Some formulas for 2&2 to work on or for people to have a background of simple epi info. Everyone has been hammered with R0 so should have a good grasp of that concept, bigger the R0 the more spread, R0 1 means stable transmission, R0 less than 1 means declining transmission. R0 has somewhat been misconstrued in the media because R0 in the traditional sense is a stable basic reproductive number, which is important in the case of removing social distancing. We are artificially changing R0 based on social distancing but the actual R0 is static, which for this virus appears to be somewhat high, most likely in the 4-6 range. Once again though this is an average, which will vary person to person, so one person may be transmitting to 1 person another may be transmitting to 10 people, based off a whole bunch of factors like viral load, immune response, respiratory capacity, movements, etc…
People may also be familiar with SIR models of disease, it’s the most basic epi model there is. You have Susceptible, Infectious, and Recovered. Each will be treated as its own bin, using an ordinary differential equation. You can make this model as simple or as complex as you want, you can add birth rate to into susceptible, but that can probably be eliminated for Covid-19, but you probably want to eliminate deaths from the recovered bin. The whole process then becomes cyclical; Susceptible population (infectious rate) to infected population (recovery rate) to recovered population (minus deaths), then rate of protection decay back to part of the susceptible population. Seems simple enough, the problem in an emerging disease is its extremely difficult to know what data to input into the model. So original modeling coming from China was an SIR model, with low transmission rates and no concept of asymptomatic spreaders.
In early February the model was complicated by taking into account 2&2’s favorite thing, asymptomatic spreaders. To put these into the model you end up with an SEIR model, or Susceptible, Exposed, Infectious, Recovered. You have a group of individuals that are exposed but not infectious, and then a group that’s exposed and infectious, but within the infectious group you then bin two different differential equations, one for symptomatic infections and one for asymptomatic infections. You then need to determine the infectious rate for both bins, do they vary (probably), is an asymptomatic spreader having a lower infectious force but same rate as infectious caused by increased rates of exposure. You are now adding equations on top of equations, and in an emerging disease you are making a lot of assumptions because the data is not great.
I guess the take away is that the models are fluid and are meant to provide a tool to make informed decisions. They are complicated, you can’t just extrapolate your simple denominator math or exponential growth because it doesn’t work like that. The models are only as good as the data that is input into them, its why the models are pretty bad despite our best efforts. It’s also why the lack of testing is the biggest problem with figuring out what to do next. If anyone tells you they know what will happen or what was going to happen they are full of shit. Everything put out even by the media either doesn’t have or fails to mention confidence intervals. So whenever something is printed look at the range, do you gain any information when you are determining R0 and you have a 95% CI that its between .5 and 2.5, that means either you are having exponential growth or transmission reduction, it tells you nothing.
Now for 2&2’s homework, solve
dE/dt = S(t)/N((R0/Di)I(t) + z(t)) – E(t)/De – (Lwj/N + Lw,c(t)/N)E(t)
The answer is dE/dt = OPEN UP, AMERICA FUCK YEAH!