The following is a simple model:
1. Total Population is the total pop in some defined area. We start with a large metro area.
2. Population infected is the number of people infected day N. This becomes the factor which spreads the virus about.
3. Area is the sq miles in the city. Some are dense and some are sparse
4. We then get the Pops per sq mile
5. The important number is the prolixity density. We assume that is Pops/30 sq ft. No great reason other than proximity but it does drive the infection rate.
6. Number Infected. We always start with a Patient Zero
7. Time to Presentation. Here is the worst part about this virus as I understand it. The common cold, Rhinovirus, presents in 24-48 hours. Nose runs, throat sore, etc. This character enters most likely through the oral pharynx and then multiplies there but does not activate the immune system with the emission of cytokines. It works its way to the lungs where it is there it gets activated with the immune system. Interesting! Almost a sleuth type virus, wonder who engineered this one. The time to presentation may be 10 days thus allowing an infected person to spread.
8. The Contact Activity Ratio is the amount of time an infected person gets to infectively interact with others.
9. Contact Ratio per day is the per person interaction resulting from the above
10. Using the above and the pops we get the Contacts per infected person per day
11. Infection Rate. This is key, it is the rate at which an infected person infects another uninfected person. This is a handshake, then a face contact just at the right time and then off we go! We can drive this down by lower person to person contact and personal sanitation.
12. New Infections results from before.
The following are some person observations guesses (see Li et al for data).
Finally we display the results from above:
Kind of what we have been seeing. Now we can then ask: how do we stop this? From this simple model many factors emerge:
1. Test: This means testing as many as possible as soon as possible. The ten day gestation and shedding time is the dominant factor. It keeps the virus in the community.
2. Reduce the Density by staying in some localized areas.
3. Avoid personal contact to get that Contact Ratio down.
4. Do not make personal contacts. No hand shaking and wash hands. The entry point is usually oral or through the eyes. Wear gloves! I saw a woman in Italy on television with a mask, bare hands and then stuffing some food inside the mask. Really!
5. Measure, measure, measure.
Hopefully this makes some sense. Each element in the pandemic model is controllable. Yet once Patient Zero gets started they are all too often careless, clueless and they go on. Also we must be aware of the Typhoid Mary syndrome, namely a viral carrier.
This is a personal opinion and observation. Its intent is to elucidate some key variables and actions. Good luck!
Oh yes, Happy Ides of March!
Reference: See Murray. Mathematical Biology, Springer, 1989, pp 610-650.
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