Farr's Law says that the curve of the number currently infected during an epidemic is roughly bell-shaped. A bell-shaped curve could be made by joining an exponential curve and some other curve however that would imply an event happening at the join which seems rather contrived. Applying Occam's Razor leads to the conclusion that epidemics never grow exponentially.
1840 AD | Farr | Farr's Law |
1927 AD | Kermack & McKendrick | Standard SIR model |