Abstracts

Introduction

Several studies estimate the basic reproduction number (R₀) for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Most of those studies estimate R₀ between 2 and 4, but it is possible to reach values close to 8, considering the confidence interval range ¹1. Kuniya T. Prediction of the epidemic peak of coronavirus disease in Japan, 2020. J Clin Med 2020; 9:789.^,22. Zhao S, Lin Q, Ran J, Musa SS, Yang G, Wang W, et al. Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: a data-driven analysis in the early phase of the outbreak. Int J Infect Dis 2020; 92:214-7.^,33. Zhao S, Cao P, Gao D, Zhuang Z, Cai Y, Ran J, et al. Serial interval in determining the estimation of reproduction number of the novel coronavirus disease (COVID-19) during the early outbreak. J Trav Med 2020; 27:taaa033.^,44. Choi SC, Ki M. Estimating the reproductive number and the outbreak size of COVID-19 in Korea. Epidemiol Health 2020; 42:e2020011.^,55. Tuite AR, Fisman DN. Reporting, epidemic growth, and reproduction numbers for the 2019 novel coronavirus (2019-nCoV) epidemic. Ann Intern Med 2020; 172:567-8.^,66. Fang Y, Nie Y, Penny M. Transmission dynamics of the COVID-19 outbreak and effectiveness of government interventions: a data-driven analysis. J Med Virol 2020; 92:645-59.^,77. Wang Y, Wang Y, Chen Y, Qin Q. Unique epidemiological and clinical features of the emerging 2019 novel coronavirus pneumonia (COVID-19) implicate special control measures. J Med Virol 2020; 92:568-76..

Considering a R₀ of 8, it would be necessary to reduce the contact rate for each infectious case by about 90%, and for asymptomatic people by about 78%, to reach a R₀ of less than 1 if we want to achieve effective results of social distancing measures ⁸8. Diaz-Quijano FA, Rodriguez-Morales AJ, Waldman EA. Translating transmissibility measures into recommendations for coronavirus prevention. Rev Saúde Pública 2020; 54:43..

However, this contact rate reduction considers the average dynamics of transmission and do not provide information about specific situations such as household transmission or close contacts, in schools or offices.

The secondary attack rate (SAR) is the probability that an infection occurs among susceptible people within a specific group, which can indicate transmission risk related to social interactions. The estimated SAR among close contacts of SARS-CoV-2 is 35% ⁹9. Liu Y, Eggo RM, Kucharski AJ. Secondary attack rate and superspreading events for SARS-CoV-2. Lancet 2020; 395:E47..

In our study, we used an agent-based model (ABM) to evaluate contact rate reduction goals for household and close contacts and provide preventive recommendations during the coronavirus pandemic.

Methods

ABM is a computer simulation technique used for model behaviors of independent individuals or groups. Individual interactions are used to explore the individual impact on aggregate level. ABM can simulate complex systems by setting up simple rules for their agents ¹⁰10. Allen TT. Introduction to discrete event simulation and agent-based modeling. London: Springer; 2011..

We used NetLogo (http://ccl.northwestern.edu/netlogo/), a programmable modeling environment, to simulate the SARS-CoV-transmission within close contacts and the RNetLogo package to embed ABM model into the R environment for analysis ¹¹11. Thiele JC. R marries NetLogo: introduction to the RNetLogo package. J Stat Softw 2014; 58:1-41..

