Past exam of the short options course of the University of Oxford / 2017 / 9 / b / i / Solution

Assume $S_0>0$ and scale by the initial susceptible count:Substitution into the SIR model equations givesThe initial data become $u(0)=1$, $v(0)=v_0$, $w(0)=0$. The conserved total is $u+v+w=1+v_0$, since the scaling is by $S_0$, not by $S_0+I_0$. With this normalization, ${\mathcal{R}}_0$ is the reproduction ratio at the initial susceptible level.