Corona Virus Model

Hey, I’m a physicist (Dr Alan Wilson since 1982). What do physicists do? Try to understand the world. One way to do that, make models. My model is quite simple but comparing its results to the number of new cases in the Australian 2019 flu season it gives the peak at 70,000 within ~10 days with an infection rate of 1.2 (i.e. on average a person with the flu infects 1.2 other people). Okay for a simple approach. The results I have given below are to demonstrate how Social Distancing can work, why we are doing it and how long it needs to occur for.

Parameters: Start with 4,000,000 people with an initial 1000 infected. Assume a natural infection rate of 2.5 per week. A person is infectious for 1 week and not infectious after that and can not be reinfected (i.e. immune), and is taken out of the pool who can be infected. Introduce a Social Distancing Factor (SDF) to roughly represent the reduction in the number of personal interactions. The effective infection rate is now taken to be 2.5xSDF.

The model calculates new infections every week which are due to the previous weeks infected people. Immunity is allowed for by proportioning infections to non immune people. Example: if 10,000 infected people would infect 25,000 over a week (SDF=1, i.e. no distancing), but 2,000,000 out of 4,000,000 have already had the virus, then there are only 12,500 new cases (i.e. a half).

The Graphs. A: Shows the time to reach less than 1 new infection (i.e. kill it off locally). If you want to kill it fast, everyone has to stay away from people. The reduction in days to <1 new infection above ad SDF = 0.4 is because so many people are infected (see graph B) and the virus has a lack of hosts. Note the scale on graph 1: shows it is not short term deal! An SDF = 1/5 still takes 70 days, if we let it rip we are looking at 105 days but hell, who is counting in this scenario. The worse thing to do is be wishy-washy, sort of try the SDF approach, but half hearted: 2500/365 = 6.8 years.

Conclusions: Social Distancing is to avoid infections and thus deaths. It must be rigorous, half -hearted is really bad particularly in terms of time. The biggest risk I see is people are good for a few weeks and then get sick of if and relax. Even with a much reduced virus count only a few cases can rapidly multiply up again. Of course, this ignores active contact tracking and testing to reduce the effective rate.

Disclaimer: models are for interest and general information only. Not government or any other agency approved.

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