Special report AFP/GETTY Staff at a car-manufacturing plant in Wuhan, China, observe social-distancing measures during their lunch break. had a day off since mid-January.” Research does not get much more policy-relevant than this. When updated data in the Imperial team’s model1 indicated that the United Kingdom’s health service would soon be overwhelmed with severe cases of COVID-19, MODELLING and might face more than 500,000 deaths if the government took no action, Prime Minister Boris Johnson almost immediately announced stringent new restrictions on people’s move- ments. The same model suggested that, with no action, the United States might face 2.2 million THE PANDEMIC deaths; it was shared with the White House and new guidance on social distancing quickly The simulations driving the world’s followed (see ‘Simulation shock’). response to COVID-19. By David Adam Governments across the world are relying on mathematical projections to help guide deci- sions in this pandemic. Computer simulations account for only a fraction of the data analyses hen Neil Ferguson visited than 36 hours later, he announced on Twitter that modelling teams have performed in the cri- the heart of British govern- that he had a fever and a cough. A positive test sis, Ferguson notes, but they are an increasingly ment in London’s Downing followed. The disease-tracking scientist had important part of policymaking. But, as he and Street, he was much closer become a data point in his own project. other modellers warn, much information about to the COVID-19 pandemic Ferguson is one of the highest-profile faces in how SARS-CoV-2 spreads is still unknown and than he realized. Ferguson, a the effort to use mathematical models that pre- must be estimated or assumed — and that limits mathematical epidemiologist dict the spread of the virus — and that show how the precision of forecasts. An earlier version at Imperial College London, government actions could alter the course of of the Imperial model, for instance, estimated Wbriefed officials in mid-March on the latest the outbreak. “It’s been an immensely intensive that SARS-CoV-2 would be about as severe as results of his team’s computer models, which and exhausting few months,” says Ferguson, influenza in necessitating the hospitalization of simulated the rapid spread of the coronavirus who kept working throughout his relatively those infected. That turned out to be incorrect. SARS-CoV-2 through the UK population. Less mild symptoms of COVID-19. “I haven’t really The true performance of simulations in this 316 | Nature | Vol 580 | 16 April 2020 ©2020 Spri nger Nature Li mited. All ri ghts reserved. ©2020 Spri nger Nature Li mited. All ri ghts reserved. pandemic might become clear only months or SIMULATION SHOCK works on models of disease transmission at years from now. But to understand the value A model by Imperial College London in mid-March Technological University Dublin. of COVID-19 models, it’s crucial to know how predicted a total of more than 500,000 UK deaths Agent-based models build the same kinds of from COVID-19, and more than 2.2 million in the they are made and the assumptions on which United States if no action was taken to stop the virus virtual world as the equation-based ones, but they are built. “We’re building simplified spreading in those countries. each person can behave differently on a given representations of reality. Models are not United Kingdom United States day or in an identical situation. “These very crystal balls,” Ferguson says. 25 specific models are extremely data hungry,” says Kathleen O’Reilly, an epidemiologist at Coronavirus models: the basics 20 the London School of Hygiene and Tropical Many of the models simulating how diseases Medicine (LSHTM). “You need to collect infor- spread are unique to individual academic 15 mation on households, how individuals travel groups that have been developing them for to work and what they do at the weekend.” years. But the mathematical principles are simi- 10 lar. They are based on trying to understand how Which model to choose? Deaths per day per Deaths per day 100,000 population 100,000 5 people move between three main states, and The Imperial team has used both agent-based how quickly: individuals are either susceptible 0 and equation-based models in this pandemic. (S) to the virus; have become infected (I); and Mar Apr May Jun Jul Aug Sep The 16 March simulations that the team ran to 2020 then either recover (R) or die. The R group is inform the UK government’s COVID-19 response presumed to be immune to the virus, so can no used an agent-based model built in 2005 to see longer pass on the infection. People with natu- A SECOND WAVE what would happen in Thailand if H5N1 avian flu ral immunity would also belong to this group. In the United States, implementing measures to mutated to a version that could spread easily contain the virus could stop people with COVID-19 2 The simplest SIR models make basic from immediately overwhelming the country’s between people . Ferguson told Nature in 2005 assumptions, such as that everyone has the critical-care hospital-bed capacity, a simulation from that collecting detailed data on Thailand’s popu- Imperial College London suggests. But a second wave same chance of catching the virus from an of the pandemic might be expected later in the year. lation was harder than writing the programming infected person because the population is code for the model. That code was not released Estimated critical-care bed capacity perfectly and evenly mixed. More-advanced when his team’s projections on the coronavirus Do nothing models, which make the quantitative predic- pandemic were first made public, but the team is Case isolation, household quarantine tions policymakers need during an emerging and general social distancing working with Microsoft to tidy up the code and pandemic, subdivide people into smaller School and university closure, case isolation make it available, Ferguson says. groups — by age, sex, health status, employ- and general social distancing On 26 March, Ferguson’s team released ment, number of contacts, and so on — to set 250 global projections of the impact of COVID-19 who meets whom, when and in which places. Interventions remain that use the simpler equation-based in place 3 Using detailed information on population 200 approach . It divides people into four groups: size and density, how old people are, transport S, E, I and R, where ‘E’ refers to those who have links, the size of social networks and health- 150 been exposed, but who are not yet infectious. care provision, modellers build a virtual copy “They give broadly similar overall numbers,” of a city, region or an entire country using dif- 100 says epidemiologist Azra Ghani, who is also ferential equations to govern the movements in the Imperial group. For instance, the global 50 and interactions of population groups in space population per 100,000 projections suggest that, had the United States and time. Then they seed this world with an beds occupied Critical-care taken no action against the virus, it would have 0 infection and watch how things unfold. Mar May Jul Sep Nov Jan seen 2.18 million deaths. The earlier agent- SOURCES: REF. 1 REF. SOURCES: But that, in turn, requires information that 2020 2021 based simulation, run with the same assump- can be only loosely estimated at the start of an tions on mortality rate and reproduction epidemic, such as the proportion of infected immune to reinfection in the short term. number, estimated 2.2 million US deaths1. people who die, and the basic reproduction A simulation run using these parameters The different kinds of model have their own number (R0) — the number of people, on aver- would always give the same forecast. But strengths and weaknesses, says Vittoria Colizza, age, to whom one infected person will pass the simulations called stochastic models inject a modeller at the Pierre Louis Institute of Epide- virus. The modellers at Imperial, for instance, randomness: rolling a virtual dice to see whether miology and Public Health in Paris, who is advis- estimated in their 16 March report1 that 0.9% someone in the I group infects an S person when ing the French government during the current of people infected with COVID-19 would die (a they meet. This gives a range of possibilities emergency. Being able to bunch one group into figure adjusted to the United Kingdom’s spe- when the model is run multiple times. a compartment inside an equation-based model cific demographics); that the R0 was between Modellers also simulate people’s activities makes things simpler — and quicker — because 2 and 2.6; and that SARS-CoV-2 takes 5.1 days in different ways. In ‘equation-based’ models, the model doesn’t need to run at the high-reso- to incubate in an infected person. Those fig- individuals are sorted into population groups. lution level of treating everyone as an individual. ures depended on other kinds of modelling: But as the groups are broken into smaller, When Colizza and her team wanted to test the rough estimates by epidemiologists who tried more-representative social subsets to better effects on infection rates of compelling large to piece together the virus’s basic properties reflect reality, the models get increasingly com- parts of the French population to work from from incomplete information in different plicated. An alternative approach is to use an home, for example, she used an equation-based countries during the pandemic’s early stages.