COVID Vaccine Calculator



How long will it be before we reach herd immunity?


In light of the recent increase of vaccinations around the world, SEDGE - a cloud AI tool that easily processes and analyzes vast amounts of data - created a Covid Calculator that can determine how long it would take for a town, a country, and the world to reach herd immunity.


Covid Calculator Makes Herd Immunity Predictions Possible


The Covid Calculator takes several variables into account against specified assumptions and parameters outlined later on in this article. With the help of AI and machine learning, the calculator then predicts the date at which your population will reach herd immunity and no longer be susceptible to the devastating effects of Covid-19.


Figure 1: Sample calculation

To explain the graph, the Y-axis shows the number of people in the population, and the X-axis is the number of days over time. Zero is the current day. The blue curve is the number of susceptible people in the population, the orange shows those who are recovered. Dark green and pink lines show those who are infected normally and severely respectively. Additionally, present in the model are those exposed (lilac), vaccinated (light blue) and deceased (red) during this timeline. The vertical green line labeled 80% shows when herd immunity is reached.


When the blue line (susceptible) becomes almost flat at a certain timeline, it means the whole population has reached immunity - be it naturally or by vaccination.

How to Use the Covid Calculator


To start, simply select the country you wish to calculate from the drop down list labelled "Country". The date for which the latest information is available will show on in the Date field.


The country's data will automatically populate all of the required fields in the calculator. If vaccinations have yet to commence, the Vaccination Rate Per Day and Vaccinated Population quantities will be zero and marked red. However, these can be manually overwritten as an academic exercise to predict outcomes based on the vaccination scenarios.


Click Run Model to see the results.


Figure 2:

The UK Example


Now that we have briefly explained the Covid calculator, let’s see what predictions are generated when applied in a real-world setting. We took figures from the UK and used Covid data from https://ourworldindata.org/coronavirus-source-data and used SEDGE to process figures that compare the effects of the vaccine on the UK population starting from 02 March 2021. We considered all the initial conditions for Susceptible, Vaccinated, Recovered, etc. populations from the source.


The Findings


With a vaccination rate per day of around 1% of the susceptible population, the Covid Calculator, as of 9th March, predicts that herd immunity will be reached in 132 days, i.e., by July 2021 with a vaccine.


Figure 3:

Therefore, SEDGE shows that, once vaccinations are applied and if mobility from other external population groups is restricted, peak curvature of infected people and deaths is significantly lowered, and the number of susceptible people drops radically from the first day.


SEDGE's ability to make meaningful predictions in the face of real-world challenges is powerful. Access to personalized forecast data is significant to governments, leaders, and key decision-makers, considering that once herd immunity is reached, no more people in the population will be susceptible to the disease. And with it, significant far-reaching economic, financial, health, and mental well-being implications.



How The Model Was Prepared


Assumptions And Definitions


To build the model in SEDGE for this analysis, we have based the parameters on several key assumptions and definitions outlined below.


What is Herd Immunity?


With the ultimate goal being to determine when the focus population group will reach herd immunity, we first need to understand what is meant by herd immunity. According to WHO: 'herd immunity', also known as 'population immunity', is the indirect protection from an infectious disease that happens when a population is immune either through vaccination or immunity developed through the previous infection. Herd immunity varies from disease to disease; for example, polio herd immunity is reached at 80%, while measles is greater than 90%.



Factors and Assumptions


In order to determine Covid-19’s herd immunity arrival date, several factors and assumptions needed to be taken into consideration.

  • SEI2Rmodel. SEI2R stands for “Susceptible, Exposed, Infected (two types: normally symptomatic and severely symptomatic), Recovered" and is a means of segmenting the population into groups concerning a disease based on their infection status. Typically, people move between these statuses in the order of the label, for example, the population is first susceptible to the disease, then exposed, then infected, etc.


Mathematical Modeling


SEDGE, the AI and machine learning cloud tool that processes masses of data quickly and efficiently to produce actionable insights are highly capable of mathematical modeling. This functionality was used to predict the number of days it would take for a population to reach herd immunity.

Here is the mathematical equation, the values, and assumptions the model incorporated.

  • Average Incubation Period (AIncP) - This is the parameter that states how long a person takes to display symptoms. We have set AIncP as 7 days for our model

  • Average Infectious Period (AIP) - This parameter states how long a person will spread infection. We have set AIP as 14 days for our model. This impacts how quickly or slowly the infection peak takes place.

  • Vaccination Rate - This is the pace at which the people of this population group are being vaccinated. In our model, we assume that 1% of the population is being vaccinated at any given point in time. This works out to a 0.01 vaccination rate.

  • Birth Rate - This considers the country's birth rate as the population grows naturally.

  • Death Rate of Infection - This takes the mortality rate due to the pandemic into consideration and is split between severely symptomatic (0.035/AIP) and normally symptomatic (0.01/AIP).

  • Normal Death Rate - This is the country’s normal rate of morbidity outside of Covid-19.

  • Susceptible Population - The calculator determines the number of people who have yet to contract the virus.

  • Contact Rate - This is the rate of contact an infectious person - be they normally or severely symptomatic - has with other people. This is based on the level of lockdown your country is currently in. If the lockdown is severe, the level of the exposed population is lower, and conversely, a lighter lockdown means greater exposure. This affects how quickly susceptible people will move into the next stages of SEI2R. Typically severely symptomatic people have a lower contact rate as they are likely to be hospitalized and in a low-contact, sterile environment. The contact rate for normal or low-symptomatic people is likely to be higher. In our model, we assume a contact rate for severely symptomatic to be 0 and normal symptomatic 0.2.

  • Vaccinated but not immune - This is the percentage of people who have been vaccinated but are not immune. For this example, we have assumed that everyone vaccinated is immune, however, this parameter can also be modeled into the problem.

Factors and Assumptions Continued

  • Covid-19 herd immunity. According to the World Health Organization (WHO), there is no real clarity yet on the actual number of the population that must be vaccinated against COVID-19 to begin inducing herd immunity. The Mayo Clinic cites estimations that herd immunity in the U.S will be reached when 70% of the population — over 200 million people — have been vaccinated or have recovered from COVID-19. In our model, we used 80% as the herd immunity assumption based on the formula 1 - s > 1 - 1/R0. With an R naught value of 5, 80% would be the required immunity level to ensure herd immunity.

  • Vaccine efficacy. According to Pfizer data published in December 2020, the Pfizer-BioNTech vaccine is roughly 52% effective after the first dose and takes approximately 12 - 14 days to realize immunity, with a second dose strongly advised. There are several other big players in the vaccine space, all with varying efficacy data, waiting periods, and days of immunity. Therefore, for purposes of this article, we have applied efficacy at 90% with immediate efficacy, and the duration of efficacy is set at lifelong.

  • Population. For this study, we have assumed that a population is the number of living people within a predefined area.

Bring the Power of Predictive Analytics into Your Business


SEDGE can do mathematical modeling with ease, and our team is standing by to help provide real-time, critical data analysis, predictions, and actions.


Ask us about how SEDGE can prepare you for what is to come, with enough time and insight to act wisely.

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