๐ผ
= 2.14 ๐ผ โ 0.14 ๐ผ
= 0.14 ๐ผ
Whilst complex for us, a computer program can easily map the effect of these functions. Starting with a population of 11 people โ 10 of whom are susceptible, 1 who is infected and 0 who are immune gives the following outcome:
Infection spread is rapid.
By day 2, 8 people are infected.
By day 10 most people are immune but the illness is still in the population
By day 30 the entire population is immune and the infection has died out.
Let us change the population size; here we have 1000 individuals, 0 immune and only 1 infected. By day 5, more than 75% of the population have already been infected, showing how quickly the disease is able to spread even from just one person. The final graph, below, shows the effect of herd immunity- this time there are 100 susceptible people, but because 900 people are recovered (immune), the infection cannot take off- the immunity act as a buffer. It is important to note that in each of these examples; it has been assumed the recovered population are alive. However, in real life, and with more dangerous diseases, this โrecoveredโ population would also consist of all those killed by disease. Therefore, the final immunity of 100% might include 10% dead. This shows the importance of being able to model a
disease spread so that effective vaccination can be implemented.
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