COVID-19

Since the beginning of the pandemic, we worked on the development of numerical methods and statistical analysis that could help the understanding and control of the pandemic. Most studies refer to analyses obtained from mobile mobility data, along with mathematical and statistical models. The studies involve a large team and a wide collaboration network (collaborators)

Opening Lecture at the Brazilian National Congress of Applied and Computational Mathematics (CNMAC, 2023): “Emergência matemática: modelagem da dinâmica epidemiológica na pandemia” – PDF – Slides: 16×9, 3×4

Mobility Data

Most of our studies used data from a company called InLoco, which changed its name to Incognia in 2021. The company provides digital intelligence services based on mobile geolocation data. The company has a great concern for data safety and privacy (politica de privacidade) and opened aggregated and anonymous data only for research during the pandemic.

How are data collected?

During 2020, the InLoco Software Development Kit – SDK was installed in over 1 fourth of the Brazilian population.

GPS
Wi-Fi
Bluetooth-LE
Phone
Activity

Time and space resolution is very high, but no personal information is tracked.

How are the data processed?

We received the data already anonymized and aggregated to a maximum resolution of hundreds of meters.

Mobility

Mobility between places (usually cities) is measured from trip counts from users’ sequences of positions.

We aggregate millions of trips between cities to infer flux between cities.

H3 Grids (https://h3geo.org/) :

Social Isolation
Mobility between places

Levels:

Cities
Neighborhoods (H3 level 8, ~460 m wide)
States and larger regions

Social Isolation Index

Panel with the index for thousands of Brazilian cities. Click on the map to see data!

The index represents the percentage of people who stayed at home during a given day. We produce 2 graphs:

Daily isolation index and its weekly moving average.
Relative variation of the index from a period prior to pandemic (relative to Feb 2020).

This analysis uses a sample from InLoco company, which does not take into account all the population and may have biases.

(Click on the map to see indexes)

Isolation Index

Mobility Analyses

Trips between Brazilian cities

Estado de São Paulo

Zoom Nordeste

Zoom Litoral Nordeste

Zoom Centro Sudeste

Zoom Sudeste – Sul

Evolução de viagens entre municípios incluindo isolamento social

Modeling future spread of infections via mobile geolocation data and population dynamics

Risk analysis for 2 states of Brazil, based on a spreading model using mobile geolocation data. Plos One, (medrxiv)

Network spreading model equations — Network model

Dissemination video – Thanks to LM|Assessoria Estatística (Portuguese only)

Warning: This model is not intended to capture the correct amount of infected individuals, but it captures the spreading patterns.

Spatial-temporal infection model simulation assuming an infection rate of 0.4 and 1 infected person on the 1st of March in the city of São Paulo. More details in the PLOS-ONE paper.

Infection rank and confirmed cases by city — Rank of infection (filled circles, left axis) and number of confirmed COVID19 cases (filled triangles, right axis) for São Paulo state on the 1st of May 2020.

Spatial-temporal infection model simulation assuming an infection rate of 0.4 and 1 infected person on the 1st of March in the city of Rio de Janeiro. More details in the PLOS-ONE paper.

Social Distancing and epidemic dynamics

A snapshot of a pandemic: The interplay between social isolation and COVID-19 dynamics in Brazil. Published in Patterns (Cell Press). (DOI)

During the coronavirus disease 2019 (COVID-19) pandemic, governments used mobility data to assess the effectiveness of social distancing policies, but is it really possible to measure the effectiveness of epidemic control measures using mobility data? In this work, we found that the relationship between mobility data and epidemic metrics is far from being simple in heterogeneous countries such as Brazil, but there are clear relations between them if other factors are taken into account. We have found two regimes under which the outcome of epidemic control measures are related to mobility data, which depend on when social distancing policies were implemented. Early implementation of social restrictions as a preventive measure leads to lower incidence peaks with an overall smaller intensity of the restrictions, while the implementation at later stages, as a remedy for high epidemic metrics, while effective, requires a greater intensity of the restrictions and may bring a greater burden to the health system.

Relative isolation versus case growth — The dispersion between the mean relative isolation index of 1 week ago and the 7-day moving average of incidence for 32 cities during the upward phase. Colors refer to the stage. The line is a LOESS . The value of S is the skewness coefficient of the normalized LOESS curve.

Evolution and epidemic spread of SARS-CoV-2 in Brazil

Effort in collaboration with CADDE and other collaborators (MEDRXIV , DOI), published in Science.

