## Calculating the number of cases that must have been isolated

An epidemic comes to an end when community case to community case effective reproduction number (effR in the community) is 1 or less. The threshold effR is 1, and less is better. The number of community cases a day (Nc1) if the effR = 1 can be calculated from Equation A described in the Epidemic Model. And therefore all the remainder of the days cases must have been in isolation for the wave to end.

The formula for the number of cases (Nt+n+1) that can be expected on day t+n+1 is:

x = t+n

Nt+n+1 = effR * (P – EV)/P * Σ (ax Nx) = Nc1 from

x = t

where Nt+n+1 is the number of cases on day t+n+1

effR is the reproduction number which in this case is set to 1 for community to community spread

P is the total population

EV is the efficacy of full vaccination to prevent spread multiplied by the number fully vaccinated

Σ (ax Nx) is the sum of: the number of cases over past days multiplied by the respective probability of having been infected on those days (based on the known distribution of incubation periods for Covid-19). Past infection with Covid-19 is small compared with the population size and is not included here).

The maximum number of daily cases that can be infected in the community Nc1 is subtracted from the total daily new cases. And that is the number of cases that should have been in isolation.

Nc1 = Nt+n+1 as calculated above with effR set to 1

Number necessary to have been isolated = total daily cases - Nc1

The formula for the number of cases (Nt+n+1) that can be expected on day t+n+1 is:

x = t+n

Nt+n+1 = effR * (P – EV)/P * Σ (ax Nx) = Nc1 from

**(Equation A)**x = t

where Nt+n+1 is the number of cases on day t+n+1

effR is the reproduction number which in this case is set to 1 for community to community spread

P is the total population

EV is the efficacy of full vaccination to prevent spread multiplied by the number fully vaccinated

Σ (ax Nx) is the sum of: the number of cases over past days multiplied by the respective probability of having been infected on those days (based on the known distribution of incubation periods for Covid-19). Past infection with Covid-19 is small compared with the population size and is not included here).

The maximum number of daily cases that can be infected in the community Nc1 is subtracted from the total daily new cases. And that is the number of cases that should have been in isolation.

Nc1 = Nt+n+1 as calculated above with effR set to 1

Number necessary to have been isolated = total daily cases - Nc1