In the model, the variable trans is the rate of infection per day and recov is the rate infected persons move to recovered persons. Hence, if an infected person can during their infectious period of n days infects on average say 4 people trans = 4/n. If the average infectious period is n days then 1/n recover each day.
Ro = trans/recov, if > 1 there is spread
example: assume mean recovery period is 8 days, hence recov = 1/8 = 0.125 and that an infectious person can infect 5 people in 8 days, hence set trans = 5/8 = 0.625. This gives Ro = 0.625/0.125 = 5, which > 1 hence spread.
1-1/Ro gives an estimate of the herd immunity percentage, using our example we have 1-1/5 = 0.80 suggesting a threshold of 80% of the population needs to be fully vaccinated to see a gradual decline in infections.
****Please let me know if I have these concept incorrect
SIR Model using a Spreadsheet
To get a handle on what 80% herd immunity means we need to consider first that there are around 4,700,000 children aged less than 15 (19% of the population), assume this is the cut-off age for vaccination. Hence we are really talking about 80% of the remaining adults and this would give around 4,000,000 adults who would not be vaccinated. Together 40% of our 25m would be unvaccinated. Let’s get an estimate of cases and deaths.
Look at the models and use different parameters. You will see that the curve representing infections peaks at around the top of the green curve – 50%! of the unvaccinated and some much smaller percentage vaccinated.
In the UK they currently have about 30,000 cases per day (this includes children) from an unvaccinated adult population of 8m and 13m children less than 15. If we extrapolate that to Australia we get a very rough approximation of 12,000 cases per day. There would also be a death rate of around 15-20 per day or 600 per month. Both cases and deaths would decrease as further vaccination percentage increased.
Please note these figures are purely estimates to show the dimension of the cases.
As has been reported in the News, there are around 160,000 deaths per year in Australia, Flu accounts for approximately 700-800 deaths per year and it fluctuates yearly, currently, there are few direct deaths from Flu. Pneumonia deaths are about 3500 per year and some of these are related to the Flu.