# blab / ncov-phylodynamics

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 @@ -45,16 +45,17 @@ The Mathematica notebook ncov-phylodynamics.nb contains code to analyze result ### Rate and TMRCA We find substitution rate consistent with previous work of 0.9 × 10-3 (95% CI 0.5-1.4 × 10-3) substitutions per site per year. We find a median TMRCA of 3 Dec, 2019 (95% CI 30 Oct to 17 Dec). We find a median TMRCA of 3 Dec (95% CI 30 Oct to 17 Dec). ### Effective population size and exponential growth rate These phylodynamic approaches can estimate effective size of the virus population by examining rates of coalesce through time. These phylodynamic approaches can estimate effective size of the virus population by examining rates of coalescence through time. Here, we estimated the exponential growth rate as 35.4 (95% CI 9.6-50.0) per year. This translates to a doubling time of 7.2 (95% CI 5.0-12.9) days. This coincides closely with doubling time reported by modeling groups looking at reported cases in China ([Wu et al][Wu et al]). Here, we plot timescale of coalescence {% eqinline N_e \tau %} through time: ![netau](figures/netau.png) {% eqinline N_e \tau %} is what is directly measured by phylodynamic methods and is measured in years. @@ -67,21 +68,22 @@ We assume generation time {% eqinline \tau %} to be 7.5 days following [Li et al Additionally, effective population size {% eqinline N_e %} can be translated into prevalence with knowledge of the variance in offspring distribution. High variance in distribution of secondary cases reduces prevalence relative to {% eqinline N_e %} as described by [Volz et al][Volz et al]. This reduction is equal to {% eq \sigma^2 = \frac{1}{E[R_0]} + \frac{1}{k} + 1 %}, {% eq \sigma^2 = \frac{1}{E[R_0]} + \frac{1}{k} + 1, %} where {% eqinline E[R_0] %} is the mean number of secondary cases and {% eqinline k %} is the dispersion parameter of secondary cases. We assume {% eqinline E[R_0] %} to be between 1.8 and 2.8 following [Wu et al][Wu et al] and others. We assume that variance of secondary cases is at most like SARS with superspreading dynamics with {% eqinline k=0.15 %}, but allow for less variance with {% eqinline k=0.30 %}. Thus, we convert BEAST estimates of {% eqinline N_e \tau %} to point prevalence {% eqinline I %} by following {% eq I = N_e \tau \times \frac{\sigma^2}{\tau} %} Thus, we convert BEAST estimates of {% eqinline N_e \tau %} to point prevalence {% eqinline I %} by following {% eqinline I = N_e \tau \times \sigma^2 / \tau %}. We arrive at the following estimate of prevalence through time: ![prevalence](figures/prevalence.png) We estimate a median prevalence on 8 Feb of 28,500 currently infected with a 95% uncertainty interval of between 7500 and 104,300 currently infected. ### Total incidence We estimate incidence in each serial interval and then calculate a cumulative incidence total: ![incidence](figures/incidence.png) We estimate a median total incidence on 8 Feb of 55,800 total infections since start of epidemic with a 95% uncertainty interval of between 17,500 and 194,400 total infections.