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My modelling the end of covid-19 pandemic

The UK: There are N people currently residing in the country, numbering (or indexed) from 1, 2, …., N. 

This population is partitioned into two: those that have been tested (E) and those that are yet to be tested (Y).

It follows that N = E + Y; E ≤ N.

K is number of confirmed cases, so that K < E.

There are K = 52k+ confirmed cases in the UK as of April 7. But this figure is less than the total actual number of infected persons in the country, which can be known by testing everybody in the country.

If we assumed that the physical distancing preventive measure works out perfectly so that there are no more cases of person-person transmission, then the daily number of confirmed cases will still be rising as long as the entire population is still being tested.

It is assumed that all the borders in the country are closed: there are no travellers entering in and leaving the country.

If the entire population is tested, then the total number of infected persons in the country will be X [= 41k + Y], where Y is the fraction that tested positive at date T = is the date in which the country has tested the Nth person, i.e. 100% of its population.

X is divided into two: R (fraction that recovered from the virus) and D (fraction that did not).

At the moment 0 < [C =D/R] < 1 because not all that are infected by the virus will eventually be killed by the virus.     
C = case fatality ratio

The goal of the healthcare system is to minimise the value of C, i.e. tending it towards zero which is equivalent to maximising recovery rate, R.

Since person-to-person transmission is assumed to be zero, we have,  
C = f (X, H, U), H = measures the robustness of the healthcare system (e.g. medical supplies, doctors, nurses and other medics) in responding to covid-19 patients, and U = a vector of individual characteristics of covid-19 carriers (e.g. age, initial medical conditions, etc).

If L is the covid-19 lifespan in human bodies (i.e. the time it will take for a patient to recover if the patient will survive, and the time it will take to kill a patient if the patient will not survive the virus), then the average of L over X is the expected duration by which the virus will be wiped out of humans in the country.

Limitations: some of the assumptions are not feasible: E.g., people will still go out, shopping and offering essential services. These are channels of transmission.

 2nd, it may not be possible for the UK to test over 60 million of its population.

Blog by @dapelzg

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