How Society Responds to an Epidemic
How does society adjust to deal with a new infectious disease?
this is part of a series on modeling infectious diseases. start here to catch up
If we go back to the characteristics of a virus, we know that there are only 3 variables that influence the trajectory of an infectious disease:
Reproductive Number, Recovery Time and Proportion of Susceptible Individuals
The Reproductive Number is the expected number of individuals that one infected person will infect during the course of the illness.
The Recovery Time is the expected amount of days it takes for an individual to recover from the virus.
The Proportion of Susceptible Individuals is the percentage of the population that have not yet been exposed to the new infectious disease
Lets look at certain things society has done, or will do, in the wake of Coronavirus:
- Implemented guidelines on Hand Washing
- Implemented Social Distancing, Self Isolation, and Shelter in Place
- Implemented a Total Quarantine
- Discovered Treatment to deal with infections
- Discovered Vaccines to make people not susceptible to infection
Hand Washing
An infectious diseases most commonly spreads when a person comes into contact with an infected individual, gets some of the virus on their hands, and then touches their face.
By washing your hands you are reducing the likelihood of becoming infected.
If we go back to our example of treating infections as interactions, washing hands effectively reduces the number of successful infections that an infected person carries out.
Let’s go back to our Reproductive Number of an infectious disease.
The Reproductive Number is the expected number of individuals that one infected person will infect during the course of the illness.
By society increasing washing hands, it is effectively reducing the Reproductive Number a virus.
While before, the Reproductive Number could have been 4.0, it now has reduced since many of the interactions between infected and susceptible individuals do not result in a new infection.
In these two models, you can clearly see that by reducing the Reproductive Number, the peak of the infections curve has flattened.
In reality hand washing wouldn’t reduce the Reproductive Number by ~40%, but more like ~10%.
Social Distancing, Self Isolation, and Shelter in Place
The effects of implementing Social Distancing, Self isolation, and Shelter in Place has the same effect on the SIR Model as washing your hands.
Instead of reducing the likelihood of spreading an infectious disease in an interaction, you are instead reducing the number of interactions that take place.
One big difference between this method of reducing the reproduction number and washing your hands is that it is time sensitive
While you can wash your hands for the entire course of an epidemic, you can’t keep isolation policies in place for long without external consequences. In order for people to contribute to the economy, exchange goods and services, exercise, etc, these policies cannot last forever (realistically).
Here is a simulation of a virus with a Reproductive Number of 4.0 and a Recovery Time of 10 days
Let’s say that at Day 10, local Government initiates a Shelter in Place policy. During this time the Reproductive Number falls to .5
After 30 Days, the Government sees the numbers dropping, and decides to open everything back up. This is what happens:
As you can see, Shelter in Place, and other isolation policies, only delay the outbreak. As long as there are Susceptible People in the population remaining, the normal course of the epidemic will resume.
Total Quarantine
One caveat to isolation policies is under the circumstance where a Total Quarantine is put in place.
Consider this as Shelter in Place, but much more strict.
Instead of reducing the Reproductive Number to below 1.0, the effect would reduce it to 0.0
Let’s say the same Government initiates a strict mandatory quarantine for 80 days.
This works since it eradicates the Virus completely from the population.
In this simulation, at Day 81 the number of Infected Individuals hits 0. If no one has the virus, no one can spread it.
This can have the same flaws as other isolation policies if done incorrectly (not testing and tracking the number of infected properly), but if done right is an effective way to end an epidemic.
Improved Treatment
Throughout these policies, we have been focused on reducing the Reproductive Number of a virus.
Another way to impact an epidemic is to discover new treatment options that reduce the Recovery Time.
Here is another simulation of a virus with a Reproductive Number of 4.0, and Recovery Time of 10 Days
Let’s say that a new treatment is discovered that reduces the Recovery Time from 10 days to 5 days. This effectively reduces the Reproductive Number of a virus in half as a person would have half the time to be infectious.
This is an effective way of flattening the infectious curve as the amount of infections decrease, and the rate of recovery increases.
Vaccines
the single best way for society to handle an epidemic is to develop an effective vaccine.
A Vaccine works by essentially by giving those who are susceptible to infection a shortcut to recovery.
This is how an infectious disease normally works:
This is how it works with a vaccine:
With a Vaccine, an individual skips Infection, and becomes “Recovered” as they have the same antibodies that an infected individual would develop.
Here is our example of
- Reproductive Number = 4.0
- Recovery Time = 10 days
- Now with 1 Million People
Let’s say right before the infections start ramping up again, the Government finds a vaccine. The Government then starts vaccinating 10% of the susceptible population each day. This is what that looks like:
You can see that the vaccine significantly reduces the infectious curve, and effectively stops the epidemic.
The real lesson throughout examining all of these reactionary strategies to an epidemic is that they each have their flaws:
- Washing Hands doesn’t reduce the Reproductive Number enough
- Shelter in Place and Quarantine isn’t feasible for extended periods of time
- Treatment can decrease the rate, but not substantially unless it is very quick and effective
The only strategy that works effectively is to develop a vaccine.
As long as there are susceptible individuals in a population, a virus will have fuel to spread and infect.
To deal with Coronavirus, I would recommend that we utilize all of the methods above in concert to flatten the curve.
While doing this we should dedicate 100% of our resources into finding a vaccine. That is unfortunately the only way out of this mess.
If you want to play with the models yourself, you can find all the necessary code in my github
