COVID-19 dynamics: simple coronavirus models

1. From deaths to current number of infections

The deaths reported in a country are usually the cumulative deaths so far. By the time someone has died though (they caught the infection a while ago) the infection has since increased. Here's a model which takes both these facts into account.

Assumptions

(1) lethality rate is 2%;
(2) average time to die after infection is one week (conservative assumption);
(3) numbers doubling time is 7 days (during the early, exponential phase of the infection).

Note that in a sequence which doubles, the latest figure is half the total so far. Thus 1, 2, 4, 8, 16. The current figure, sixteen, is approximately half the total of thirty one.

Example:a country which reports 16 deaths so far - also [n deaths].

1. Deaths (overall) = 16  [n]

2. Deaths in the latest iteration = 8  [n/2]
   - assume the 8 people caught it 7 days ago=1 iteration.

3. Infected cases 7 days ago = 50 * number now dead @ 2% lethality
    infected = 50 * 8 = 400   [25n]

5. Number infected now (twice as many) = 800  [50n].

So when you hear on the news that so many people are reported dead in some country, multiply by 50 to get the current number of cases.

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2. The pattern of number of cases

If the infection was spreading in a closely-coupled population with no obvious barriers then the number of cases would increase as the logistics curve at the top of the page above. But countries are engaged in lockdown. This means that the logistics curve will apply inside the quarantine area - perhaps with a smaller R0 if people self-quarantine at home - but that spread outside will be impeded.

However, this is a hard virus to lockdown completely given asymptomatic transmission. So it's quite likely that - with a delay - new cities and regions will be infected ... and then locked down.

This gives a waviness modulating the global logistics curve. The global curve is a series of mini-logistics-curves glued together. It makes the overall pandemic a more protracted affair, which obviously helps in terms of public health logistics, but it's unlikely to stop the virus in its tracks.

It also creates periodic illusions that 'the infection is levelling off'.

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3. The case of Iran

Iran's Shia theocracy is culturally not like the West, or indeed China. I wonder whether their current policy is not so much incompetence as a simple resignation to letting the virus just run to completion.

The reactionary theocrats running Iran may believe that their middle-class opponents are more likely to suffer as a consequences of the pandemic (the conservative rural multitudes will just soak it up) plus they are mostly surrounded by enemies: Israel, Arabs and Sunnis. What's not to like about being a country-level superspreader?

This would be interesting if true: Covid-19 as implicit biological warfare.