{"id":373679,"date":"2021-01-22T18:25:12","date_gmt":"2021-01-22T21:25:12","guid":{"rendered":"https:\/\/revistapesquisa.fapesp.br\/?p=373679"},"modified":"2021-01-28T15:39:27","modified_gmt":"2021-01-28T18:39:27","slug":"predicting-the-course-of-epidemics","status":"publish","type":"post","link":"https:\/\/revistapesquisa.fapesp.br\/en\/predicting-the-course-of-epidemics\/","title":{"rendered":"Predicting the course of epidemics"},"content":{"rendered":"

It is difficult to recall a time when mathematical modeling of infectious diseases gained as much visibility and interest as it has in the current crisis. \u201cThis likely reflects the sense of perplexity created by the epidemic\u2014nobody was expecting it to be so devastating,\u201d says epidemiologist Eduardo Massad, who took a position last year as a professor of applied mathematics at Funda\u00e7\u00e3o Getulio Vargas (FGV), after retiring from the University of S\u00e3o Paulo School of Medicine (FM-USP).<\/p>\n

\u201cNever before has modeling been as necessary as it is now in dealing with such a rapidly escalating epidemic,\u201d adds public-health physician and epidemiologist H\u00e9lio Neves, a professor at the School of Medical Sciences at Santa Casa S\u00e3o Paulo (FCM-SC-SP) and chair of the Technical-Scientific Committee on Covid-19 at the S\u00e3o Paulo Department of Health.<\/p>\n

Read:<\/strong>
\n– The reality of data<\/a>
\n– Natural guests<\/a>
\n– Brazil begins testing<\/a>
\n– Sergio Machado Rezende: Together against COVID-19<\/a>
\n– Restoring trust<\/a>
\n– Calculating in the dark<\/a>
\n– The size of the pandemic<\/a>
\n– The child enigma<\/a>
\n– Research during the quarantine<\/a>
\n<\/div>\n

Although all models involve uncertainty, as the dynamics they describe are fluid and the data they rely on are incomplete, their ability to make predictions of cases or deaths is supported by at least 250 years of cumulative research.<\/p>\n

It was Dutch mathematician and physicist Daniel Bernoulli (1700\u20131782) who developed the first mathematical model of the spread of infectious diseases, in an attempt to demonstrate the effectiveness of preventive inoculation against smallpox, then a widespread disease in Europe.<\/p>\n

Bernoulli published his ideas in two articles in 1760, one in the journal\u00a0M\u00e9moires de math\u00e9matique et de physique<\/em>\u00a0and the other in Mercure de France<\/em>, using the same parameters used today to predict the progression of epidemics.<\/p>\n

Bernoulli divided the population into two groups: susceptibles, i.e. those who have not yet been infected, and immunes, i.e. those who have been immunized after infection. His equations used three variables by which people move from the first to the second group. The first was the disease-reproduction rate or force of infection, which describes transmission from infected individuals to susceptible individuals. The second was the case fatality rate, and the last was life expectancy at the time of infection. His calculations assumed the immunization rate would be 100%\u2014inoculations were administered using a bifurcated needle\u2014and that there would be no risk of virus transmission from inoculated individuals to susceptible individuals. He concluded that inoculation could increase life expectancy from 26 years and 7 months to 29 years and 9 months.<\/p>\n

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Snow, J. On the Mode of Communication of Cholera, 2nd<\/sup> Ed., John Churchill, New Burlington Street, London, England, 1855\u2009\/\u2009Wikimedia <\/span><\/a> John Snow\u2019s original map of the London district of Soho, in 1854. The black squares and rectangles represent homes where people contracted choleraSnow, J. On the Mode of Communication of Cholera, 2nd<\/sup> Ed., John Churchill, New Burlington Street, London, England, 1855\u2009\/\u2009Wikimedia <\/span><\/p><\/div>\n

Cholera in London<\/strong>
\nThe cholera outbreak in London in 1854, which killed 127 people over the space of three days in early September, revealed the importance of supplementing mathematical modeling with investigation on the ground. English anesthesiologist John Snow (1813\u20131858), though not a trained epidemiologist, was able to trace the outbreak to contaminated water from a pump on Broad Street, now renamed Broadwick Street. His theory conflicted with his colleagues\u2019 and government authorities\u2019 belief, under the influence of miasma theory, that the disease had been caused by the city\u2019s foul air.<\/p>\n

Snow created a map showing that the homes of those who had died were near the contaminated pump. The map led reverend Henry Whitehead (1825\u20131896) to embrace Snow\u2019s theory of waterborne transmission and to set out in search of the index case\u2014the first case of the disease\u2014so he could then trace the path of transmission, aided by his familiarity with the district of Soho, where the outbreak had begun. \u201cWhitehead ultimately supplied [Snow] the crucial evidence for establishing the pump\u2019s role\u201d in the cholera outbreak, American linguist Steven Johnson wrote in the book\u00a0The Ghost Map<\/em>\u00a0(Zahar, 2008).<\/p>\n

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Justinc\/WIKIMEDIA<\/span><\/a> Street pumps like the one pictured here helped to spread cholera bacteria in mid-nineteenth century LondonJustinc\/WIKIMEDIA<\/span><\/p><\/div>\n

