Set $\tau=t-t_*$. The <Logistic solution of the SI model> becomes
$$
\Lambda(\tau)=\frac{N\beta e^{-\beta\tau}}
{(1+e^{-\beta\tau})^2}
=\frac{N\beta}{4\cosh^2(\beta\tau/2)}.
$$
It is a symmetric, unimodal bell-shaped curve about the incidence peak $\tau=0$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 3 / e / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-207/3/e/solution