Mathematical model points to the need for total blockade in the state to help contain the expansion of covid-19
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 on Tuesday (12) / 05).
Between May 8 and 10, an average of 1,839 new daily cases of covid-19 were recorded across the state, with 1,033 in the capital alone. There were also 93 deaths in the capital and 168 in the state (also over the three-day average). If the contagion rate (R0) – which is the number of people to whom an infected person transmits the virus – is observed in the thirty days prior to May 10, at the end of June São Paulo will account for 53,500 new infections by day, with 20,800 daily cases in the city of São Paulo alone. The number of daily deaths will reach 2,500 in the state, of which 1,100 will occur in the city of São Paulo. During this period, it is estimated that the number of new cases doubled every 11.5 days for the state and every 12.9 days for the capital. For deaths, the number was doubling every 13.5 days in the state and every 14.7 days in the city.
Lockdown in SP: covid-19 case projection map
Projections made by a Unicamp researcher indicate that, if the rate of contagion of the new coronavirus observed until the beginning of May is maintained, by the end of June São Paulo will account for 53,500 new infections and 2,500 deaths per day, 20 of which , 8 thousand cases and 1.1 deaths in the capital alone (image: Intelligent Monitoring System / Government of the State of São Paulo)
Projection for the number of new daily cases of covid-19 for São Paulo, state and capital, 05/12 to 06/30.
Basic number of reproduction (R0) and number of days to double the number of daily cases.
O calculation was made considering the real data of growth of 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. That is, at the end of april, every 100 infected paulistas transmitted the new coronavirus to almost 150 people, on average (over a period of about 7.5 days after becoming infected, according to the model used).
“These projections have a high chance of being underestimated, since the level of isolation has been falling since the beginning of April (see figure) and, between May 5 and 9, it did not exceed 50%, which will cause the rate of contagion to increase. 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 contagion level 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, because the level of occupancy of ICU beds [Unidade de Terapia Intensiva] it is already above 80%. If the isolation is not increased urgently, the state will have to adopt more drastic measures of containment, as occurred in Italy, or the situation will become unsustainable ”, says mathematician Renato Pedrosa, professor at the Unicamp Geosciences Institute and coordinator of the Special Program FAPESP Science, Technology and Innovation Indicators.
Level of social isolation in São Paulo (%) with trend lines, state and capital, 3/21 to 5/9.
Level of social isolation in São Paulo (%) with trend lines,
state and capital, 3/21 to 5/9
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). O model allows estimating 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 when the country or region reached the mark of 100 cases).
To develop the model, Pedrosa used data from 50 US states and 110 other countries, including Brazil. Countries were selected for which sufficient information was available to calculate the exponential growth rate in the period when the hundredth case of the disease was recorded. The meteorological information was obtained from a database of the National Oceanic and Atmospheric Administration (NOAA), an institution that is part of the United States Department of Commerce. Data on the expansion of covid-19 until April 10 came from two sources: the Center for Systems Science 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 find it more difficult to spread in countries with hot and humid climates. But, according to this model, the effect of climatic variables on the initial rate of disease expansion was not significant when including population density variables and / or the date of disease onset [100º caso]. This confirmed the experience of Brazil and other countries that were in the summer period, with hot and humid weather, and suffered severe expansion from COVID-19 ”, says Pedrosa.
“The date of the 100th case came up in an interesting way. The later this event occurred in a given location, the lower the initial expansion rate of covid-19. A possible explanation for this finding is that, in places where the virus was slow to arrive, the population was gaining awareness of the need to adopt protective measures, such as washing hands, using gel alcohol, avoiding handshakes and agglomerations. It is decreased the transmission speed the same in the initial stages ”, he evaluates.
According to Pedrosa, once this effect is discounted, the population density of the different regions analyzed – measured by the number of inhabitants per square kilometer – became the most relevant variable to estimate the free expansion rate of covid-19, that is, without any mitigation effect from different sources, and how contagion would be in this situation. The more densely populated the region, the higher the rate of free contagion, something expected conceptually, but, according to Pedrosa, applied for the first time in the analysis of the contagion rate of covid-19
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Based on these results, Pedrosa decided to estimate the rate of contagion attenuation that would be necessary to control the disease in all Brazilian capitals and in 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 Fortress (7,786 inhab./km2), Sao Paulo (7,398 inhab./km2), Belo Horizonte (7,167 inhab./km2), Recife (7,040 inhab./km2) and Rio de Janeiro (5,267 inhab./km2). If no social distance measure had been adopted to contain the advance of the new coronavirus in these municipalities, calculates the researcher, everyone would 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 New York City, in the United States, where the number of cases doubled every 1.4 days during the week of greatest pandemic intensity, right at the beginning. The population density of New York reaches more than 25 thousand inhabitants / km2 in Manhattan, and the case was analyzed in the article resulting from the research ”, observes the researcher.
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“To control the disease in the four most densely populated cities in the country, it is necessary to reduce the rate of free contagion by 84%, which would be possible with at least 60% of social isolation combined with the mandatory use of good quality masks, for example ”, Estimates Pedrosa.
O mask protection potential can be calculated, according to a study available in the arXiv repository (also in a preprint version), which evaluated the efficiency of several models to mitigate contagion, which can be very significant, depending on the coverage of the 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 mask types varies widely, from practically zero for homemade masks of unsuitable material to more than 90% for masks of type N95, used by professionals and that cost a lot, being inaccessible to the majority of the population ”, says the researcher.
According to him, the effect of the recent measures will take some time to be evaluated, which will delay the measures to be adopted, which are urgent and will have an impact, likewise, only in two or three weeks.
Pedrosa points out that RMSP encompasses several high-density cities, that have reproduction numbers [R0] close to that 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 the very short term if measures leading to increased isolation fail ”, Concludes Pedrosa.
* Text updated on May 12, 2020.