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# The Math Behind Social Distancing

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## The Math Behind Social Distancing

As we wait for scientists and healthcare professionals to develop a vaccine for COVID-19, there is another, more readily available tool at our disposal.

Social distancing, defined as measures taken to reduce physical contact, is the first line of defense for containing an infectious disease like COVID-19. Thatâ€™s because these infections spread when people cough, sneeze, or touch surfaces on which the virus resides.

To help us grasp the impact these measures can actually have, todayâ€™s infographic illustrates how a reduction in social exposure can theoretically contain the spread of infection.

## Theoretical Potential

The calculations used to create todayâ€™s infographic come from Signer Laboratory, a stem cell research lab located in the Moores Cancer Center at the University of California San Diego.

Using a summation formula makes it possible to estimate the number of new infections over a 30 day period, across three scenarios.

Scenario5 Day Period30 Day Period
No social distancing practiced1 person infects 2.5* others406 people infected as a result
50% reduction in social exposure1 person infects 1.25* others15 people infected as a result
75% reduction in social exposure1 person infects 0.625* others2.5 people infected as a result

*For estimations only. It is not possible to infect only a fraction of another person.

To arrive at the figures reported above, Robert A.J. Signer, Ph.D., and his team made a number of key assumptions.

First, they estimated the basic reproduction number (R0) of COVID-19 to be 2.5, a figure supported by recent research. This means that, on average, an infected individual will spread the disease to 2.5 other people.

Next, they assumed that an infected individual will unknowingly spread COVID-19 over the median five day incubation period. After this period, the individual will begin to develop symptoms, immediately self quarantine, and no longer pose a threat.

Finally, they assumed a direct linear correlation between social interactions and R0. This means that when an infected person reduces their physical contact with others by 50%, they also spread the disease by an amount 50% less.

## Timing is Everything

While the figures above are the results of mathematical estimations, researchers have actually studied social distancing from a variety of angles.

One study used simulations to determine the magnitude and timing of social distancing measures required to prevent a pandemic. The distancing measures simulated were:

MeasureDetails
School closureTeachers and students spent weekday daytime cycles at home, rather than at school.
Increased case isolationUpon becoming symptomatic, adults (90%) and children (100%) would self quarantine for the duration of the infection.
Workplace non-attendanceEach day, a person had a 50% chance of staying home instead of attending their workplace.
Community contact reductionIndividuals reduced their physical contact with community members by half, each day.
Combination of all fourAll four measures combined.Â

The results, for a community of 30,000 people and an epidemic with R=2.5, are charted below. We can define the final illness attack rate as the share of people from an at risk population who ultimately catch the disease.

Results showed that when no action was taken, 65% of the population contracted the disease. However, if a combination of all four distancing measures were implemented instead, the attack rates were:

• 45% (distancing begins after a 4 week delay)
• 21% (distancing begins after a 3 week delay)
• 7% (distancing begins after a 2 week delay)

What’s clear is that social distancing was significantly more effective when implemented with minimal delay—the final illness attack rate rose quickest beyond the third week. These findings draw a parallel to the visualizations in today’s infographic, which showed us just how quickly a disease can spread.

Social distancing interventions are important as they represent the only … measure guaranteed to be available against a novel strain of influenza in the early phases of a pandemic.

Kelso, J.K., Milne, G.J. & Kelly, H., BMC Public Health 9, 117 (2009)

We arrive at a similar conclusion when it comes to the types of distancing measures implemented. In the simulations, none of the four measures taken on their own were able to have a similar effect as when they were combined.

## We All Have a Part to Play

With the global number of COVID-19 cases still rising, many governments have issued quarantine orders and travel bans.

The math supports these decisions—reducing our physical contact with others, even when we arenâ€™t experiencing any symptoms, is crucial. Studies like the one summarized above also prove that taking action sooner, rather than later, can go a long way in reducing the spread of infection.

The key takeaway from all of this? Social distancing is a powerful disease control tool, but only if we all participate.

## Visualizing How COVID-19 Antiviral Pills and Vaccines Work at the Cellular Level

Despite tackling the same disease, vaccines and antiviral pills work differently to combat COVID-19. We visualize how they work in the body.

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## Current Strategies to Tackle COVID-19

Since the pandemic started in 2020, a number of therapies have been developed to combat COVID-19.

