Simulating social distancing measures in household and close contact transmission of SARS-CoV-2 Simulação de medidas de distanciamento intradomiciliar e transmissão do SARS-CoV-2 por contatos próximos Simulando medidas de distanciamiento social en el hogar y transmisión del SARS-CoV-2 por contacto cercano

We sought to evaluate contact rate reduction goals for household and close contacts and to provide preventive recommendations during the coronavirus pandemic. We applied an agent-based model to simulate the transmission dynamics of SARS-CoV-2 within household or close contacts through a social network of 150 nodes. 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 people are 149.85; for five nodes, 148.97; and for four nodes, 141.57. On the other hand, for three nodes, total infected are 82.39, for two nodes, 13.95; and for one node, 2.96. This model indicates a possible pitfall if social distancing measures are not stepwise suspended and close surveillance of cases are not provided, since the relationship between average links per node and number of infected people seems to be s-shaped, and not linear. Infectious Disease Transmission; Biological Models; Severe Acute Respiratory Syndrome Correspondence C. Garcia Filho Universidade de Fortaleza. Av. Washington Soares 1321, Fortaleza, CE 60811-905, Brasil. cgarciafilho@gmail.com 1 Universidade de Fortaleza, Fortaleza, Brasil. doi: 10.1590/0102-311X00099920 Cad. Saúde Pública 2020; 36(5):e00099920 COMUNICAÇÃO BREVE BRIEF COMMUNICATION This article is published in Open Access under the Creative Commons Attribution license, which allows use, distribution, and reproduction in any medium, without restrictions, as long as the original work is correctly cited.


Introduction
Several studies estimate the basic reproduction number (R 0 ) for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Most of those studies estimate R 0 between 2 and 4, but it is possible to reach values close to 8, considering the confidence interval range 1,2,3,4,5,6,7 .
Considering a R 0 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 R 0 of less than 1 if we want to achieve effective results of social distancing measures 8 .
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% 9 .
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 10 .
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 11 .

Model description
The model is an adaptation and extension of Virus on a Network 12 and Virus 13 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 14 . SAR value was obtained on a study of household transmission 9 . 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) 15 . Immunity length was set to 365, although duration of immunity to SARS-CoV-2 infection is not yet known 15 . We estimated the case isolation lag as the median incubation period (approximately five days) 16 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 15 . 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% 17 . They were considered able to transmit the disease and were not isolated from susceptible people, although their role in transmission is unsettled 15,17 .

Results
Results are based on mean number of infected people after 100 simulations of the model (Figures 1  and 2 Cad. Saúde Pública 2020; 36(5):e00099920

Figure 2
Total estimated cases over time by average number of links per node in the network graph.

Figure 1
Estimated cases over time by average number of links per node in the network graph.

Discussion
Contact rate reduction is a widespread preventive measure adopted against SARS-CoV-2 pandemics and simulations confirms its effectiveness 18 . In Brazil, social distancing measures started on March 11th in the Federal District, subsequently expanded to other Federation Units 19 ; however, there is a claim to relax these measures given the impacts on economic growth 20 . Household and close transmission should be evaluated as community transmission, since contact patterns between individuals are dynamic and heterogeneous across distinct scenarios 9 .
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 15 . Third, the interpretation of R 0 is complex and its value is affected by biological, sociobehavioral and environmental factors, thus, it cannot be considered the same within different scenarios 21 .
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.