Dennis' COVID-19 Visualizer

Total Cases To Date

Data As Of

• functionsMethodology

  Fitted Logistic Curves

  *For beginners check out this Video by 3Blue1Brown on the math behind pandemic growth

  The total confirmed, deaths, and recovery curves of a pandemic roughly follow a logistic curve over its course in a community. Of course, there are a lot more factors that come into play when modeling an pandemic. This study makes NO attempts to account for explicit factors.

  Each curve in the dataset is fitted to the following ideal logistic model

  $$f(x;A,\mu ,\sigma)=A[1-\frac{1}{1+e^{\alpha}}]$$

  Where

  $$\alpha=\frac{x-\mu}{\sigma}$$

  In this model, A accounts for the amplitude of the curve, essentially predicting the ceiling of the pandemic

  𝜇 represents the center of the logistic curve, it marks the estimated inflection point of the pandemic

  𝜎 represents the growth factor of the curve, aka the "sharpness"

  Each curve is fed through a least-square gradient decent optimizer against the ideal model to compute the parameters. Note that not all datasets can be successfully fitted, the optimizer can't converge on those datasets with too little data points or non-ideal shape.

  I decided to plot ahead the fitted curve 10 days ahead of now so you could visualize the current trend. Please also note that this is NOT a prediction of the course of the pandemic, it's merely a rough forecast from the current known data points. No one can predict the future.

  Derivatives of Logarithmic Data

  During exponential growth, the log plot shows a linear growth. The slope of the log chart therefore informs the speed of the growth. The slope chart s(t) is defined as

  $$s(t)=\frac{\mathrm{d} }{\mathrm{d} t}log_{10}(y)$$

  Simalar logic folows. In a polynomial function, the second derivative indicates concavity. The second derivative on the linearized data gives us the concavity of the growth curve. Positive value on this curve means accelerating spread, while negative value points to decelerating spread. The concavity chart is defined as

  $$c(t)=\frac{\mathrm{d^2} }{\mathrm{d} t^2}log_{10}(y)$$