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.

Ottar Bjørnstad^{1,2}, Katriona Shea^{1}, Martin Krzywinski^{3*}, Naomi Altman^{4}

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.

https://github.com/martinkrz/posepi1

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

Initial public release.

Minor text changes. Fixed typos.