manning.com

### Discovering Disease Outbreaks from News Headlines

3 min read · 2020-04-17 · In this liveProject, you’ll take on the role of a data scientist at the World Health Organization (WHO). The WHO is responsible for responding to international epidemics, a critical component of which…

briandatablog.rbind.io

### Coronavirus test data (technical)

1 min read · 2020-04-14 · This is the same information I posted earlier, but with the script exposed for those interested in replicating it. # libraries library(tidyverse) library(rvest) library(lubridate) # read the web page…

briandatablog.rbind.io

### Coronavirus test data

2020-04-14 · 1 min read 2020-04-14 The Centers for Disease Control give a daily update on the number of Covid-19 tests reported to the agency. Here’s the data as of April 14. The CDC notes that the data for last 7…

rud.is

### New Package — {cdccovidview} — To Work with the U.S. CDC’s New COVID-19 Trackers: COVIDView and COVID-NET

2 min read · 2020-04-11 · posted in R on 2020-04-11 by hrbrmstr The United States Centers for Disease Control (CDC from now on) has setup two new public surveillance resources for COVID-19. Together, COVIDView and COVID-NET p

github.com

### reconhub/covid19hub

2020-04-09 · Community-driven COVID-19 analytics in R. Contribute to reconhub/covid19hub development by creating an account on GitHub.

fabiandablander.com

### Infectious diseases and nonlinear differential equations

2020-03-23 · Last summer, I wrote about love affairs and linear differential equations. While the topic is cheerful, linear differential equations are severely limited in the types of behaviour they can model. In this blog post, which I spent writing in self-quarantine to prevent further spread of SARS-CoV-2 — take that, cheerfulness — I introduce nonlinear differential equations as a means to model infectious diseases. In particular, we will discuss the simple SIR and SIRS models, the building blocks of many of the more complicated models used in epidemiology. Before doing so, however, I discuss some of the basic tools of nonlinear dynamics applied to the logistic equation as a model for population growth. If you are already familiar with this, you can skip ahead. If you have had no prior experience with differential equations, I suggest you first check out my earlier post on the topic. I should preface this by saying that I am not an epidemiologist, and that no analysis I present here is specifically related to the current SARS-CoV-2 pandemic, nor should anything I say be interpreted as giving advice or making predictions. I am merely interested in differential equations, and as with love affairs, infectious diseases make a good illustrating case. So without further ado, let’s dive in! Modeling Population Growth Before we start modeling infectious diseases, it pays to study the concepts required to study nonlinear differential equations on a simple example: modeling population growth. Let $N > 0$ denote the size of a population and assume that its growth depends on itself: As shown in a previous blog post, this leads to exponential growth for $r > 0$: where $N_0 = N(0)$ is the initial population size at time $t = 0$. The figure below visualizes the differential equation (left panel) and its solution (right panel) for $r = 1$ and an initial population of $N_0 = 2$. This is clearly not a realistic model since the growth of a population depends on resources, which are finite. To model finite resources, we write: where $r > 0$ and $K$ is the so-called carrying capacity, that is, the maximum sized population that can be sustained by the available resources. Observe that as $N$ grows and if $K > N$, then $(1 - N / K)$ gets smaller, slowing down the growth rate $\dot{N}$. If on the other hand $N > K$, then the population needs more resources than are available, and the growth rate becomes negative, resulting in population decrease. For simplicity, let $K = 1$ and interpret $N \in [0, 1]$ as the proportion with respect to the carrying capacity; that is, $N = 1$ implies that we are at carrying capacity. The figure below visualizes the differential equation and its solution for $r = 1$ and an initial condition $N_0 = 0.10$. In contrast to exponential growth, the logistic equation leads to sigmoidal growth which approaches the carrying capacity. This is much more interesting behaviour than the linear differential equation above allows. In particular, the logistic equation has two fixed points — points at which the population neither increases nor decreases but stays fixed, that is, where $\dot{N} = 0$. These occur at $N = 0$ and at $N = 1$, as can be inferred from the left panel in the figure above. Analyzing the Stability of Fixed Points What is the stability of these fixed points? Intuitively, $N = 0$ should be unstable; if there are individuals, then they procreate and the population increases. Similarly, $N = 1$ should be stable: if $N < 1$, then $\dot{N} > 0$ and the population grows towards $N = 1$, and if $N > 1$, then $\dot{N} < 0$ and individuals die until $N = 1$. To make this argument more rigorous, and to get a more quantitative assessment of how quickly perturbations move away from or towards a fixed point, we derive a differential equation for these small perturbations close to the fixed point (see also Strogatz, 2015, p. 24). Let $N^{\star}$ denote a fixed point and define $\eta(t) = N(t) - N^{\star}$ to be a small perturbation close to the fixed point. We derive a differential equation for $\eta$ by writing: since $N^{\star}$ is a constant. This implies that the dynamics of the perturbation equal the dynamics of the population. Let $f(N)$ denote the differential equation for $N$, observe that $N = N^{\star} + \eta$ such that $\dot{N} = \dot{\eta} = f(N) = f(N^{\star} + \eta)$. Recall that $f$ is a nonlinear function, and nonlinear functions are messy to deal with. Thus, we simply pretend that the function is linear close to the fixed point. More precisely, we approximate $f$ around the fixed point using a Taylor series (see this excellent video for details) by writing: where we have ignored higher order terms. Note that, by definition, there is no change at the fixed point, that is, $f(N^{\star}) = 0$. Assuming that $f’(N^{\star}) \neq 0$ — as otherwise the higher-order terms matter, as there would be nothing else — we have that close to a fixed point which is a linear differential equation with solution: Using this trick, we can assess the stability of $N^{\star}$ as follows. If $f’(N^{\star}) < 0$, the small perturbation $\eta(t)$ around the fixed point decays towards zero, and so the system returns to the fixed point — the fixed point is stable. On the other hand, if $f’(N^{\star}) > 0$, then the small perturbation $\eta(t)$ close to the fixed point grows, and so the system does not return to the fixed point — the fixed point is unstable. Applying this to our logistic equation, we see that: Plugging in our two fixed points $N^{\star} = 0$ and $N^{\star} = 1$, we find that $f’(0) = r$ and $f’(1) = -r$. Since $r > 0$, this confirms our suspicion that $N^{\star} = 0$ is unstable and $N^{\star} = 1$ is stable. In addition, this analysis tells us how quickly the perturbations grow or decay; for the logistic equation, this is given by $r$. In sum, we have linearized a nonlinear system close to fixed points in order to assess the stability of these fixed points, and how quickly perturbations close to these fixed points grow or decay. This technique is called linear stability analysis. In the next two sections, we discuss two ways to solve differential equations using the logistic equation as an example. Analytic Solution In contrast to linear differential equations, which was the topic of a previous blog post, nonlinear differential equations can usually not be solved analytically; that is, we generally cannot get an expression that, given an initial condition, tells us the state of the system at any time point $t$. The logistic equation can, however, be solved analytically and it might be instructive to see how. We write: Staring at this for a bit, we realize that we can use partial fractions to split the integral. We write: The exponents and the logs cancel each other nicely. We write: One last trick is to multiply by $e^{-rt + Z}$, which yields: where $Z$ is the constant of integration. To solve for it, we need the initial condition. Suppose that $N(0) = N_0$, which, using the third line in the derivation above and the fact that $t = 0$, leads to: Plugging this into our solution from above yields: While this was quite a hassle, other nonlinear differential equations are much, much harder to solve, and most do not admit a closed-form solution — or at least if they do, the resulting expression is generally not very intuitive. Luckily, we can compute the time-evolution of the system using numerical methods, as illustrated in the next section. Numerical Solution A differential equation implicitly encodes how the system we model changes over time. Specifically, given a particular (potentially high-dimensional) state of the system at time point $t$, $\mathbf{x}_t$, we know in which direction and how quickly the system will change because this is exactly what is encoded in the differential equation $f = \frac{\mathrm{d}\mathbf{x}}{\mathrm{d}t}$. This suggests the following numerical approximation: Assume we know the state of the system at a (discrete) time point $n$, denoted $x_n$, and that the change in the system is constant over a small interval $\Delta_t$. Then, the position of the system at time point $n + 1$ is given by: $\Delta t$ is an important parameter, encoding over what time period we assume the change $f$ to be constant. We can code this up in R for the logistic equation:

