandemics and epidemics.

We also assumed that 80% of vaccination coverage would be achieved by May 31st, 2021. However, the Brazilian health system, including research and healthcare infrastructure, has been underfunded in recent years(5252. Bigoni A, Malik AM, Tasca R, Carrera MBM, Schiesari LMC, Gambardella DD, et al. Brazil’s health system functionality amidst of the COVID-19 pandemic: an analysis of resilience. Lancet Reg Health Am 2022; 10: 100222. https://doi.org/10.1016/j.lana.2022.100222
https://doi.org/10.1016/j.lana.2022.1002... ), which could significantly compromise the achievement of vaccination coverage within this period.

Our study has some limitations. Our model addresses multiple doses by assuming that all vaccinated individuals have taken two doses of vaccine, even as we know that not all vaccinated individuals have taken both doses and we do not focus on the necessity of each vaccine brand; however, other studies(4545. Ferreira LS, Marquitti FMD, Silva RLP, Borges ME, Gomes MFC, Cruz OG, et al. Estimating the impact of implementation and timing of the COVID-19 vaccination programme in Brazil: a counterfactual analysis. Lancet Reg Health Am 2023; 17: 100397. https://doi.org/10.1016/j.lana.2022.100397
https://doi.org/10.1016/j.lana.2022.1003... ,5151. Silva PJS, Sagastizábal C, Nonato LG, Struchiner CJ, Pereira T. Optimized delay of the second COVID-19 vaccine dose reduces ICU admissions. Proc Natl Acad Sci U S A 2021; 118(35): e2104640118. https://doi.org/10.1073/pnas.2104640118
https://doi.org/10.1073/pnas.210464011... ) explicitly analyze the use of multiple doses. We also adopt as vaccine effectiveness the adjusted value for this parameter obtained using the collected data, without directly considering the number of vaccines of each brand used and the timely availability of each vaccine.

Another limitation of our work is the official data used to estimate the parameters of our model. Since the number of infections is not available, we assumed that the number of cases equals the number of infections. However, we recognize that this may underestimate the actual number, as underreporting and delays in the reporting are known and testing rates vary by region. For example, Paes et al.(5353. Paes NA, Ferreira AMS, Moura LA. Proposta metodológica para avaliação de registros de óbitos por COVID-19. Cad Saúde Pública 2023; 39(1): e00096722. https://doi.org/10.1590/0102-311XPT096722
https://doi.org/10.1590/0102-311XPT09672... ) proposed a methodology to calculate the number of deaths from COVID-19, which shows a 37.4% increase compared to official records for Paraíba in Brazil. In this sense, our simulations represent a conservative scenario for the COVID-19 pandemic in Brazil, suggesting that the impact of NPIs and vaccination strategies would be higher than the results presented in this paper. Therefore, we recommend conducting a sensitivity analysis to assess the reliability of the results and provide insight into the robustness of the model.

Due to a lack of microdata, different infection rates were not applied to individuals based on health profile, age, or geographic location. Future work is required in this direction. Another challenging future research direction is to incorporate the changes in COVID-19 vaccine effectiveness over time into the modeling. Finally, we suggest future research on integrating the proposed SEIRS model into logistics vaccination networks for vaccine demand estimation and increasing its effectiveness in combating epidemics and pandemics.

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ACKNOWLEDGMENTS:

This work was partly supported by FAPEMIG (APQ-0037421), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) [Finance Code 001], and CNPq in Brazil.

SUPPLEMENTARY MATERIALS:

Code and data: https://zenodo.org/record/7805587#.ZC7D33bMKUk.

  • FUNDING:

    This work was partly supported by FAPEMIG (APQ-0037421), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brazil (CAPES) [Finance Code 001], and CNPq in Brazil.

Publication Dates

  • Publication in this collection
    01 Dec 2023
  • Date of issue
    2023

History

  • Received
    02 May 2023
  • Reviewed
    24 Aug 2023
  • Accepted
    18 Oct 2023
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Associação Brasileira de Pós -Graduação em Saúde Coletiva São Paulo - SP - Brazil
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