Epidemic Calculator

Day
218
Susceptible
6,138,598 (87.69%)
Δ -76 / day
Population not immune to disease.
Exposed
528 (0.01%)
Δ -26 / day
Population currently in incubation.
Infectious
342 (0.00%)
Δ -17 / day
Number of infections actively circulating.
Removed
860,532 (12.29%)
Δ -196 / day
Population no longer infectious due to isolation or immunity.
Recovered
832,700 (11.90%)
Full recoveries.
Hospitalized
9,007 (0.13%)
Δ -281 / day
Active hospitalizations.
Fatalities
16,479 (0.24%)
Δ 25 / day
Deaths.
0 50,000100,000150,000200,000Day 020406080100120140160180200
Rt=0.73\mathcal{R}_t=0.73
R0=2.20\mathcal{R}_0=2.20
Intervention on day 100
(drag me)
to decrease transmission by
66.67%
First death
Peak: 74,738 hospitalizations
linear scale
Transmission Dynamics
Clinical Dynamics
Population Inputs
Size of population.
7,000,000
Number of initial infections.
1
Basic Reproduction Number R0\mathcal{R}_0
Measure of contagiousness: the number of secondary infections each infected individual produces.
2.2
Transmission Times
Length of incubation period, TincT_{\text{inc}}.
5.20 days
Duration patient is infectious, TinfT_{\text{inf}}.
2.9 Days
Mortality Statistics
Case fatality rate.
2.00 %
Time from end of incubation to death.
32 Days
Recovery Times
Length of hospital stay
28.6 Days
Recovery time for mild cases
11.1 Days
Care statistics
Hospitalization rate.
20.00 %
Time to hospitalization.
5 Days

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: dSdt=RtTinfIS,dEdt=RtTinfISTinc1E,dIdt=Tinc1ETinf1I,dRdt=Tinf1I\frac{d S}{d t}=-\color{#CCC}{\frac{\mathcal{R}_{t}}{T_{\text{inf}}}} \cdot IS,\qquad \frac{d E}{d t}=\color{#CCC}{\frac{\mathcal{R}_{t}}{T_{\text{inf}}}} \cdot IS- \color{#CCC}{T^{-1}_{\text{inc}}} E,\qquad \frac{d I}{d t}=\color{#CCC}{T^{-1}_{\text{inc}}} E-\color{#CCC}{T^{-1}_{\text{inf}}}I, \qquad \frac{d R}{d t}=\color{#CCC}{T^{-1}_{\text{inf}}}I 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
R0\mathcal{R}_0
Incubation Period
TincT_{\text{inc}} (in days)
Infectious Period
TinfT_{\text{inf}} (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.

Please DM me feedback here or email me here. My website.

Model Details
The clinical dynamics in this model are an elaboration on SEIR that simulates the disease's progression at a higher resolution, subdividing I,RI,R 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.

Export parameters: