Projections made with a mathematical model developed at the State University of Campinas (Unicamp) indicate that the adoption of mandatory lockdown in the State of São Paulo will be inevitable if the level of social isolation does not rise significantly in the coming weeks, starting this Tuesday (12 /05).
Between the 8th and 10th of May, an average of 1.839 new daily cases of COVID-19 were recorded across the state, 1.033 of which were in the capital alone. If the contagion rate (R0) – which is the number of people to which an infected person transmits the virus – observed in the 30 days prior to May 10 is maintained, at the end of June São Paulo will record 53,5 thousand new infections due to day, with 20,8 thousand daily cases in the city of São Paulo alone. During this period, it is estimated that the number of new cases will double every 11,5 days for the state and every 12,9 days for the capital, in the coming weeks.
The calculation was made considering real data on the growth in the number of cases over the last month, which indicate a contagion rate of 1,49 for the state and 1,44 for the city of São Paulo. In other words, at the end of April, every 100 infected São Paulo residents transmitted the new coronavirus to almost 150 people, on average (over a period of around 7,5 days after becoming infected, according to the modeling used).
“These projections are highly likely to be underestimated, as the level of isolation has been falling since the beginning of April and, between May 5th and 9th, it did not exceed 50%, which will cause an increase in the contagion rate. This will be reflected in 15 or 20 days in the number of new cases, then in the number of deaths. But, even if the estimated level of contagion is maintained until May 10, the projected values indicate that this month the public health system in the Metropolitan Region of São Paulo [RMSP] will reach the limit, as the level of occupancy of hospital beds ICU [Intensive Care Unit] is already above 80%. If the isolation is not urgently expanded, the state will have to adopt more drastic containment measures, as occurred in Italy, or the situation will become unsustainable”, says mathematician Renato Pedrosa, professor at the Unicamp Institute of Geosciences and coordinator of the Special Program FAPESP Science, Technology and Innovation Indicators.
The estimates were made using a model developed by Pedrosa and described in an article available on the medRxiv platform in a preprint version (not yet peer-reviewed). The model makes it possible to estimate the transmission dynamics of COVID-19 in different locations, taking into account climatic variables (temperature and absolute humidity), population density and the timeline of the onset of the disease (date on which the country or region reached the 100 case mark).
To develop the model, Pedrosa used data from 50 North American states and 110 other countries, including Brazil. Countries were selected for which there was sufficient information available to calculate the exponential growth rate in the period in which the hundredth case of the disease was recorded. The meteorological information was obtained from a database from the National Oceanic and Atmospheric Administration (NOAA), an institution that is part of the United States Department of Commerce. The data regarding the expansion of COVID-19 until April 10th came from two sources: the Center for Systems Sciences and Engineering at Johns Hopkins University (United States) and the European Center for Disease Control and Prevention, based in Sweden.
“Initial studies suggested that the new coronavirus would have more difficulty spreading in countries with hot and humid climates. However, according to this model, the effect of climate variables on the initial rate of disease expansion was not significant when including population density variables and/or the date of disease onset [100th case]. This confirmed the experience of Brazil and other countries that were in the summer period, with hot and humid weather, and suffered severe expansion of COVID-19”, says Pedrosa.
“The date of the hundredth case appeared in an interesting way. The later this event occurred in a given location, the lower the initial rate of spread of COVID-19. A possible explanation for this finding is that, in places where the virus was slow to arrive, the population became aware of the need to adopt protective measures, such as washing hands, using alcohol gel, avoiding handshakes and crowds. And this reduced the transmission speed even in the initial stages”, he assesses.
According to Pedrosa, once this effect was discounted, the population density of the different regions analyzed – measured by the number of inhabitants per square kilometer – became the most relevant variable for estimating the rate of free expansion of COVID-19, that is, without any mitigation effect from different sources, and what contagion would be like in this situation. The more densely populated the region, the higher the free contagion rate would be, something conceptually expected, but, according to Pedrosa, applied for the first time in the analysis of the COVID-19 contagion rate.
Attenuated contagion
Based on these results, Pedrosa decided to estimate the contagion attenuation rate that would be necessary to control the disease in all Brazilian capitals and the Federal District, depending on the population density of each city.
At the top of the list of the most densely populated in the country are Fortaleza (7.786 inhabitants/km2), São Paulo (7.398 inhabitants/km2), Belo Horizonte (7.167 inhabitants/km2), Recife (7.040 inhabitants/km2) and Rio de Janeiro (5.267 inhabitants/km2). If no social distancing measures had been adopted to contain the spread of the new coronavirus in these municipalities, the researcher calculates, they would all have a contagion rate above 5,8 and the number of infections would double in less than two days.
“This occurred at the beginning of the pandemic in other countries, such as in New York City, in the United States, where the number of cases doubled every 1,4 days during the week of greatest intensity of the pandemic, right at its beginning. New York's population density reaches more than 25 thousand inhabitants/km2 in Manhattan, and the case was analyzed in the article resulting from the research”, observes the researcher.
“To control the disease in the four most densely populated cities in the country, it is necessary to reduce the free contagion rate by 84%, which would be possible with at least 60% social isolation combined with the mandatory use of good quality masks, for example ”, estimates Pedrosa.
The protective potential of masks can be calculated, according to a study available in the arXiv repository (also in preprint version), which evaluated the efficiency of different models to mitigate contagion, which can be very significant, depending on the coverage of use and the type of mask. “The difficulty in using the results of this study to estimate the effect of mandatory use is that the efficiency of the types of mask varies greatly, from practically zero for masks made at home from inappropriate materials to more than 90% for masks of the type N95, used by professionals and which are very expensive and inaccessible to the majority of the population”, says the researcher.
Pedrosa highlights that the RMSP encompasses several cities with high population density, which have reproduction numbers [R0] close to those observed in the capital or even higher, such as Diadema, Carapicuíba and Osasco. “Therefore, for a region with more than 21 million inhabitants, the situation could become even more serious in a very short term if measures that lead to increased isolation fail”, concludes Pedrosa.
Read article in full with graphics and photos on the Agência Fapesp website.
Access research article by professor Renato HL Pedrosa at the Scientific Repository - Covid19/Unicamp.