Regional Spreading Factors

Study of several regional spreading factors. Collaboration with Miguel Nicolelis (Consórsio Nordeste/Duke) and other partners. The preprint was divided into 2 papers, one with the spreading study, published in Nature Scientific Reports, and the other, with Dengue related studies, was strongly modified and is under review in another journal.

Federal highways and case evolution — **Maps of Brazil representing the routes of the main federal highways**, as well as the evolution of the geographic distribution of COVID-19 cases on three dates (April 1st, June 1st, and August 1st), and the distribution of COVID-19 deaths on August 1st (last column).

Brazilian boomerang effect — **Quantification of the Brazilian “boomerang effect”:** Representation of all “boomerangs” that occurred around major Brazilian state capitals and mid-size cities across the whole country. In this map, arcs represent the flow of people from the interior towards the capital. The arc color code represents the number of interior cities that sent severely ill patients to be admitted in hospitals in a capital or mid-size town; red being the highest number of locations, orange and yellow next, while a smaller number of locations are represented in light blue.

Dengue versus COVID-19: arrival in cities — **Dengue versus COVID:** (A) Bars represent the day the first COVID-19 case (blue bars) was officially reported in each state (using São Paulo’s first case on February 26^(th) , 2020 as the 0 reference), the number of days estimated by a mathematical model for each state to reach 500 cases per 100,000 inhabitants (yellow bars), and the days in which each of Brazilian states actually reach the mark of 500 cases per 100,000 inhabitants (orange bars). Notice how much longer it took for MT, BA, SC, SP, GO, MS, PR, MG to reach the 500/100,000 milestone. (B) Comparison of the evolution of COVID-19 (yellow line), dengue 2019 and dengue 2020 new cases per epidemiological week. (C, D, and E) Comparison between the geographic distribution of COVID-19 cases (C), and incidence (C) until June 30^(th) , 2020, and dengue fever cases and incidence in Brazil (D and D’) until May 31^(st), 2020, and for dengue cases and incidence (E and E’) summing data from 2019 and until May 31^(st), 2020.

Robot Dance: optimal control of the pandemic

Study of optimal control based on social distancing and hospital bed sharing on a complex network (Euro J. Comp. Optimization). Preprint, DOI

Robot Dance: connections around São Paulo — **Robot dance in action**: The left map zooms in the connections between the SP city and the SW district. The link SP-SW is critical for the network, but preventing commuting eliminating the link) is not the solution. The middle graph shows that cutting the circulation in the link has practically no effect on the situation in SW/SP. By contrast, as shown in the bottom graph, allowing for commuting between the nodes (keeping the link) while implementing a pool of ICU beds improves significantly the overall state for SW without affecting much the situation in SP.

Attack rate in Manaus compared to São Paulo

Paper “Three-quarters attack rate of SARS-CoV-2 in the Brazilian Amazon during a largely unmitigated epidemic”, Science, 2020. See also comment in Lancet, 2021.

Antibody prevalence in Manaus and São Paulo — SARS-CoV-2 antibody prevalence estimates in Manaus (A) and São Paulo (C) with a range of corrections. Error bars are 95% confidence intervals. Grey bars are standardized daily mortality using confirmed COVID-19 deaths from the SIVEP-Gripe (<https://covid.saude.gov.br/>) notification system and standardized by the direct method using the total projected Brazilian population for 2020 as reference. Black lines are rescaled cumulative deaths, such that the maximum is set to the maximum seroprevalence estimate for each city.

Spreading of P1 variant (Manaus)

Genomics and epidemiology of the P.1 SARS-CoV-2 lineage in Manaus, Brazil. Pre-print, Science.

Trips from Manaus to other cities — Trips registered in November from Manaus to other cities of the country (InLoco data).

Social and Racial Vulnerabilities in São Paulo

Higher risk of death from COVID-19 in low-income and non-White populations of São Paulo, Brazil. MEDRXIV, BMJ Global Health

Relative risk of SARI hospitalisation for the GMSP (A). Seven-day moving average of daily median levels in social distancing by race (B) and income (C). Difference in daily social isolation by race (D) and income groups (E) after the introduction of NPI. In Panels (B) and (C), solid lines show population-weighted median isolation levels and shaded areas show population-weighted interquartile range (25%-75%). Dashed vertical lines indicate the dates of NPIs that closed schools (March 13 state NPI) and non-essential activities (March 18 and 22, municipal and state NPIs respectively).

