The Running Dead
The Z-virus is a deadly virus that turns the infected people into zombies. The prevalence rate of the infection is 20% of all citizens, and the incidence rate of new zombies is about 2.5% per hour. With some strict measures, many zombies are terminated until the population has reached a steady state, where the prevalence rate is stabilized and the incidence rate equalizes the termination rate.
Averagely, how many hours do the zombies last before being put down?
Credit: Resident Evil 5 (Constantin Film)
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1 solution
This is a very adaptive version of epidemics, where we have P = prevalence rate (rate of the infected), I = incidence rate (rate of the new cases), and D = duration (time since onset of the disease till cure or death).
If a population is in a steady state, that means the rate of new cases are weighted out equally by the disease termination (cure or death) rate.
The new cases have to arise from the healthy population of N persons: N ( 1 − P ) × I .
The termination rate will be calculated from the infected population divided by time D (number of zombies terminated per hour): D N P
Hence, N ( 1 − P ) × I = D N P or D × I = 1 − P P
Thus, D × 2 . 5 % p e r h o u r = 1 − 0 . 2 0 0 . 2 0 = 0.25
D = 0 . 0 2 5 0 . 2 5 hours = 10 hours.
As a result, the zombies last for averagely 10 hours before being terminated.
Note: In case the prevalence of a disease is low (e.g. cancer), we can approximate 1-P as 1 and so use equation P = ID instead.