GoKawiilForeword: I am not an epidemiologist and I don’t claim to be. I am, however, a math major and an academic and I feel like I’ve done my due dilligence in reporting this accurately and correctly. The full code used is at the end of the post, if you’d rather not sift through data.
If you’ve been watching the news, I assume you’ve heard about the COVID-19 pandemic. In light of the CDC releasing a model predicting 62% of Americans will become infected1, I became interested in how they came to those numbers. In fact, how do we come to any conclusions as to the spread of disease at all?
There are plenty of well established models for disease spread. The simplest model is the SIR model5, but it comes with a few caveats. The first caveat is that it assumes that once a disease runs its course in a single person, that person will now be permanently immune to the disease. The second caveat is that the model assumes that all infectious people immediately begin to show symptoms. Neither of these assumptions are accurate for COVID-19: the disease has a 14% reinfection rate6, and it takes 10 to 14 days for symptoms to appear.
The model that has been used for the current COVID-19 pandemic is the SEIRS model*,4,5. With the SEIR model, we have 4 states that any particular person can be in: “Susceptible”, “Exposed”, “Infectious”, and “Recovered”7.
A person is susceptible if they are at risk for catching a disease.
if they are at risk for catching a disease. A person is exposed if they have caught the disease or are carrying the disease without any symptoms. This happens during the incubation period.
if they have caught the disease or are carrying the disease without any symptoms. This happens during the incubation period. A person is infectious if they have now caught the disease and are experiencing symptoms. This is when people go to the hospital, require intensive care, etc.
if they have now caught the disease and are experiencing symptoms. This is when people go to the hospital, require intensive care, etc. A person is recovered if they have gotten over the disease and now have some semblance of immunity.
We have 4 variables we can tweak: \(\beta, \sigma, \gamma, \xi \). They are all rates over a generic unit of time.
\(\beta\) is the rate at which susceptible people become exposed.
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