The leading options for preventing infection include social distancing, mask-wearing, and vaccination. They are still recommended during the upsurge of the coronavirusâ€™s latest mutation, the Omicron variant.

But in December 2021, The United States Food and Drug Administration (USDA) granted Emergency Use Authorization to two experimental pills for the treatment of new COVID-19 cases.

These medications, one made by Pfizer and the other by Merck & Co., hope to contribute to the fight against the coronavirus and its variants. Alongside vaccinations, they may help to curb extreme cases of COVID-19 by reducing the need for hospitalization.

Despite tackling the same disease, vaccines and pills work differently:

VaccinesPills
Taken by injectionTaken by mouth
Used for prevention Used for treatment only
Create an enhanced immune system by stimulating antibody productionDisrupt the assembly of new viral particles

## How a Vaccine Helps Prevent COVID-19

The main purpose of a vaccine is to prewarn the body of a potential COVID-19 infection by creating antibodies that target and destroy the coronavirus.

In order to do this, the immune system needs an antigen.

Itâ€™s difficult to do this risk-free since all antigens exist directly on a virus. Luckily, vaccines safely expose antigens to our immune systems without the dangerous parts of the virus.

In the case of COVID-19, the coronavirusâ€™s antigen is the spike protein that covers its outer surface. Vaccines inject antigen-building instructions* and use our own cellular machinery to build the coronavirus antigen from scratch.

When exposed to the spike protein, the immune system begins to assemble antigen-specific antibodies. These antibodies wait for the opportunity to attack the real spike protein when a coronavirus enters the body. Since antibodies decrease over time, booster immunizations help to maintain a strong line of defense.

*While different vaccine technologies exist, they all do a similar thing: introduce an antigen and build a stronger immune system.

## How COVID Antiviral Pills Work

Antiviral pills, unlike vaccines, are not a preventative strategy. Instead, they treat an infected individual experiencing symptoms from the virus.

Two drugs are now entering the market. Merck & Co.’s LagevrioÂ®, composed of one molecule, and Pfizerâ€™s PaxlovidÂ®, composed of two.

These medications disrupt specific processes in the viral assembly line to choke the virusâ€™s ability to replicate.

### The Mechanism of Molnupiravir

RNA-dependent RNA Polymerase (RdRp) is a cellular component that works similar to a photocopying machine for the virusâ€™s genetic instructions. An infected host cell is forced to produce RdRp, which starts generating more copies of the virusâ€™s RNA.

Molnupiravir, developed by Merck & Co., is a polymerase inhibitor. It inserts itself into the viral instructions that RdRp is copying, jumbling the contents. The RdRp then produces junk.

### The Mechanism of Nirmatrelvir + Ritonavir

A replicating virus makes proteins necessary for its survival in a large, clumped mass called a polyprotein. A cellular component called a protease cuts a virusâ€™s polyprotein into smaller, workable pieces.

Pfizerâ€™s antiviral medication is a protease inhibitor made of two pills:

1. The first pill, nirmatrelvir, stops protease from cutting viral products into smaller pieces.
2. The second pill, ritonavir, protects nirmatrelvir from destruction by the body and allows it to keep working.

With a faulty polymerase or a large, unusable polyprotein, antiviral medications make it difficult for the coronavirus to replicate. If treated early enough, they can lessen the virusâ€™s impact on the body.

## The Future of COVID Antiviral Pills and Medications

Antiviral medications seem to have a bright future ahead of them.

COVID-19 antivirals are based on early research done on coronaviruses from the 2002-04 SARS-CoV and the 2012 MERS-CoV outbreaks. Current breakthroughs in this technology may pave the way for better pharmaceuticals in the future.

One half of Pfizerâ€™s medication, ritonavir, currently treats many other viruses including HIV/AIDS.

Gilead Science is currently developing oral derivatives of remdesivir, another polymerase inhibitor currently only offered to inpatients in the United States.

More coronavirus antivirals are currently in the pipeline, offering a glimpse of control on the looming presence of COVID-19.

Authorâ€™s Note: The medical information in this article is an information resource only, and is not to be used or relied on for any diagnostic or treatment purposes. Please talk to your doctor before undergoing any treatment for COVID-19. If you become sick and believe you may have symptoms of COVID-19, please follow the CDC guidelines.