As governments and public health agencies work to treat infected people and control the spread of covid-19, researchers are using mathematical models to estimate how contagious it is and how far it could spread.
Simulating the covid epidemic
This is a simplified model of an epidemic. The main factor, the rate a disease is able to spread through a susceptible population, is called the basic reproductive number, or R0. For a new disease, like covid-19, almost everyone in the population is susceptible — a prime scenario for an epidemic.
The basic reproductive number (R0) of the virus causing covid-19 is estimated to be 2.3, meaning that each person infected with the virus will spread it to 2.3 others, on average, over the course of their illness. This simulation shows a virus with an R0 of 2.3 in a completely susceptible population of 4,000 people, without any vaccinations, masks or quarantines.
In this model, after contracting the disease, people either fully recover or die. Once infected and recovered, a person cannot be reinfected in this model.
“The higher R0 is, the faster the epidemic takes off,” said David Fisman, an epidemiologist and infectious-disease physician at the University of Toronto’s Dalla Lana School of Public Health. Fisman and Ashleigh R. Tuite developed a model of covid-19 to estimate its reproductive rates.
As an epidemic spreads through the population, the number of people left to infect goes down. The growth rate of an epidemic in progress is described by its effective reproductive number, or Re. Once that value falls below 1, the epidemic will stop spreading.
In the real world, populations aren’t completely isolated. A sick person could leave this group of 4,000 and bring the virus to a new population.
Highly contagious outbreaks
Studies of measles outbreaks have calculated a basic reproductive number of between 12 and 18, although it can vary even more widely. Here’s what a virus with a reproductive number of 18 looks like in a completely susceptible population. Because each person spreads it to an average of 18 others, it will infect everyone in the population extremely quickly.
Measles outbreaks like this fictional one are prevented by vaccinations — 86 percent of children under age 2 worldwide had received a measles vaccine by the end of 2018, according to the World Health Organization. In this simulation, nobody has been vaccinated.
Less contagious isn’t less deadly
A virus with a lower basic reproductive number can still be very dangerous — Ebola’s reproductive number in past outbreaks has been 2 or less, but it kills half the people who become infected, a much higher fatality rate than for measles or covid-19.
These simplified simulations show how an epidemic can eventually end even without intervention: The disease runs out of susceptible people to infect.
So why are there still people who haven’t been infected? An epidemic doesn’t affect a population uniformly — some people, such as supermarket cashiers or doctors, come into contact with many people every day, while others may be in contact with only one or two people. This simplified model uses a pre-calculated “final size” to determine how many people would become ill.
“Real epidemics, whether it’s [covid], whether it’s the black plague in London — they go up, growth slows, it peaks, and then the number of cases goes down the other side,” Fisman said.
But we don’t have to wait for an epidemic to spread across the entire world before it ends. Quarantines and personal hygiene work to slow an epidemic by limiting the ability of infectious people to spread the virus to others.
Slowing the spread
In this simulation, a third of people who get a hypothetical disease wear protective items such as masks and gloves that make further spreading of the disease much less likely.
The Centers for Disease Control and Prevention does not currently recommend face masks for people who aren’t infected with covid-19, but they should be used by people who are infected and those in close contact with them.
Quarantines are effective because they limit the number of people exposed to a disease. This scenario shows what happens if a quarantine is established quickly after the first few cases are discovered.
This quarantine would stay in place until the people inside it are no longer infectious, effectively reducing the population exposed to the epidemic.
Real quarantines aren’t perfect. In this scenario, the quarantine is established as soon as one person is infected, but in actuality, we often don’t find out about a new disease until it’s already an epidemic.
Efforts to contain the much larger real-world covid-19 outbreak are much more complex. Governments are using these and other strategies to slow the spread of the virus, and their effectiveness will determine whether the epidemic is wiped out or continues to grow.
Correction: A previous version of this story identified the coronavirus as covid-19. The virus SARS-CoV-2 causes a disease known as covid-19.
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Sources: National Center for Biotechnology Information (NCBI); World Health Organization (WHO); More than 140,000 die from measles as cases surge worldwide from WHO; After Ebola in West Africa — Unpredictable Risks, Preventable Epidemics report from WHO; Ebola Virus Disease from WHO; The basic reproduction number (R0) of measles: a systematic review from NCBI; The Epidemiological Characteristics of an Outbreak of 2019 Novel Coronavirus Diseases (COVID-19) — China, 2020 from Chinese Center for Disease Control and Prevention; Serial Intervals of Respiratory Infectious Diseases: A Systematic Review and Analysis from Epidemic from American Journal of Epidemiology; Reporting, Epidemic Growth, and Reproduction Numbers for the 2019 Novel Coronavirus (2019-nCoV) from Annals of Internal Medicine