key: cord-0982980-p3d5b1ia
authors: Valiati, Naiara C.M.; Villela, Daniel A.M.
title: Modelling policy combinations of vaccination and transmission suppression of SARS-CoV-2 in Rio de Janeiro, Brazil
date: 2021-12-31
journal: Infect Dis Model
DOI: 10.1016/j.idm.2021.12.007
sha: 77cac431ae3b04dd4331e48b04a1407fae509f1a
doc_id: 982980
cord_uid: p3d5b1ia

COVID-19 vaccination in Brazil required a phased program, with priorities for age groups, health workers, and vulnerable people. Social distancing and isolation interventions have been essential to mitigate the advance of the pandemic in several countries. We developed a mathematical model capable of capturing the dynamics of the SARS-CoV-2 dissemination aligned with social distancing, isolation measures, and vaccination. Surveillance data from the city of Rio de Janeiro provided a case study to analyze possible scenarios, including non-pharmaceutical interventions and vaccination in the epidemic scenario. Our results demonstrate that the combination of vaccination and policies of transmission suppression potentially lowered the number of hospitalized cases by 380+ and 66+ thousand cases, respectively, compared to an absence of such policies. On top of transmission suppression-only policies, vaccination impacted more than 230+ thousand averted hospitalized cases and 43+ thousand averted deaths. Therefore, health surveillance activities should be maintained along with vaccination planning in scheduled groups until a large vaccinated coverage is reached. Furthermore, this analytical framework enables evaluation of such scenarios.

1 Introduction symptoms, be hospitalized, and die. Therefore, these individuals evolve to different but relatable classes of individuals, as shown in Fig. 1 with the classes that end with the letter "v". The reduced 66 parameters related to these different degrees of severity were previously reported (Hogan et al.) . 67 The infection rate between susceptible individuals and symptomatic is β, and with asymptomatic 68 individuals is β A . When they become exposed individuals, the time to evolve to infected is the 69 incubation time τ inc . At the end of this time, the individual has a probability ρ S of developing 70 symptoms.

The time required for an asymptomatic individual to evolve to death is α −1 A , whereas for the 72 symptomatic individuals is α −1 . It is expected that α > α A due to higher morbidity in the former 73 case, besides the fact that asymptomatic individuals do not present themselves as clinical cases.

Symptomatic individuals can evolve to a severe case with a risk probability of α H . The symptomatic 75 (C) and severe cases (H) individuals are modeled separately due to their different epidemiological 76 mechanisms Siordia Jr, 2020) , and to allow the test of non-pharmaceutical 77 methodologies that target these individuals separately. The separation between these individuals is 78 mainly based on their symptoms, e.g., mild/symptomatic and symptoms requiring hospitalization.

Severe cases exhibit clinical conditions for hospitalization, such as oxygen saturation lower than 93%, 80 dyspnea, or multiple organ failure (Wu and McGoogan, 2020; Betti and Heffernan, 2021; Musa et al., 81 2021; Chevrier et al., 2021) . Both can evolve to death (or the symptomatic case can evolve to the severe 82 case) separately with different case-fatality ratios, as shown in the literature (Wu and McGoogan, 83 2020). It is vital to understand whether isolating only the severe cases is an adequate measure to 84 mitigate the pandemic or if we should apply a broader approach when applying non-pharmaceutical 85 interventions.

The parameters related to asymptomatic individuals, such as β A and α A are calculated through 87 a product between a reducing factor (Byambasuren et al., 2020) f A and the original parameter for 88 symptomatic individuals β and α respectively. Regarding the individuals that were vaccinated but 89 are not immunized, another reducing factor is considered (Palacios et al., 2021) , f v . This factor 90 applies to reduce the infection rate β with the product β · f v . These individuals also have a reducing 91 factor applied to their hospitalization risk (Palacios et al., 2021) , f v,H .

The recovery of infected individuals (symptomatic and severe) is controlled by the recovery time from illness onset to dyspnea clinical condition . We calculated the recovery rate of individuals (γ H = 1 τ disc −τ dysp ) using both the discharge and dyspnea time, as we considered a 100 stochastic implementation of our model.

The ODE system which resumes this model is: β I and β Im for the specific age groups. Due to imperfect application of social distancing intervention, 106 each intervention is controlled by a success rate.

The fact that the model is stratified by age groups opens a new range of different scenarios, e.g.

when applying the social distancing intervention to younger age groups, we can simulate limitation 109 of school activities. The reduction is applied to the R 0 value, from which the infection rates are 110 calculated, by multiplying it with the reduction factor κ = 0.65. The social distancing applied to the

The application of isolation interventions is made by reducing the encounter probability between 115 susceptible and infected individuals. Different scenarios are tested in this work. In the lockdown 116 scenario (L), we alter the susceptible flow equation to

Another intervention possibility is when tests are applied to the individuals, and a quarantine 118 is applied where symptomatic cases are isolated with a probability σ and asymptomatic with a 119 probability σ A , this condition is labeled as TQ-C. In this scenario, we modify the susceptible flow 120 equation to

If we only isolate the symptomatic cases (scenario TQ), we change the susceptible individuals 122 flow equation to

