# Back of the envelope calculation of R_0 for the SARS-Cov-2 Delta strain

A few months ago, the Delta strain made its conspicuous landing in the US. This strain is more contagious than the original SARS-Cov-2, but by how much?

Recently, I came across an interesting paper that tried to estimate $R_0$, the viral reproductive number in the absence of all social distancing measures and in a completely susceptible population.

The paper is fairly involved, and makes use of extensive mathematical modeling to achieve its main claim that **Delta is 40 - 100% more transmissible than SARS-Cov-2**. I was wondering if a super quick back of the envelope calculation would reach a similar conclusion.

## Methodology

In the following notebook, I:

- Calculated the new cases per day, smoothed using a wavelet transform (for no particular reason other than to familiarize myself with this method)
- Calculated a poor man’s viral reproductive number by dividing the reported cases each day by the reported cases a week previous.
- Found the maximal reproductive number for the ancestor lineage per state between the dates of 2020/05/01 and 2021/07/01; similarly, I found the maximal reproductive number for delta per US state by searching in the period where Delta became prevalent (2021/07/01 and onwards).
- Compared and contrasted the observed reproductive number, adjusting for fraction of the population that is susceptible at each time.

## Findings

The conclusions from my back of the envelope calculations are that:

- Without adjustment for susceptible fraction, Delta’s effective viral reproductive number is about 15% greater than the ancestor lineage.
- Adjusted for susceptibles, Delta is probably twice as transmissible as the ancestor lineage.
- Accounting for susceptible fractions and governmental interventions, Delta’s viral reproductive number is about 8! Current estimates put Delta’s reproductive number, R0, at around 6-9, with most estimates around 8-8.5. Not a bad estimate, though this number is quite terrifyingly large.

Written on November 18, 2021