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Reopening Calculator – Coronavirus

Created by Álvaro Díez
Reviewed by Jack Bowater
Last updated: Nov 13, 2023

We are living through difficult times, in which we have to choose between saving lives today or being free to live our lives as normal. With reports indicating that around half of the world's population is, or has been, in lockdown, the economic effects of this pandemic seem as terrifying as the actual pandemic.

Since the number of new cases worldwide has stabilized, you might wonder why don't we just go back to our normal lives immediately. The problem is that it is not that simple. Our behaviors greatly affect the spread of a disease, and loosening the restrictions too much or too soon will bring about a second outbreak that could be even worse than the first one.

This doesn't mean that we should remain quarantined for a long period of time; the key is a fine balance between reactivation of the economy and control of the virus. Where is this fine line? We will let you find it using our Back to (Normal) Life Calculator. This tool lets you change and control what policies are applied and when, with the results shown to you instantly. Can you save lives and protect people's livelihood at the same time?

What the calculator does

The Back to (Normal) Life Calculator is a tool that simulates the spread of an infectious disease and how our behaviors can affect its spread. The simulation is based on two parameters that define any infectious disease: recovery time and the infectiousness of the disease.

Infections are spread through direct or indirect interactions with infected people, so our habits play a huge role in how fast the disease can spread. Now, more than ever, it is important to understand the impact of our actions and how we can slow down an infection.

Using the Back to (Normal) Life Calculator, you can simulate multiple scenarios in which restrictions are applied to the affected population. These restrictions can be applied based on the time elapsed or the number of infected individuals.

We hope that by using this simple tool, you will gain more insight into the magnitude of people an infectious disease can affect and the importance of managing it. More importantly, you will be able to see firsthand the impact that different isolation methods have and how you can combine them to limit the damage an infectious disease can inflict on the population.

How to use the calculator

The calculator contains several presets that allow you to simulate different scenarios, even if you have no preexisting knowledge about epidemics. Most presets have a custom option that allows for finer control for the adventurous or those who have learned about infections.

We will now walk you through a typical simulation.

  1. Input the initial data. This includes the total population of the area, as well as the initial percentage of infected individuals and those immune (if any).

  2. Select a scenario. You can select from 4 different standard scenarios, 2 with an abrupt end to the lockdown and 2 with a gradual return to normality. There is a custom option that lets you fine-tune the restrictions and how they are applied.

  3. Select isolation measurements. You can select No isolation (what would happen if no actions were taken to stop the disease), Time Elapsed (each new restriction is applied after a fixed amount of time), or Number of cases (restrictions are applied depending on the number of active infections).

  4. Set total simulation time. How long into the future from your initial conditions do you want to simulate? The maximum simulation time is currently 5 years since most infections can be controlled within this time.

  5. Select the data. You can choose one of 5 options to be shown in the graph. By default, the 3 major metrics of an infection are shown: Susceptible people, Infected people, and Recovered people. Time is shown in days on the X-axis.


Use the Advanced Mode to compare your current scenarios with a set of different restrictions, or to a different infection

SIR model and lockdown scenarios

Now that we know how to use the calculator, let's talk about what makes it tick. These simulations are all based on the SIR model for infectious diseases. This powerful mathematical model can reproduce the behavior of an infection by dividing the population into 3 groups:

  • Susceptible: Those who are not infected and have no immunity to the infection;

  • Infected: Individuals who have been infected but have not yet recovered from the disease. They can infect those in the susceptible group; and

  • Recovered: The rest; they cannot be infected and are not contagious. This group includes those that have survived the disease, those who have died during the epidemic, and those that had immunity before the infection started.

From the initial number of people in each of the groups, we can predict the evolution of the infection if we know two very important parameters of the disease:

  • γ: The recovery rate of the disease. It is calculated as the inverse of the mean duration of the infectious process, i.e.: from the time of infection to full recovery; and

  • β: The infection rate. It calculated as the inverse of the mean time between infections (the average time it takes for a newly infected individual to infect another).

Using these two parameters we can know the number of people in each population at any given time.

Another parameter that is used widely in epidemiology is the basic reproduction number R₀ = β / 𝛾. It is a dimensionless number that represents the number of people that each patient will infect before they recover. A value of R₀ > 1 indicates that the infection will spread over time, while a value R₀ < 1 indicates that the infection will eventually die. The bigger the value of R₀, the more infectious a disease will be, meaning it will spread faster and infect more people.

