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October 16, 2014

# Exponential Ebola

Exponential expansion of an infectious disease occurs when the rate of growth is proportional to the number of people currently infected. The mathematical formula for exponential growth is:
[x_t = x_0(1+r)^t]
In the case of Ebola, xt represents the total number of people infected, xₒ represents the number of index cases at the starting point, r represents the rate of disease transmission (believed to be about 2 for Ebola, i.e.: each Ebola victim transmits the disease on average to 2 other people), and t (as an exponent) represents the time interval used for measurement (months). The formula reduces to xt = 3ᵗ for a transmission rate of two with a single index case. Since 70% of Ebola patients die, and since the survivors no longer transmit the disease, the formula for Ebola cases further reduces to xt = 2ᵗ.
With a transmission rate of 2 and a one-month transmission time, there would be 2 active Ebola cases at the end of the first month,...(Read Full Post)