## (47 days)
## Since 1st case (21 days)
Solid lines depict 3-day moving averages:
Assuming a logistic growth model, our growth rate defined as:
\[ \frac{dN}{dt}= rN(1-N/K)\] where \(r\) is the rate of growth, \(N\) is the number of infected individuals, and \(K\) is some measure of carrying capacity. The closed form solution for the above growth rate is:
\[ N(T)=\frac{N_0 e^{rT}}{1+N_0(e^{rT}-1)/K} \]
where \(N_0\) is the population of infected individuals at time \(t=0\). See below for plots and estimates:
Here are the estimated parameters:
| County | r | k | R2 |
|---|---|---|---|
| Ulster | 0.187 | 1379.475 | 0.9750 |
| Monroe | 0.252 | 129.935 | 0.9595 |
The instantaneous effective reproduction number is defined as
\[R_t=\frac{I_t}{\sum_{s=1}^t I_{s-t}w_s} \] \(R_t\) is nothing more than the ratio of the number of new infections up to time \(t\), namely \(I_t\), to the weighted (by infectivity function \(w_s\)) sum of total infections. \(R_t\) is similar to \(R_0\) in that \(R_t\) defines the number of secondary infections at time \(t\). Using serial interval point estimates from Chinese COVID-19 data (e.g. mean and standard deviation are 3.96 and 4.75 respectively), I compute \(R_t\) for both counties.
I use 2016 election data at the county level to evaluate: (i) whether a county voted for Hillary or for Donald; and, (ii) the margin of the candidate’s victory. For instance, if Hillary won a county by 28% points, then this county would first be coded “D” and then “D (25-50)” since Hilary’s margin of victory was between 25-50%.
## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'
Note that levels here are presented in log units.
Less clear patterns when it comes to \(R_t\)