Model description

The model is an adaptation and extension of Virus on a Network ¹²12. Stonedahl F, Wilensky U. NetLogo virus on a network model. http://ccl.northwestern.edu/netlogo/models/VirusonaNetwork (accessed on 29/Apr/2020).
http://ccl.northwestern.edu/netlogo/mode... and Virus ¹³13. Wilensky U. NetLogo virus model. http://ccl.northwestern.edu/netlogo/models/Virus (accessed on 01/Apr/2020).
http://ccl.northwestern.edu/netlogo/mode... models that shows how SARS-CoV-2 spreads through a social network. Each node represents a person and all links represent reciprocal relationships. We model the progress of an infection through these links. Each node may be in one of four states: healthy and susceptible to infection, sick and infectious (a symptomatic or asymptomatic person transmitting the virus to other people), sick and not infectious (an infected and symptomatic person that ceases physical contact with susceptible people), and healthy and immune. Each step of the simulation, named “tick”, represents one day, and the simulation comprises 365 ticks. People may die due to the infection according to the chance of recovery. All links of dead people are excluded.

Model parameters (Box 1)

We estimated the number of possible close contacts of a person using de Dunbar’s number ¹⁴14. Dunbar R. Grooming, gossip, and the evolution of language. Cambridge: Harvard University Press; 1998.. SAR value was obtained on a study of household transmission ⁹9. Liu Y, Eggo RM, Kucharski AJ. Secondary attack rate and superspreading events for SARS-CoV-2. Lancet 2020; 395:E47.. Chance-recover was set based on Brazilian lethality data (Brazilian Ministry of Health. https://covid.saude.gov.br/, accessed on 26/Apr/2020). We estimated duration as the sum of max incubation period (from 2 to 14 days) and the recommendation for discontinuation of transmission-based precautions (7 days have passed since symptoms first appeared) ¹⁵15. Centers for Disease Control and Prevention. Clinical questions about COVID-19: questions and answers. https://www.cdc.gov/coronavirus/2019-ncov/hcp/faq.html (accessed on 26/Apr/2020).
https://www.cdc.gov/coronavirus/2019-nco... . Immunity length was set to 365, although duration of immunity to SARS-CoV-2 infection is not yet known ¹⁵15. Centers for Disease Control and Prevention. Clinical questions about COVID-19: questions and answers. https://www.cdc.gov/coronavirus/2019-ncov/hcp/faq.html (accessed on 26/Apr/2020).
https://www.cdc.gov/coronavirus/2019-nco... . We estimated the case isolation lag as the median incubation period (approximately five days) ¹⁶16. Lauer SA, Grantz KH, Bi Q, Jones FK, Zheng Q, Meredith HR, et al. The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: estimation and application. Ann Intern Med 2020; 172:577-82. plus two days, which simulate a delay on diagnosis and isolation. Those values are imprecise, since the period of infectiousness for SARS-CoV-2 is not yet established ¹⁵15. Centers for Disease Control and Prevention. Clinical questions about COVID-19: questions and answers. https://www.cdc.gov/coronavirus/2019-ncov/hcp/faq.html (accessed on 26/Apr/2020).
https://www.cdc.gov/coronavirus/2019-nco... . Therefore, we assume that all symptomatic cases are diagnosed and isolated from susceptible people two days after the onset of symptoms. Asymptomatic cases proportion was set to 18% ¹⁷17. Mizumoto K, Kagaya K, Zarebski A, Chowell G. Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020. Euro Surveill 2020; 25:2000180.. They were considered able to transmit the disease and were not isolated from susceptible people, although their role in transmission is unsettled ¹⁵15. Centers for Disease Control and Prevention. Clinical questions about COVID-19: questions and answers. https://www.cdc.gov/coronavirus/2019-ncov/hcp/faq.html (accessed on 26/Apr/2020).
https://www.cdc.gov/coronavirus/2019-nco... ^,1717. Mizumoto K, Kagaya K, Zarebski A, Chowell G. Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020. Euro Surveill 2020; 25:2000180..

Results

Results are based on mean number of infected people after 100 simulations of the model (Figures 1 and 2).

The peak of cases is 149.76 (95%CI: 149.57-149.95) for six links per node; 142.99 (95%CI: 140.76-145.22) for five links per node; 113.69 (95%CI: 108.68-118.70) for four links per node; 46.41 (95%CI: 40.17-52.65) for three links per node; 11.98 (95%CI: 10.30-13.66) for two links per node; and 3.00 (95%CI: 2.59-3.41) for one link per node. Visual inspection of the curve suggests a flattening of the curve on three links per node level.