Snow died of a heart attack at 45 years of age, without receiving recognition for his ideas. Whitehead would go on to investigate another cholera outbreak in London, in 1866, this time in the company of British epidemiologist William Farr (1807\u20131883), one of the founders of medical statistics. With his knowledge of Snow\u2019s ideas and as a member of the government\u2019s health committee, Farr investigated the water supplied by two companies to residents in the city. On discovering that one company was supplying contaminated water, he immediately ordered that notices be posted in the area advising residents not to drink any water which had not been previously boiled.<\/p>\n

Biochemist William Ogilvy Kermack (1898\u20131970) and epidemiologist Anderson Gray McKendrick (1876\u20131943) of the Royal College of Physicians, in Edinburgh, later developed a theory of disease transmission that they presented in a 1927 article in the\u00a0Proceedings of the Royal Society A<\/em>. This theory laid the groundwork for today\u2019s modeling methods. Their SIR model, named after the initials of three groups\u2014susceptibles, infected, and recovered\u2014built further on Bernoulli\u2019s earlier concepts. During an epidemic, people move from one group to the other when an infected individual transmits the disease-causing agent to a community of individuals who are more or less susceptible. An epidemic spreads at a rate depending on the transmission rate and case fatality rate\u2014which vary over the course of the epidemic\u2014and ends when susceptibles are infected and either recover and become immune, or die.<\/p>\n

The SIR model has since been refined, especially since the 1970s with the introduction of computerized mathematical modeling. The R now stands for \u201cremoved\u201d to include not only those who have recovered, but also those who have died.<\/p>\n

Using these concepts, since 1980 Massad has investigated the mechanisms of transmission of malaria, measles, dengue fever, yellow fever and, more recently, Severe Acute Respiratory Syndrome (SARS), Zika, and other infectious diseases, often developing new strategies for prevention. In 1992, his calculations helped the S\u00e3o Paulo State Department of Health (SES-SP) to save around US$15 million by vaccinating only children aged 1 to 10, rather than following the Pan American Health Organization\u2019s (PAHO) recommendation of vaccinating the entire population between 9 months and 15 years of age with a trivalent vaccine against measles, mumps, and rubella (see<\/em> Pesquisa FAPESP issue no. 8<\/em>). S\u00e3o Paulo\u2019s strategy, which was explored in detail in a 1993 article in Epidemiology & Infection<\/em>, proved successful.<\/p>\n

\u201cWe still use the SIR model, but with many more compartments\u201d, explains physicist Roberto Kraenkel, a professor in the Institute of Theoretical Physics at S\u00e3o Paulo State University (IFT-UNESP). He, along with colleagues at USP and the Federal University of ABC (UFABC), have been tasked with coordinating the COVID-19 BR Observatory, an online platform launched on March 15 to track case numbers in Brazil. \u201cWe divide the population into compartments defined as susceptible, exposed but not infectious, and infectious, with the latter compartment further divided into mild or severe cases, and individuals hospitalized or not hospitalized. Last comes the removed compartment\u2014individuals who have either become immune or have died,\u201d he explains.<\/p>\n

The Observatory team currently consists of 40 researchers based in Brazil, the US, and Germany. \u201cThey are very quick to respond,\u201d says Neves, of Santa Casa and the Municipal Health Department, who is responsible for providing data about reported cases in S\u00e3o Paulo City. \u201cI present them with a problem, they do the calculations and estimates, and have results within three hours.\u201d<\/p>\n

Case and death projections, he says, have informed the expansion of testing laboratories and hospital beds, the use of schools and sports centers to accommodate people with the milder form of COVID-19, and the management of public cemeteries. \u201cMunicipal hospital occupancy rates have remained below 60% as we have consistently expanded our bed capacity,\u201d says Neves. \u201cThe biggest problem is not knowing when the epidemic will peak.\u201d<\/p>\n

One of the Observatory groups worked to identify the cities in Brazil\u2019s three southern states and nine northeastern states that are at greatest risk of virus spread from the country\u2019s epicenter states of S\u00e3o Paulo, Rio de Janeiro, and Minas Gerais, based on road traffic. The studies were published in April as a preprint in the online science library SciELO.<\/p>\n

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\u201cThe potential for virus spread depends as much on the size of the city as on the number of road or bus links to other cities,\u201d says ecologist Paulo Guimar\u00e3es, a researcher at the Institute of Biosciences at USP, who is coordinating analysis efforts in S\u00e3o Paulo. That is why Campinas and S\u00e3o Jos\u00e9 do Rio Preto, with their links to respectively 214 and 135 other cities, are more vulnerable than their size would suggest.<\/p>\n

\u201cNetworking among experts in different fields has been highly productive,\u201d says epidemiologist Maria Am\u00e9lia Veras of FCM-SC-SP, who is collaborating with the Observatory by analyzing data and submitting conclusions. \u201cModeling can also be used to approximate reality based on parameters known from similar diseases,\u201d she explains. For example, a group of epidemiologists at Oswaldo Cruz Foundation used data from an influenza database in Brazil, Infogripe, to model the behavior of the COVID-19 pandemic. Another group, at the University of Bras\u00edlia, adapted a mathematical model used during the measles pandemic to measure the extent of the coronavirus pandemic in Greater S\u00e3o Paulo.<\/p>\n

\u201cThe biggest limitation of models is the quality of the information they are fed with, as we are dealing with phenomena that are highly fluid,\u201d says Veras. Although there is evidence that COVID-19 symptoms are less severe in people under 60, the rate of transmission across different age groups and the precise number of people infected remain unknown, since only hospitalized patients are being tested.<\/p>\n