From the graph below it seems that Victoria needs to do more to contain the current cluster. Australia's new cases are plotted in green (log scale). The the yellow graph is 'fitted' to the recent new case (green graph) by trying various values of R0 and i until the slope of the yellow graph approaches the slope of the green graph. The values of R0 and i and are input into the yellow box on the left of the graph. It appears that an R0 of 1.3 and an i if 6 produce a graph that best matches the actual new Australian cases. R0 is the infection rate (the number of cases infected directly by each infectious person) and i is the number of days that a person is infectious. i may be smaller than otherwise reported because it is the 'number of days that a person is infectious to others in reality' and lasts from when the person becomes infectious until they are detected and isolated; they may remain 'positive' to tests after this but they cease to be 'infectious' in reality because they are isolated or in hospital and not usually able to infect others. An R0 of 1.3 is greater than 1 which means that the spread of infection is increasing exponentially and is 'locally epidemic'. Further restriction need to be put in place to reduce the R0 to less than 1 in Victoria.The graph below also suggests that Victoria needs to do more to reduce the infection rate, R0. The new cases a day in Australia is shown in the blue graph. The R0 calculated by the model (
explained here) is shown in orange. R0 is calculated over a number of days (8 days in this case, and therefore called R8) and for a particular value of i (6 days in this case); These values are input into the orange box to the left of the graph.Blue arrows show where the R8 (R0 estimated from new cases over the last 8 days) approaches or exceeds 1 (an exponential infectious rate seen in epidemics). Since the 13 June 2020 the R8 (R0) has been mainly over 1 showing that tighter restrictions are required to suppress an epidemic rate of rise in cases. R8 also approached 1 at the time of the meat works and the nursing home clusters. The R8 also exceeded 1 on the 20 February and should have been a red flag warning of an exponential spread of the virus in the population entering Australia and in the population from which they were travelling. It is not probable mathematically for there to be an exponential increase in infection in those entering Australia if there was not already an exponential increase in infection in the population from which they came. That is, the infection was already epidemic in practice (R0 greater than 1) on 20 February, a month before adequate restrictions were put in place.
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