The SIR model of infection spread

Effect of R0 mitigation on infection spread

Effect of vaccination on infection spread

Susceptible $$\frac{dS}{dt} = - \frac{\beta I S}{N}$$ Infectious $$\frac{dI}{dt} = \frac{\beta I S}{N} - \gamma I$$ Recovered $$\frac{dR}{dt} = \gamma I$$ Recovery rate $$\gamma = \frac{1}{\text{infectious period}}$$ Basic reproduction number $$R_0 = \frac{\beta}{\gamma}$$

Infection trajectories show a numerical solution to the SIR equations with 1,000 time steps and initial parameters

$$S(0) = 0.999 - p$$ $$I(0) = 0.001$$ $$R(0) = p$$ $$S + I + R = N = 1$$

where p is the vaccination fraction.

Points of Significance: Modelling infectious epidemics

Ottar Bjørnstad1,2, Katriona Shea1, Martin Krzywinski3, Naomi Altman4

1. Department of Biology, The Pennsylvania State University, State College, PA, USA.

2. Department of Entomology, The Pennsylvania State University, State College, PA, USA.

3. Canada’s Michael Smith Genome Sciences Center, Vancouver, British Columbia, Canada.

4. Department of Statistics, The Pennsylvania State University, State College, PA, USA.

Download code

https://martinkrz.github.io/posepi1/

Citation

Bjørnstad, O., Shea, K., Krzywinski, M. & Altman, N. Points of Significance: Modelling infectious epidemics. (2020) Nature Methods 17:455–456.

Version history

9 April 2020 v1.0.0

Initial public release.

17 April 2020 v1.0.1

Minor text changes. Fixed typos.

13 May 2020 v1.0.2

UI tweaks.

18 June 2020 v1.0.3

Added link to SEIRS column.

17 August 2020 v1.0.4

Added link to uncertainty and management column.

30 October 2024 v1.0.5

Fixed bug in figure legend of plot 1 that was showing incorrect value for epidemic peak.

31 October 2024 v1.0.6

Fixed bug in figure legend of plot 1 that was showing incorrect value for beta.

RELATED COLUMNS

Bjørnstad, O., Shea, K., Krzywinski, M. & Altman, N. Points of Significance: The SEIRS model for infectious disease dynamics. (2020) Nature Methods 17:557–558. (interactive figures, download code).

Shea, K., Bjørnstad, O., Krzywinski, M. & Altman, N. Points of Significance: Uncertainty and the management of epidemics. (2020) Nature Methods 17 (in press). (interactive figures, download code)