# Estimating The Infected Population From Deaths

Estimating the number of infected people by country based on the number of deaths and case fatality rate.

**Warning:**This analysis contains the results of a predictive model. There are a number of assumptions made which include some speculation. Furthermore, this analysis was not prepared or reviewed by an Epidimiologist. Therefore, the assumptions and methods presented should be scrutinized carefully before arriving at any conclusions.

Latest Country Estimates

**Tip:**Click (Shift+ for multiple) on countries in the legend to filter the visualization.

Latest Observed vs. Estimate of Infected Cases

We argue that the number of infected in the past can be inferred using today's number of deaths and average fatality rate from confirmed cases in the following way:

$$I_{t-j} = \frac{D_t}{{CFR}_t}$$

where $I_t$ = number of infected, $D_t$ = number of deaths, and ${CFR}_t $ = case fatality rate = $\frac{D}{C}$. The $j$ depends on the average number of days that covid patients die after having the first symptoms.

**Assumption 1**: The case fatality rate is a good proxy for the fatality rate of the infected population

Then, in order to estimate the current number of infected $I_t$ we need to estimate its growth rate from $t-j$ to $t$.

$$I_t = (1+\hat{g})^j I_{t-j}$$

**Assumption 2**: The growth rate of infected $\hat{g}$ is an unbiased estimate of $g$ .

For now we estimate $g$ using the average growth rate since having the first infected person.

**Assumption 3**: It takes on average 8 days to die after having the first symptoms.

This analysis was conducted by Joao B. Duarte. Relevant sources are listed below: