Given the huge surge of cases in recent weeks in the US and Italy in particular, it’s evident social distancing is not working, as I predicted weeks ago. Thus there is no reason then to finish this series given that I am already right, but will so do anyway because I want to finish the math proof. Some also attribute this surge to increased testing, but the increase in cases cannot be attributed to just testing alone. This has lead to more drastic measures such as self-quarantines, stay-at-home orders, and shut-downs, none of which will work that well either. The problem, the virus is very contagious, infecting about 2x more people per carrier than the flu. Second, it probably takes a totalitarian regime to enforce an effective quarantine. It was quoted 100 years ago that “stopping the influenza is like stopping the wind.” People will otherwise break the quarantine by talking to each other in small groups or going outside.
We’re going to have a lot more cases and deaths and there is nothing anyone can do about it. I’m tired of hearing about ventilator shortages and overcrowded hospitals. Many of these same liberals who profess to be pro-science and pro-evolution, suddenly when confronted with the harsh realities of nature and natural selection, rather than supporting the survival of the fittest, seek to divert resources to protect the weakest at large cost to everyone else. 1% of people dying, who are mostly old people and hence beyond their peak productive and child-bearing years or people who are otherwise unhealthy and at high risk such as smokers, of this virus does not justify shutting down the economy and inconveniencing everyone else.
Anyway, enough of that. So going back to part 2, we have the modified r formula:
.006*(r_2+r_1)+.994*(r_2)=r
or simply:
r_2+.006r_1=r
r_1 is the additional rate of infection due to risky behavior such as large crowds and events
r_2 i the baseline rate , which is non-social behavior
.006 is the proportion of people who engage in such behavior in the 5-day asymptomatic window
r can be easily extrapolated from the r-naught value
So I will assume that people who engage in risky behavior infect 2 extra people, in addition to the baseline rate. Being infected and in a crowd of does not necessarily mean everyone else will be infected, because the radius of spread is only 6 feet.
r=.27,which is the observed rate . This corresponds to an R_O of 2.35
Define R1 as the r-naught of the risky behavior in isolation
Refine R2 as the r-naught of the safe behavior in isolation
the goal is to solve for these values
This leads to the system of equations:
R2+.006R1=2.35
R1-R2=2
So R1=4.32 and r2=2.32
Assuming R1, which is the risky behavior, is stopped, that leaves R2, which when converted back to r gives r=.264, which is not small enough from the original value (r=.27) to flatten the curve much.
The above formula can be generalized to:
r_2=((R0+d)/(1+k)-d-1)/s
s=asymptomatic spread period
R0 is observed r-naught
d=increased spread from risky behavior
k=proportion of population engaging in risky behavior
The big problem is we don’t really know what k and d are. All we have to go on are estimates based on human behavior and susceptibility of crowds to infection.
To be continued