Social Isolation and seismic vibrations

Geophys. Res. Lett.: “Using Seismic Noise Levels to Monitor Social Isolation: An Example from Rio de Janeiro, Brazil” (pre-print , published)

Seismic noise versus social isolation — Comparison of seismic noise level (blue and dark blue lines, in nm/s, left scale) with the “InLoco” Social Distancing Index (Ik, red line, fraction of the population staying at home).

Scale free (fractal) dynamics of COVID-19

In modeling the spread of diseases, a major question is how to formulate the mechanism of contact between infectious individuals and others in the population. Some of the key issues are: if one person is infected with the disease, how many other people will be at risk? How does the number of contacts differ from person to person? And how does this number change in face of social-distancing measures? In this paper, we describe a model for disease spread in which each infectious individual has a small number of contacts that is independent of the stage of the epidemic and of population size. We find that a “scale-free” or “fractal” model of contagion describes detailed data obtained from a city in Brazil better than traditional models of infectious diseases.

Scale-free dynamics of Covid-19 in a Brazilian city. Applied Mathematical Modelling, 2023, 121, pp.166-184. DOI

Social isolation in São Caetano do Sul — Social Isolation Metrics for the city of São Caetano do Sul indicating the percentage of people that stayed home during the respective day. Two indexes are shown: in blue, the index from the InLoco company and in green the official index from the state government of São Paulo. The daily index is shown in light colours and the seven-day moving average is shown in dark colours, for each source. Horizontal bars indicate the average social isolation index, using the official government dataset, of the first and second waves. The figure shows how adherence to social distancing policies was drastically reduced in the second wave compared to the first wave

Collaborators, partners and acknowledgements – Thanks!

Team, collaborators and partner organizations:

Colegas e alunos do Departamento de Matemática Aplicada do IME-USP: Sérgio Oliva, Cláudia Peixoto, Renato Vicente, Diego Marcondes (doutorando), Milena Oliveira (mestranda).
InLoco, em especial o Afonso Delgado. Boa parte das pesquisas realizadas são essencialmente baseadas em dados de mobilidade fornecidos pela empresa, que tem sido uma parceira de primeira desde 2018, em estudos relacionados a dissiminação de dengue no país.
Governo de Estado de São Paulo, via Patrícia Ellen e assessores (especialmente a Bárbara Régis) e Dimas Covas (diretor do Instituto Butantan), na confiança e parceria dentro do centro de crise do estado.
Consórcio Nordeste, via Rafael Raimundo (UFPB) e Miguel Nicolelis (Duke).
Observatório-COVID19-BR , em particular via Renato Coutinho (UFABC), Roberto Kraenkel (IFT-UNESP) e Paulo Prado (USP).
CADDE, especialmente Ester Sabino (USP), Nuno Faria (Oxford/Imperial), e Rafael Pereira (IPEA), além dos alunos e outros pesquisadores envolvidos.
COVID-RADAR, em particular o Sami Yamouni (Serasa) e Fabrício Vasselai (Michigan), além de outros pesquisadores envolvidos na iniciativa.
CEPID-CeMEAI, em particular os pesquisadores Paulo Silva e Silva (UNICAMP), Luis Nonato (ICMC), Claudia Sagastizábal (UNICAMP) e Tiago Pereira (ICMC) na iniciativa RobotDance e outros.
Itaú – Todos pela Saúde, em particular nos projetos de revisão de Mortalidade (Paulo Lotufo – FM-USP) e no projeto de análise de imunidade de rebanho no Amazonas (Ester Sabino IMT-USP e CADDE).
Diversos professores e pesquisadores da USP, muitos que participaram de discussões iniciais, incluindo o reitor Vahan Agopyan, o pró-reitor Carlos Carlotti e o Diretor do IME, Junior Barrera, por ajudar a estreitar a parceria com o governo do estado.
Lorena Barberia (USP e Rede Pesquisa Solidária) e colaborades.
Martin Schreiber (TU Munich) – Long-time collaborator, helped out on the parallelization of geocoding for mobility data, allowing coupled mobility analysis of the whole country.
Mariana Pereira de Melo (Escola de Engenharia de Lorena – USP) e Cláudia Pio (UNESP)
Helder Nakaya (FCF-USP)
Sílvio Ferreira (UFV) e alunos Wesley Cota e Guilherme Costa
Marcelo Assumpção (IAG-USP) e colegas no divertido cruzamento de isolamento com vibração sísmica.
Airton Deppman (Física-USP) e colegas da física na análise “fractal” da covid-19.
Raquel Rolnik (FAU-USP) e colaboradores
LM|Assessoria Estatística e Laryssa Costa
Vários outros pesquisadores que temos colaborado nessa empreitada da COVID-19!