Modelling Infectious Epidemics

Infectious period, 1/γ (days)

R₀

vaccination level, p (%)

log₁₀ y-axis scale

interpretive text

figure captions

The SIR model of infection spread

Infectious period, ip (days)

R₀

R₀ with mitigation

Hospital capacity, C %

show intermediate trajectories

interpretive text

figure captions

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 Bjørnstad^1,2, Katriona Shea¹, Martin Krzywinski^3*, 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.

* martink@bcgsc.ca

Download code

https://github.com/martinkrz/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.

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).