Kaggle

### COVID19 Local US-CA Forecasting (Week 1)

2020-03-20 · Forecast daily COVID-19 spread in California, USA

Kaggle

### COVID19 Global Forecasting (Week 1)

2020-03-20 · Forecast daily COVID-19 spread in regions around world

access.datanatives.club

### access.datanatives.club/webinar-3ew/l/9kogz6g1

1 min read · 2020-03-16 · It’s official - WHO declared COVID-19 a pandemic. As the virus spreads exponentially and containment is not an option anymore, the strategies for slowing the spread of the infection will have a…

github.com

### FoldingAtHome/coronavirus

2020-03-15 · Folding@home COVID-19 efforts. Contribute to FoldingAtHome/coronavirus development by creating an account on GitHub.

foldingathome.org

### Folding@home update on SARS-CoV-2 (10 Mar 2020)

3 min read · 2020-03-14 · March 10, 2020by John ChoderaThis is an update on Folding@home’s efforts to assist researchers around the world taking up the global fight against COVID-19.After initial quality control and limited…

statsandr.com

### Top 5 R resources on COVID-19 Coronavirus

20+ min read · 2020-03-12 · Best R resources about Coronavirus (COVID-19). These resources are Shiny app, R packages or code that you can use freely to analyse the Coronavirus outbreak.

bnosac.be

### Corona in Belgium

4 min read · 2020-03-12 · I lost a few hours this afternoon when digging into the Corona virus data mainly caused by reading this article at this website which gives a nice view on how to be aware of potential issues which can…

r-posts.com

### Covid-19 interactive map (using R with shiny, leaflet and dplyr)

1 min read · 2020-03-12 · The departement of Public Health of the Strasbourg University Hospital (GMRC, Prof. Meyer) and the Laboratory of Biostatistics and Medical Informatics of the Strasbourg Medicine Faculty (Prof.…

ramikrispin.github.io

### The 2019 Novel Coronavirus COVID-19 (2019-nCoV) Dataset

3 min read · 2020-03-02 · Provides a daily summary of the Coronavirus (COVID-19) cases by state/province. Data source: Johns Hopkins University Center for Systems Science and Engineering (JHU CCSE) Coronavirus .