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Redesign of the didactics of S(E)IR(D) -> SI(EY)A(CD) models of infectious epidemics

Thomas Colignatus

This notebook and package redesign the didactics of the classic SIR, SIRD and SEIRD models. A first step is to relabel to SI(EY)A(CD). The acquitted A = C + D are the cleared or deceased. This avoids the triple use of R for removed, recovered and reproductive number. The infected I = E + Y are the exposed and infectious. The basic structure is given by the Euler-Lotka renewal equation. The format of ordinary differential equations (ODE) should not distract. The deceased are a fraction of the acquitted, D = φ A, with φ the infection fatality factor (IFF). The ODE format D' = μ I or D' = μ Y can be rejected since it turns the model into a course in differential equations, with the need to prove D = φ A what can already be stated from the start. The ODE format also causes distracting questions what μ might be and whether there is a difference between a lethal acquittal period and a clearing acquittal period, and how parameters values must be adapted when the acquittal rate γ changes. The didactic redesign is discussed with the example of the SARS-CoV-2 pandemic. The common formula on herd immunity 1 - 1 / R0 assumes a steady state, but unless infections are zero then they actually proceed in a steady state, and thus not with the promised protection. SI(EY)A(CD) has only an asymptotic steady state so that this formula does not even apply. For SI(EY)A(CD) a notion of "near herd immunity" might be 95% of the limit values. For SARS-CoV-2, RIVM (the Dutch CDC) has mentioned R0 = 2.5 and herd immunity of 60%, presumably using another type of model. In SI(EY)A(CD) an infection with R0 = 2.5 proceeds after 60% till the limit value of 89.3%, which, with IFF = 1.5%, would mean another 78,000 deceased in Holland, compared to 9,000 at the end of May. For Public Health, it is important to balance medical and economic issues. A better understanding of the SI(EY)A(CD) family of models helps to gauge exit strategies for the pandemic and its economic crisis. A possible strategy is to eradicate the virus: with test, test, and test it would be possible to put positively tested persons in quarantine till they have cleared. Another possible strategy is that the vulnerable (elderly and comorbid younger) are put into quarantine while the less vulnerable are infected (in cohorts dictated by ICU capacity), effectively using the virus as its own vaccine, for a period of 12-16 months until there is a proper vaccine for the vulnerable compartment of society. It is remarkable that these scenario's are so little discussed in policy making circles, where there seems to be a preference for a lock-on-off approach, that is risky and prolongs the economic crisis. Epidemiology exists for longer than a century and there have been many warnings about the risk of pandemics. Lessons learnt at the level of cities and nations are now learnt at world level. There is something fundamentally wrong in the relation between society in general and science & learning. For the democratic setup of each nation it is advisable to have both an Economic Supreme Court and a National Assembly of Science and Learning. We want to save lives and livelihoods but let us not forget fundamental insights about democracy and science & learning.

The PDF is available at 10.5281/zenodo.3894161
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