You can find research papers with measurements of R₀ for the most common diseases, usually given as a range. It is because,in reality, this parameter depends very much on each person's behavior, and it's very difficult to measure. For the calculator, we have used the average of the published values.

Possible reactions and outcomes

As with almost every situation in life, when it comes to dealing with infectious diseases, the best defense is a good offense. Prevention is crucial, and for that, our best allies are vaccines. They have almost eradicated some of the most deathly epidemics of the past, such as measles, varicella, polio... and they provide herd immunity to those that cannot be vaccinated and to those for which vaccination is not effective.

As undeniably amazing as they are, new vaccines are costly to develop and take time. Cases like the current coronavirus pandemic require a reactionary response rather than a preventive one. In this case, we have many possible scenarios, so let's take a look at three of them and how they relate to the current COVID-19 pandemic.

React quickly and catch it early

The sooner you can stop an infection from spreading, the easier it is to have it under control. This is how we stopped the deadly Ebola epidemic in the developed world (sadly, it is still a big concern in Africa). To react quickly, we need to have detailed knowledge about the risk of infection and the damage that the infection can cause.

Taking the necessary actions to stop a disease can be a monumental effort and can have serious repercussions for a country's economy. Before pulling the trigger, you need to know that the sacrifices you will make are worth it so that you don't compromise the livelihood of millions of people trying to stop an infection that would've never spread very far anyway.

With the SARS-Cov-2 outbreak in 2019-2020 involving a new virus, it was almost impossible to predict its effects. Even though now, with hindsight, it is clear we should have, we never did activate those mechanisms which could have stopped the epidemic before it became a pandemic, so we missed our first and most deadly shot.

Lockdown and abrupt de-escalation

Once the epidemic becomes a great point of concern, you need to take extreme measures. The countries most heavily affected have declared a state of alarm and confined their citizens to their homes, leaving for only chores which are absolutely necessary, like grocery shopping, commuting (when remote working is not an option), emergency trips and dog walking.

As you can see in the simulations, once the disease has reached a certain number of people, only extreme actions can truly stop its spread. The question is, though, what's the best way to return to regular life? Naively, one might think that once the number of cases is low enough, we can have our old lives back, just like they were before.

This could have devastating consequences. If you free the population to go back to their old habits too soon, what you will see is a rapid increase in the number of infected people, that is, a second peak. Such a situation would force a second lockdown, and with a demoralized population and a decimated economy after the first isolation period, nothing good will come out of that.

Lockdown and smooth de-escalation

To avoid a second resurgence of the disease, we need to create what is called herd immunity. Herd immunity means that there are so many immune people that the disease has no way to travel from a susceptible individual to another one, and therefore ends up dying (or at least not spreading very far).

On the other hand, since we don't have a vaccine for SARS-Cov-2, the only way to get immunity is to survive being infected with the disease. As far as we can tell, the COVID-19 disease is not a severe risk to most of the population, but many still need treatment and intensive care after becoming infected.

When you go from full isolation to an intermediate between total confinement and normal life, you allow the infection to spread and even increase the number of infected people, but you keep it under control. Effectively, you are draining the diseases of new prey by converting the susceptible population into immune/recovered non-carriers.

The infection rate you want to maintain is very complicated to calculate and enforce. You want to maximize the number of infections (with looser restrictions to reactivate the economy) while at the same time staying under the maximum capacity of your healthcare system so that you can provide the best treatment for those with complications during the infected period.

Calculating these values goes beyond the capabilities of this calculator and depends on your healthcare system's capacity. However, these simulations can help you better understand what factors you need to balance to achieve herd immunity while giving everyone the best fighting chance of staying alive when this is all over.

How to defeat an infection

The key to defeating an infection that has already infected a significant part of the population is not to stop it but gain immunity to it. Sometimes this is not possible (see HIV/AIDS), but when it is, that's the best path to follow.

Immunity can be gained by nature (being born with it), via vaccination, or by recovering from the disease. Yes, what I'm saying is that the best way to defeat an infection is to get everyone infected. Allow me to explain.

"Get everyone infected" is a bit of a stretch since any disease with a high death rate is not a desirable one to go through. And herein lies the key to combating an infection: quickly turn susceptible people into immune (recovered) with the least amount of deaths.

