At the time of writing, the coronavirus disease of 2019 remains a global health crisis of grave and uncertain magnitude. To the non-expert (such as myself), contextualizing the numbers, forecasts and epidemiological parameters described in the media and literature can be challenging. I created this calculator as an attempt to address this gap in understanding.
This calculator implements a classical infectious disease model — SEIR (Susceptible → Exposed → Infected → Removed), an idealized model of spread still used in frontlines of research e.g. [Wu, et. al, Kucharski et. al]. The dynamics of this model are characterized by a set of four ordinary differential equations that correspond to the stages of the disease's progression: In addition to the transmission dynamics, this model allows the use of supplemental timing information to model the death rate and healthcare burden.
Note that one can use this calculator to measure one's risk exposure to the disease for any given day of the epidemic: the probability of getting infected on day 218 given close contact with individuals is 0.00088% given an attack rate of 0.45% [Burke et. al].
A sampling of the estimates for epidemic parameters are presented below:
Location | Reproduction Number | Incubation Period (in days) | Infectious Period (in days) | ||
---|---|---|---|---|---|
Kucharski et. al | Wuhan | 3.0 (1.5 — 4.5) | 5.2 | 2.9 | |
Li, Leung and Leung | Wuhan | 2.2 (1.4 — 3.9) | 5.2 (4.1 — 7.0) | 2.3 (0.0 — 14.9) | |
Wu et. al | Greater Wuhan | 2.68 (2.47 — 2.86) | 6.1 | 2.3 | |
WHO Initial Estimate | Hubei | 1.95 (1.4 — 2.5) | |||
WHO-China Joint Mission | Hubei | 2.25 (2.0 — 2.5) | 5.5 (5.0 - 6.0) | ||
Liu et. al | Guangdong | 4.5 (4.4 — 4.6) | 4.8 (2.2 — 7.4) | 2.9 (0 — 5.9) | |
Rocklöv, Sjödin and Wilder-Smith | Princess Diamond | 14.8 | 5.0 | 10.0 | |
Backer, Klinkenberg, Wallinga | Wuhan | 6.5 (5.6 — 7.9) | |||
Read et. al | Wuhan | 3.11 (2.39 — 4.13) | |||
Bi et. al | Shenzhen | 4.8 (4.2 — 5.4) | 1.5 (0 — 3.4) | ||
Tang et. al | China | 6.47 (5.71 — 7.23) |
See [Liu et. al] detailed survey of current estimates of the reproduction number. Parameters for the diseases' clinical characteristics are taken from the following WHO Report.
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Model Details
The clinical dynamics in this model are an elaboration on SEIR that simulates the disease's progression at a higher resolution, subdividing into mild (patients who recover without the need for hospitalization), moderate (patients who require hospitalization but survive) and fatal (patients who require hospitalization and do not survive). Each of these variables follows its own trajectory to the final outcome, and the sum of these compartments add up to the values predicted by SEIR. Please refer to the source code for details. Note that we assume, for simplicity, that all fatalities come from hospitals, and that all fatal cases are admitted to hospitals immediately after the infectious period.
Acknowledgements
Steven De Keninck for RK4 Integrator. Chris Olah, Shan Carter and Ludwig Schubert wonderful feedback. Nikita Jerschov for improving clarity of text. Charie Huang for context and discussion.