The scenario where we only isolate the severe cases is termed TQ-S, and we modify the susceptible 124 flow equation to

The exposed, vaccinated, and partially immunized compartments are also changed as the susceptible 126 flow, depending on the applied scenario. Table 1 summarizes the parameters used in the model 127 with their respective values and references. Only four parameters were fitted to represent the SARI 128 notification data for the city of Rio de Janeiro: the basic transmission rate (β) via R 0 , and the three 129 probabilities of isolation (for symptomatic cases (σ), asymptomatic cases (σ A ) and lockdown scenario 130 (σ L )). The other parameters are recovered from the literature (Table 1) . (Byambasuren et al., 2020) f A , the probability of developing symptoms (Byambasuren et al., 2020 ) ρ S , and the incubation time (Lauer et al., 2020) J o u r n a l P r e -p r o o f equations in the ODE system are used to obtain the transition probabilities (Allen, 2017 Throughout the pandemic, the scenario was altered several times due to governmental decisions 156 of applying the interventions or making them more flexible and the incomplete adherence of the 157 population. In this section, we evaluate how the model behaves when we use the same quarantine 158 severity as applied by the government for each period while comparing the results to real-time data.

Our approach is based on the Rio de Janeiro municipality and state real pandemic decrees, with slight 160 adjustments, as the accordance of the population to governmental decisions is not straightforward. 161 We consider no intervention done between 01 January 2020 and 15 March 2020 (day 1 to day 74). In order to evaluate the vaccination program, we used real vaccination data notification from the 178 city of the Rio de Janeiro applied to each group at the specific dates on which they were applied. 

where λ(t) represents cumulative deaths or hospitalization at time t, specif ic refers to the specific 192 scenario studied scenario, and non represents the scenario without vaccination and restrictions.

3 Results

The model captured the dynamics of the epidemics in Rio de Janeiro successfully regarding the 195 hospitalizations compared to SARI notified cases (Fig. 2 ). As the model does not account for all the 196 influenza-like illness, but it is limited to the SARS-CoV-2 cases, there should be a difference between peaks maintain high number of deaths and hospitalizations.

As shown in Fig.4 , there is a marked difference in the effectiveness of each intervention alone. Table 1 , with the exception of R 0 , which is 3.5.

As our model is stratified by age groups, we also observe how the different interventions change the number of deaths and hospitalizations by age, as shown by Fig.5 . The quarantine of all cases, the 225 social distancing of all individuals, and the combination of this intervention with the quarantine of 226 symptomatic cases are the three most effective interventions, as also seen by Fig.4 . In all cases, despite 227 isolating or distancing different age groups, the pattern of hospitalizations and deaths regarding age 228 groups is very similar. The major difference is observed in delaying the pandemic peak and the 229 pandemic's length, broadening its profile through time but not through age groups. Hospitalizations The main objective of NPI interventions is to mitigate the effect of the pandemic for proper health 237 care attention to mild and severe cases. As shown by Fig.4 independently from the nature of the 238 intervention (social distancing or isolation of cases), as expected and seen in many studies (Matrajt 239 and Leung, 2020; Ferguson et al., 2020; Flaxman et al., 2020; Prem et al., 2020) , delaying the epidemic 240 peak is a consequence of the reduction in transmission intensity.

As demonstrated in Fig.4 an enforced isolation measure, as the asymptomatic cases also impact the transmission dynamics.

The correct identification and consequently isolation of these cases pose a problem which has been 248 discussed in the actual pandemic (Gandhi et al., 2020; Nishiura et al., 2020) , in some cases, following 249 the correct procedure to identify and isolate these cases were responsible for ending the pandemic 250 (Day, 2020) . The isolation of only the severe cases did alter significantly the dynamics, demonstrating 251 the importance of having a model in which mild and severe cases are studied separately, as they have 252 marked differences in their epidemiology Siordia Jr, 2020) besides having some 253 studies indicating some similarities (Yilmaz et al., 2020; Wu and McGoogan, 2020 This is a crucial moment to study and show that we must yet consider the application of strict 298 interventions of social distancing, isolation, and vaccination as the risk of SARS-CoV-2 transmission is 299 present in multiple countries. The modelling in this work shows that effective control of the COVID-19 300 pandemic requires a combination of these efforts.

This study was financed in part by the Coordination for the Improvement of Higher Education Personnel(Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-CAPES) -Finance Code 001. DV is grateful to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq Refs 441057/2020-9, 309569/2019-2).

All SARI and ARI notification data are publicly available at OpenDataSUS database, maintained by the Ministry of Health, located at https://opendatasus.saude.gov.br/.

Authors declare no competing interests.

No approval by an ethics committee was necessary, since the work involved only simulations and secondary anonymized data which are publicly available.

Daniel A.M. Villela has a grant for modeling COVID-19 scenarios in Brazil, funded from the National Council for Scientific and Technological Development, a funding agency from the Brazilian federal government. Daniel A.M. Villela is Research Scientist, working for Fiocruz, the biggest research institution in public health in Brazil, which has a vaccine producing unit. All authors declare no financial benefits.

☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

X The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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