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Redesign of the Didactics of S(E)IR(D) → SI(EY)A(CD) Models of Infectious Epidemics Reference to Exit Strategies for the Economic Crisis

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Redesign of the didactics of S(E)IR(D) → SI(EY)A(CD) models of infectious epidemics Reference to exit strategies for the economic crisis. A nasty virus, asking for eradication. Could the virus be used as its own vaccine for some ? How immune will one be ? Didactics on modeling of the SARS-CoV-2 (covid-19) pandemic of 2020, with the example case of Holland. Prevent or prepare for the next pandemic, perhaps already this Fall or Winter. Thomas Colignatus June 15 2020 https://zenodo.org/communities/re-engineering-math-ed/about/ Abstract 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 2 2020-06-15-Didactics-SIEYACD.nb 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. Keywords and codes Journal of Economic Literature (JEL) codes: P16 (political economy), E66 (macro-economics, general outlook), I18 (public health), Q56 (sustainability), D60 (welfare economics), A12 (general economics and teaching, relation to other disciplines) Medical Subject Headings (MeSH) (IDs): D011634 (Public health), C000656484 (COVID-19), D004813 (Epidemiology), D000066949 (Biobehavioral sciences), D015233 (Models, Statistical), D000075082 (Proof of Concept Didactics), D017145 (Models, Educational), D004778 (Environment and public health), D000072440 (Public health systems research), D040381 (Education, public health profes- sional), D006285 (Health planning), D004989 (ethics) MSC2010: 92D30 (Epidemiology), 92C60 (Medical epidemiology), 91B64 (Macroeconomic theory), 91B76 (Environmental economics), 00-01 (Introductory exposition) Disclaimer and declaration of interest Thomas Colignatus is the scientific name of Thomas Cool, econometrician (Groningen 1982) and teacher of mathematics (Leiden 2008), in Scheveningen, The Netherlands. He worked at Erasmus Medical Center (Rotterdam 2002-2004) on (Markov) modeling for screening on the Human Papil- loma Virus (HPV) concerning cervical cancer. The article has used software of The Economics Pack. Applications of Mathematica, which has been developed by the author since 1993, which is propri- etary software, available at a price, and not falling under the CC license for the PDF. The targeted publication venue is not a journal but a book publisher. (c) Thomas Colignatus 2020 CC BY-NC-ND 2020-06-15-Didactics-SIEYACD.nb 3 Table of contents Abstract Keywords and codes Disclaimer and declaration of interest 1. Introduction 1.1. What this notebook and package do 1.1.1. Didactic redesign 1.1.2. There already is an abundance 1.1.3. Overview of this Introduction 1.2. The renaming S(E)IR(D) → SI(EY)A(CD) 1.3. Infection Fatality Factor (IFF) and symptomatic Case Fatality Factor (sCFF) 1.4. The meaning of parameters R0, α, β and γ 1.4.1. Euler 1767 1.4.2. Constant generation interval 1.4.3. Normal distribution 1.4.4. The SI(EY)A(CD) family 1.4.5. Empirical distributions 1.4.6. Interpretation of γ, also for estimation 1.5. Benefit of better didactics on SI(EY)A(CD) epidemic models. Understanding herd immunity 1.5.1. General understanding and communication 1.5.2. Interpreting official reports 1.5.3. Remarkable statistical fits 1.5.4. Limit values 1.5.5. Understanding herd immunity 1.5.6. Relevance of better didactics 1.6. A nasty virus, asking for eradication. A challenge anyway 1.6.1. A world at risk but also badly managed 1.6.2. Prevent future pandemics 1.6.3. A nasty virus, asking for eradication 1.6.4. Under normal conditions the virus can no longer be contained 1.6.5. Return to some normalcy, or consider what urgently requires improvement 1.6.6. While there is no vaccine: options for an exit strategy 1.6.7. Information that is missing now about such scenarios 1.7. Summary of a complex objective 1.8. Structure of this notebook 1.9. About the author 1.9.1. Caveat 1.9.2. Work related to medicine 2. Timeline and assumptions of the Dutch case 2.1. Introduction 2.2. Properties of SARS-CoV-2 and some support for the Dutch policy statement of 2020-03-16 4 2020-06-15-Didactics-SIEYACD.nb 2.3. Relating to the RIVM data and parameters (1) 2.4. Basic parameters R0, α, β and γ for unmitigated spreading before the lockdown 2.4.1. Choice of latency α 2.4.2. Choice of R0 2.4.3. Choice of γ 2.4.4. Consequence for β 2.4.5. General understanding about the choice of R0 2.5. Choice of Infection Fatality Factor (φ = IFF) 2.6. A timeline with scores from a SEYCD model without intervention 2.7. Dutch data are unreliable, but the 70-79 age group might be stable 2.8. Timeline of the Dutch case, to determine onset and when β changed 2.9. Relating to the RIVM data and parameters (2) 2.9.1. Introduction 2.9.2. RIVM & the Outbreak Management Team (OMT) (2020) on source and contact tracing 2.9.3. RIVM January 27 2.9.4. RIVM March 25 2.9.5. RIVM April 8 2.9.6. RIVM April 22 2.9.7. RIVM May 7 2.9.8. RIVM May 20 2.9.9. RIVM May 25 2.10. A partial result of this exercise 2.10.1. A result for us 2.10.2. A list of questions for others 3. The package 3.1. Caveat: This is didactics. The package only hints at the real world 3.2. Design / Redesign of didactics 3.2.1 Avoid using R for compartments, and instead use A and C 3.2.2. Have D = φ A as an explicit proportion 3.2.3. One single conceptual model SIA with two kinds of splits: A = C + D and I = E + Y 3.2.4. Separate models but joint options 3.2.5. Joint set of parameters and variables 3.2.6. Distinction between infections and symptomatic disease 3.2.7. Models SEYCDT and SEYCDB for estimation 3.2.8. Modularity 3.2.9. Administration of scenarios 3.3. General setting on programming 3.3.1. Reasons for choosing Mathematica 3.3.2. The Economics Pack 3.4. The SIA package 3.5. Initialisation cells for loading of The Economics Pack and Survival`SIA` 3.5.1. The Economics Pack 2020-06-15-Didactics-SIEYACD.nb 5 3.5.2. The survival packages 3.5.3. ApplySIA` (not documented) 4. Compartments 4.1. Principle 4.2.
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