## Whats “R” rate and whats heard immunity got do with it and how many people need to be vaccinated to control the COVID pandemic?

# Whats COVID got in common with Gang Violence and Financial Bubbles?

## Do Viral phenomenon like epidemics follow the rules, and how can they be forecasted and what can be learned from our experience of viral phenomenon?

I recently read the excellent book by Adam Kucharski “Rules of Contagion”, and this made me realise even something as seemingly unpredictable as COVID follows a set of rules and our success is driven by how effectively we can forecast and respond accordingly.

Everyone seems to be now on expert on forecasting with “R” rate, herd immunity becoming part of daily conversations. Yet beyond these terms, it's important to understand the rules and the basis for these forecasts and how the forecasts need to be monitored and course correction needs to be done as we get a better understanding of what is being forecast to enable more accurate forecasts. There also needs to be a recognition that the forecasts need to be viewed more from a scenario planning perspective and for planning public policy and interventions. The fundamental tenant which forecast is based on can be derived from Heraclitus’s quote :

Everything Changes and nothing stands still.

First, let's understand a few basic concepts which will help us understand the viral phenomenon.

**SEIR:**One of the most widely used epidemiological model to predict infectious disease dynamics is SEIR. This is based on compartmentalizing the population into four possible states: Susceptible [S], Exposed or latent [E], Infectious [I] or Removed [R]. This model is usually used for the phenomenon called “Dependant Happenings” as opposed to “Independent Happenings” (Theory of Happenings). The peaks and the subsequent declines can be understood based on these 4 states.**R Rate (R0):**This is the reproduction rate and is a good measure of the rate of the spread of the disease. This is an effective way to forecast as it deals with the subject rather than the agent. R rate depends on how long someone is infectious, the number of interaction while infected, probability and opportunities to transmit and average susceptibility of population. An R rate above one indicates that every individual infected is infecting more than one susceptible individual. Hence, the epidemic is growing, and hence all the efforts are to get R as below one as possible. Current COVID R rates globally are in between 0 and 3, historically Measles which is considered more infectious usually has an R rate of 20, R rate for flu was 2, and for SARS R was as high as 6. Finding how many people are susceptible is critical; hence the R calculated based on bottom up sampling is critical. R rate is used to determine the minimum people to be vaccinated for the epidemic spread to reduce.

**Herd Immunity:**One of the terms which has been very unpopular through this pandemic is “Herd immunity”. So in this context, it is important to understand that “herd immunity” is what all of the public policy is working towards so the disagreement is more about the means to the end than the end itself. So it's more about how “Herd Immunity” is acquired. To give you an example one of the ways to achieve herd immunity which ‘most’ of the people agree to is vaccination. As through vaccination, we can protect those who can’t be vaccinated through the immunity acquired bu the individual s who have had the vaccination. As an example for a disease with R=5 to get R Rate down below 1 at least 4 people need to be vaccinated, and this is called herd immunity threshold. The formula for calculating the herd-immunity threshold is 1–1/R0, which means the more people infected by each individual with the virus, the higher the proportion of the population that needs to be vaccinated to reach herd immunity. Thus if R is 1, then when 20% of the population has been exposed, infected, immunised or recovered, then growth slows due to decline in the susceptible population. If R is 4, then the herd immunity threshold will be 75%.

**Super Spreaders:**Studies have indicated that 80/20 rule can be applied to spread of infectious diseases, i.e. a small number of individuals within any population have been found to contribute to most of the transmission within the population. Thus individuals who infect disproportionately more secondary contacts, as compared to most others, are known as super-spreaders, and the events at which this happens are called super-spreading events. The closest parallel to a super-spreader is a social media influencer. This super-spreaders and super spreading events lead to clustering and long-range links.

So forecasting models need to follow Bayesian reasoning, i.e. update belief based on info depending on the strength of initial belief Vs strength of new evidence. Outbreak forecasting can influence the final number of cases as these models determine the measures which will be put in place to bring the R rate down. It's important to understand that in this context, the forecast is for scenario planning rather than prediction and has to be used to enable effective policymaking.

The effectiveness of the model is measured by evaluating the calibrations (uncertainty in making predictions), sharpness (predictions within a narrow range of possible outcomes) and bias (over or underpredicting the true values) of the forecasting model. When viewed through the lens of these criteria, it’s clear why forecasting the long term trajectory of COVID has been so challenging to model and get right. For forecasting models to be effective, it is important to understand that only what gets reported is what gets modelled. So we need to devise ways and means to ensure effective data capture, especially milder or asymptomatic cases which are grossly under-reported. For this enhanced testing is pre-requisite, so it doesn't come as a surprise that countries like South Korea, which have had a more effective testing regime have managed to gain better control over the pandemic by forecasting it better. Also, for the models to be effective, they will need to deal with messy and evolving data, and the forecast models will need to be constantly be updated in response.

For looking at the complete picture the forecasting model and the resultant impact of public policy has to be modelled together to find the right balance of interventions like lockdowns and planning for hospital beds and ventilators while minimising the negative impact on the livelihood of people and economy. It's also important to improve statistical literacy to help us better engage in a useful way with forecasts and probabilistic reasoning.

The concepts used for forecasting disease outbreaks can be reused to understand other viral phenomena like financial bubbles, social media posts, gang violence. Through this enhanced forecasting of these phenomena, a greater understanding can be gained to help mitigated against epidemics or help encourage the spread of positive ideas.

Hope you found the blog useful and please do comment about your experience with forecasting models. Also, let me know if you want to hear on any of the specific topics. In the meantime, please do check out my other blogs on Artificial Intelligence and Machine Learning:-

- A Non Mathematical guide to the mathematics behind Machine Learning
- How can Telcos use AI-powered Network Analytics to improve the quality of experience for their subscribers?
- Open AIs Revolutionary New NLP Model GPT-3
- Scaling AI for the Long Tail of Autonomous Driving
- Debiasing AI: Towards Equitable and Accountable AI

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