2-stratum SEIRS model (Beta v8.1 10/17/2020)

Preprint paper: SARS-CoV-2 waves in Europe: A 2-stratum SEIRS model solution

Select location = , Initial + following strategy =

Spread day = Day of dominant spread (Holo), Infected on spread day (implicit) =
Beginning 1st phase = (Holo)
1st phase duration: days (ends on Holo)
1st isolation to vulnerable = (Vulnerable are all >60 and <60 with underlying diseases)
1st isolation to healthy <60 = (isolation to healthy <60 apply only to individuals able to isolate from vulnerable)
Change isolation to healthy <60 and (varying infected on spread day and isolation to vulnerable)
1st phase deaths fitting

2nd phase. Duration = days (ends on Holo)
2nd phase isolations, vulnerable = , healthy <60 =
2nd phase deaths fitting

3rd phase duration = days (ends on Holo) ( show 3rd phase death minimizing alternatives and one of days, time!)
3rd isolation to vulnerable =
3rd isolation to healthy <60 = (0.99 for maximun isolation, 0.00 normal life, -1.99 for coronavirus party)
Vaccination day = (Holo), uniform effectiveness. (e.g. 0.40, 1 max) ( show final for all vaccination days, time!)
Change parameters and (and show ONE individual isolating during days starting on lockdown)

Display of daily deaths (n-day) moving average = (ma, e.g. 7)
Predicted results will show here

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More parameters

Change values and press

Sars-cov-2 virus:
Days between Exposition to Infectiousness = (Eo, best fit 5)
Days between recovered and death = (RtoD, best fit 10)
Infectiousness duration in days = (Do, best fit 2 for nR[d]=I[d-1]/Do function) (Ro/Do is the daily reproduction number)
Normal life R in location = (Ro, estimation 3.3)
Proportion of susceptible population = (So, 1 for novel virus)
Proportion of <60 that are vulnerable = (P_vul_u60, estimation 0.0342)
Mortality for Vulnerable (IFR) = (IFR_vul, Vulnerable individuals are >60 or <60 with underlying diseases)
Mortality for Non Vulnerable (IFR) = (IFR_non_vul, Non Vulnerable individuals are healthy <60)
Average positive testing period in days = (APTP, estimation 19 days)
Proportion of asymptomatic with T cell response but without IgG response (TAK = 0.35, Sekine et al study)
Average period between recovered and losing immunity (T1 = 365, guess)
Proportion of recovered losing immunity after T1 (PRLI = 0.01, guess, same for infection and vaccine)
Proportion of <60 asymptomatic (A_u60 = 0.52, best fitting guess, if changed in Spain shows fitting results)
Proportion of >60 asymptomatic (A_o60 = 0.21, best fitting guess, if changed in Spain shows fitting results)
Average ICU hospitalizations per death = (ICU_pd, estimation 1.093)
Average ICU hospitlization duration in days = (ICU_dur, estimation 8)

Early D614 like strain wave in Asia: Hypothesis

Location:
Inhabitants in location= (pop, e.g. 14800000 for AMBA). Must be a conglomerate, cannot include distant locations.
Proportion of population >60 in location = (P_o60, e.g. 0.15)
Proportion of non vulnerable in location unable to isolate from vulnerables (i.e. same household) (P_non_vul_una, estimation 0.07)
ICU beds per 100.000 inhabitants in location = (ICU_beds, e.g. 26)
Day 1 of simulation (MMM DD YYYY) = (day1_str, e.g. Jan 1 2020)
Population yearly death rate for vulnerable individuals = (PYDR_vul, estimation 0.025, for >60 natural causes CDC)
Population yearly death rate for non vulnerable individuals = (PYDR_non_vul, estimation 0.001, for <60 natural causes CDC)

Other:
Days between Phase 1 and Phase 2 isolations= (e.g. 0 for abrupt isolation level change, 30 for a 30 days straight line)
Days between Phase 2 and Phase 3 isolations= (e.g. 0 for abrupt isolation level change, 30 for a 30 days straight line)

Phase 1 cross isolaton between groups = (1 - Math.sqrt(1-Iso_1_res_una) * Math.sqrt(1-Iso_1_res_abl)
Phase 2 cross isolaton between groups = (1 - Math.sqrt(1-Iso_2_res_una) * Math.sqrt(1-Iso_2_res_abl)
Phase 3 cross isolaton between groups = (1 - Math.sqrt(1-Iso_3_res_una) * Math.sqrt(1-Iso_3_res_abl)

Theoric normal life Herd Immunity Threshold (HIT) = (HIT = (1-1/Ro))
Proportion of vulnerable population in location = P_o60+(1-P_o60)*P_vul_u60 = (P_vul)
Proportion of non vulnerable population in location able to isolate from vulnerable (able population) = 1-(P_vul+P_non_vul_una) = (P_abl)

Frequently Asked Questions

To fit a metropolitan area (e.g. Madrid):

- Location name: Community of Madrid
- Total population: 6663394
- Population older than 60 years (>60): 1550571
- Date of restrictions/lockdown (estimated): March 9 2020
- Date of first death: March 3 2020
- Daily deaths (on date of deceased):
1, 0, 1, 2, 1, 10, 9, 23, 25, 38, 48, 62, 79, 109, 107, 114, 153, 209, 234, 226, 267, 281, 282, 289, 327, 273, 242, 233, 246, 263, 246, 180, 139, 185, 188, 170, 172, 119, 154, 139, 123, 140, 132, 129, 109, 107, 92, 99, 98, 99, 83, 76, 80, 64, 58, 54, 46, 55, 54, 40, 47, 41, 46, 35, 36, 41, 40, 41, 20, 29, 33, 25, 24, 19, 15, 14, 23, 18, 17, 12, 15, 21, 19, 18, 14, 7, 9, 10, 4, 9, 9, 10, 6, 8, 4, 8, 3, 5, 5, 7, 7, 4, 1, 4, 3, 4, 2, 0, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 0, 1, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0

If available:
- Antibody seroprevalence date: July 5 2020
- Antibody seroprevalence for <60: 4.78%
- Antibody seroprevalence for >60: 6.03%

Please include urls to data sources. Daily deaths serie MUST be for the informed total population (e.g. the same daily deaths serie applied to London City population will produce different predictions than if applied to Greater London population).

Contact

For feedback and questions (English and Spanish): sars2seir@gmail.com

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© Copyright 2020. All rights reserved. This model was created, written and edited for research proposes only and even when it was done with the best efforts to be complete, accurate and correct, the authors and the copyright holders accept no liability for the infallibility or quality of the conclusions or information provided or for it being correct, complete or up to date. Any claim against the copyright holders concerning either material or intellectual damage or other detrimental results resulting from the use of any conclusions or information provided, will therefore be rejected. The content is subject to change and the claims made are non-binding. The copyright holders reserve the right to amend, add to, or delete sections of the content without prior notice. You may access to the model’s code published in www.sars2seir.com to the sole effect of understanding and verifying the content. It is expressly forbidden to use the model or any derivation of it –without prior authorization of the copyright holders of the model- for making projections, actuarial or economical calculations and for any other activity derived of the use of the model with economic ends. For any use of the model, in any extent not expressly authorized by copyright law, please request authorization to sars2seir@gmail.com.