Generalized growth model for epidemics.
See:
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Champredon, David and Earn, David JD. Understanding apparently non-exponential outbreaks Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al. Physics of Life Reviews 2016. http://dx.doi.org/10.1016/j.plrev.2016.08.012
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Viboud C, Simonsen L, Chowell G. A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks. Epidemics 2016; 15: 27–37.
The script simple-example.R provides a simple example to fit a generalized growth model to data.