ACCEPTED SOLUTION
Accepted Solutions
Nice graph!
If you play with the "rate of infection," the number of people that each sick person infects per week, you can see why the health care professionals are begging us to "flatten the curve." If the infection spreads more slowly the peak number of sick people is less so the hospitals don't get swamped.
The timing of the pulse is also affected. We can adjust these numbers as the data improves.
Update Prime six attached.
One of the problems I had with JeffH's original model was the number of people who died. Supposed experts are estimating deaths to be between 100,000 and 200,000; the model predicts significantly (order of magnitude) higher numbers. I researched the infected history in my country (USA) and used that to try to "fix" the model.
By manipulating equation 2, rate of infection, we can use this data to estimate Ro, (=b/g) . Since gamma is reasonably estimated (most infections except the tragic ones tend to run about two weeks) we can improve the model. (At least that was my assumption. If we have N measurements by using the change between measurements to estimate the rate of change of infection, and have N-1 measurements:
Two observations were made:
- At the start, where the infected numbers are very small, the computation fails, and
- At the end of the measurement list there appears to be a definite downward trend; this corresponds to my country finally recognizing that there's a problem we need to address.
Discarding the front data, and recognizing the trend, I "guesstimated" a time-changing function for Ro (and therefore beta):
The mean value estimated from the data is Ro = 4.2, the value computed for the last data point is 1.7. If we take that as the best mitigation value that can be achieved, the plot looks like this (vertical scale is millions):
With the mitigation we should expect almost 5 million deaths with a third of the population still left unexposed. And the Infection doesn't begin to subside until July, done by end of August.
STAY SAFE MY FRIENDS!
Fred,
Thanks. I downloaded your Mathcad Express file and downloaded Mathcad Express. I was hesitant because it did not have an odesolve Block; however, you reminded me that finite differencing works also. Thanks again for that. The PTC people assure me that I have a permanent and legal installation of Mathcad 15 even though it displays this. I have both my license and my product code. Both installation procedures produce this display.
I still don't have access to the help files, but that is no big deal since I have used Mathcad for so many years and it did retain access to the tutorials and Quick Sheets. PTC support is looking at this issue for me.
Back to COVID-19. I am basically an old hermit so the sequestration doesn't bother me much, but the future looks awfully dim now. I am still looking at your worksheet to remind me of finite differencing techniques. I may as well start looking at Express; it's one more thing to keep me out of mischief.
Stay safe and healthy.
Reg
Thanks again.