In simulated scenarios, there is no great difference in total infected people within modifications in number of links per node for networks with average number of links per node greater than three. For six nodes, total infected are 149.85 (95%CI: 145.28-154.43); for five nodes, 148.97 (95%CI: 141.94-156.01); and for four nodes, 141.57 (95%CI: 130.62-152.53).

On the other hand, the reduction of links implies major changes in total infected for networks with average number of links per node equal or bellow three. For three nodes, total infected are 82.39 (95%CI: 68.30-96.49), for two nodes, 13.95 (95%CI: 10.60-17.31); and for one node, 2.96 (95%CI: 2.48-3.45).

Discussion

Contact rate reduction is a widespread preventive measure adopted against SARS-CoV-2 pandemics and simulations confirms its effectiveness ¹⁸18. Koo JR, Cook AR, Park M, Sun Y, Sun H, Lim JT, et al. Interventions to mitigate early spread of SARS-CoV-2 in Singapore: a modelling study. Lancet Infect Dis 2020; [Online ahead of print].. In Brazil, social distancing measures started on March 11th in the Federal District, subsequently expanded to other Federation Units ¹⁹19. Centro de Operações de Emergência em Saúde Pública, Ministério da Saúde. Especial: doença pelo coronavírus 2019. Boletim Epidemiológico 2020. https://www.saude.gov.br/images/pdf/2020/April/06/2020-04-06-BE7-Boletim-Especial-do-COE-Atualizacao-da-Avaliacao-de-Risco.pdf.
https://www.saude.gov.br/images/pdf/2020... ; however, there is a claim to relax these measures given the impacts on economic growth ²⁰20. Ao menos 25 dos 27 governadores manterão restrições contra coronavírus mesmo após Bolsonaro pedir fim de isolamento. G1 2020; 25 mar. https://g1.globo.com/politica/noticia/2020/03/25/governadoras-reagem-ao-pronunciamento-de-bolsonaro-sobre-coronavirus.ghtml.
https://g1.globo.com/politica/noticia/20... .

Household and close transmission should be evaluated as community transmission, since contact patterns between individuals are dynamic and heterogeneous across distinct scenarios ⁹9. Liu Y, Eggo RM, Kucharski AJ. Secondary attack rate and superspreading events for SARS-CoV-2. Lancet 2020; 395:E47..

The model presented indicates a possible pitfall if social distancing measures are not stepwise suspended, since the relationship between the average links per node of networks and the number of infected people seems to be s-shaped, and therefore, not linear.

Our study has several limitations. First, since models are simplifications of reality, unforeseen factors may play a key role in the dissemination of the disease. Second, the epidemiological characteristics of SARS-CoV-2 pandemics are still uncertain, including the role of asymptomatic individuals in transmission, period of infectiousness and of immunity after infection ¹⁵15. Centers for Disease Control and Prevention. Clinical questions about COVID-19: questions and answers. https://www.cdc.gov/coronavirus/2019-ncov/hcp/faq.html (accessed on 26/Apr/2020).
https://www.cdc.gov/coronavirus/2019-nco... . Third, the interpretation of R₀ is complex and its value is affected by biological, sociobehavioral and environmental factors, thus, it cannot be considered the same within different scenarios ²¹21. Delamater PL, Street EJ, Leslie TF, Yang YT, Jacobsen KH. Complexity of the basic reproduction number (R0). Emerg Infect Dis 2019; 25:1-4..

A recommendation for public health authorities is to set a long-range schedule of social distancing suspension measures, such as organizing the return of children to school according to their grade, and to provide a close surveillance of cases.

Acknowledgments

The author would like to acknowledge the University of Fortaleza (Unifor) for supporting this research.

References

Publication Dates

History