Vaccines do this by weakening the disease so that your body will always win. When vaccines are not available, we have to rely on our healthcare system and sanitary personnel to do their best to save our lives.

As a regular citizen, the best thing you can do is stay at home and follow the recommendations of your governments so that we can all get safely infected, recovered, and immune until there is enough of us to protect the rest.

Stay safe, stay strong; we are the resistance! 💪

Disclaimer, assumptions and approximations

To make these simulations available and interactive, we have used a mathematical model (SIR) that makes some assumptions. To simulate restrictions and changes in the behavior of the population, we reduce the value of R₀ (except for Reckless behavior, in which it has been increased).

  • The restrictions simulated assume that all of the population follows the new rulings perfectly all day, every day;

  • Restrictions based on active cases have a minimum duration of 7 days to reproduce the realistic behaviors of governments and avoid changes within the same day;

  • The estimated number of real cases is far greater than the number of confirmed cases. Estimates point at 10-5 times more real cases than confirmed. This value depends on the number and nature of the tests performed. We use a factor of 5 for populations with more than 0.6% of confirmed cases over the total population, and we use a factor of 10 for populations with less than 0.6% confirmed cases. The assumption is that more confirmed cases respond to more broad testing;

  • We estimated the hospitalization rate at an optimistic 5% of (estimated) infected people;

  • The capacity of the health care system using the number of ventilators in the USA (19 for every 100,000 people). The severity and density of the hospitalizations will determine the actual capacity to treat all infected patients;

  • The percentage of "Recovered" required for her immunity depends on the infectiousness of the diseases. In our simulations, we found that for R₀ = 2.8 (median for Covid-19), 64% of the immune population is enough to prevent the number of active cases to increase. The number drops to 54% if people would follow stricter hygiene rules and be mindful of potential infections;

  • There is still a lot we need to learn about infections (especially about COVID-19). Things like the true value of R₀, accurate descriptions of the change in effective R₀ with different behaviors, mortality rate, percentage of asymptomatic cases, duration of the immunity to SARS-CoV-2, etc. As the precision and accuracy of those values improve, so will the validity of simulations like this one.

Validity of the results

The results of this simulation should not be considered accurate enough for decision-makers, but their trends and values are consistent with the reality of an infectious disease. The value of this calculator is as an educational aid and not as a prediction tool.

Álvaro Díez
This calculator was created to help you understand the importance of gradually coming out of lockdown. It showcases the potential risks of going back to a normal life before enough people are immune to the infection.
Can you create a safe action-plan to minimize the spread of the infection?
Initial values
Total population
Currently infected people
Immune (Recovered) people
Checkout the most recent (official) data about COVID-19. Remember that the actual number of cases might be higher due to shortage of test-kits. For our calculations we use a 10x or 5x factor between confirmed and estimated cases..
Mild confinement (40% as infectious)
Back to normal life scenarios
Gradually - better hygiene
This means:
  • Everyone goes into mild confinement when the number of active cases is above 2.3% (7,548,600 people).
  • Mild confinement is substituted by social distancing (2m/6ft) when active cases drop below 2% (6,564,000 people).
  • Only massive gatherings of people are forbidden when the number of cases is below 1.5% (4,923,000 people).
  • When active cases go below 1% (3,282,000 people) normal life is resumed and people follow stricter hygiene protocols .
Active cases are measured once every week
Using estimated number of cases:
  • Your action plan resulted in 209,577,184 people infected over 2 years.
  • At the highest peak, there were 13,147,985 people (4% of the population) infected at the same time. Your health care system will struggle to provide proper care to everyone.
  • You mitigated the infection. Your population experienced small secondary peaks with only 7,105,418 people infected at the same time (see Infected chart below).
  • On 11-Apr-2026, herd immunity was achieved because 210,048,000 people (64%) became immune. That is enough to control the infection even without any restrictions.
  • After 2 years, 209,816,032 people (64%) are immune. Herd immunity should protect your population in the future.
Pro-tip: You can compare two different scenarios using the 'Advanced Mode'
Evolution of the infection
Total time
Show data for...
More information
Wondering how you can help? Donate to WHO. For every $1 you donate, Google will donate $2.


This calculator uses the SIR model to reproduce the spread of an infection. The actual values, R₀, for each infection were taken from the most recent scientific papers available. Due to the lack of data, other parameters had to be estimated. Therefore the calculator cannot be used as a precise prediction tool.
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