## Estimating number of recovered people

Health organizations usually do not report the number of recovered people or the reports are wrong. I show how to estimate this number.

Let us use the following notation:

*I(t)*- The total cumulative number of people that have been infected till time
*t*. *D(t)*- The total cumulative number of people that have died till time
*t*. *R(t)*- The total cumulative number of people that have recovered till time
*t*. *A(t)*- The number of people with currently active disease at time
*t*,

A(t) = I(t) - R(t) - D(t)

Suppose that at time *t + Δt* all activelly ill people either recover or die.
Let us denote:

*ΔD*- The number of actively ill people that die during time
*Δt*,

ΔD = D(t + Δt) - D(t) *ΔR*- The number of actively ill people that recover during time
*Δt*,

ΔR = R(t + Δt) - R(t)

We have

The last equation can also be written as:

Eq. (1) can be also derived by the following consideration.
All people who have been infected till time t will be recovered
till time *t + Δt* except those who die till *t + Δt*. So, we obtain again Eq. (1)
and hence Eq. (2):

I assume that the recovery time *Δt* is 20 days for Covid-19
and use the estimation:

Let us note that the estimated *R(t)* is not necessarily a
monotonically increasing function. In fact, it can happen that *R(t)*
decreases. Consider:

It can happen that the increase of infections from *t-20* to *t-20+1*
is small or even 0 and actually less than
the increase of deaths from *t* to *t+1*
such that *R(t+1)* becomes smaller than *R(t)*.
I tolerate this behaviour and interpret it in the sense that
a person that was considered recovered dies later.

### References

- Konzept Geheilte, Basel-Landschaft (Deutsch)
- Number recovered, Vicksburg Daily News