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Estimating epidemic exponential growth rate and basic reproduction number - PubMed

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Estimating epidemic exponential growth rate and basic reproduction number

Junling Ma. Infect Dis Model. 2020.

Abstract

The initial exponential growth rate of an epidemic is an important measure of the severeness of the epidemic, and is also closely related to the basic reproduction number. Estimating the growth rate from the epidemic curve can be a challenge, because of its decays with time. For fast epidemics, the estimation is subject to over-fitting due to the limited number of data points available, which also limits our choice of models for the epidemic curve. We discuss the estimation of the growth rate using maximum likelihood method and simple models.

Keywords: Epidemic curve; Exponential growth rate; Maximum likelihood estimation; Phenomenological models.

© 2019 The Author.

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Figures

Fig. 1
Fig. 1

Cumulative Ebola cases during the 2014–16 western African Ebola outbreak, plotted in linear scale (left) and log-linear scale (right). Source: Center for Disease Control Ebola case counts (Center for Disease Control, 2016).

Fig. 2
Fig. 2

Weekly influenza mortality during the 1918 pandemic in Philadelphia, plotted in linear scale (left) and log-linear scale (right).

Fig. 3
Fig. 3

The simulated SEIR epidemic curve (upper) and the fitted exponential growth rate as a function of the end of the fitting window (lower). The epidemic curve is simulated stochastically from the SEIR model in Example 2 using the Gillespie method (Gillespie, 1976) with the parameters β=0.3, σ=1, γ=0.2, E0=10, S0=9,990. I0=R0=0. The rates have a time unit of a day. The daily cases are then aggregated by week. The data points are taken at times ti=i, i=0,1,2,…13 weeks. The theoretical exponential growth rate is λ=0.547 per week.

Fig. 4
Fig. 4

The comparison of the results of fitting the SIR, exponential, logistic, and Richards models to a simulated weekly incidence curve, as a function of the end point of the fitting window (upper). The epidemic curve (lower) is shown as a reference. The epidemic curve and the theoretical exponential growth rate are the same as Fig. 3 s.

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