The classic Susceptible-Infected-Susceptible epidemic model is the following:
Each node is in one of the two states: Susceptible or Infected:
Susceptible->Infected->Recovered.
Let s and i respectively represent the percentage of susceptible and infected nodes, $\beta$ represent the infection rate, and $gamma$ represent the recover rate. The differential equation system for the model is:
\begin{equation} \begin{aligned} \dfrac{ds}{dt}=\gamma i - \beta s i \\ \dfrac{di}{dt}=\beta s i - \gamma i \end{aligned} \end{equation}
with \begin{equation} s+i=1 \end{equation}
Given the value of $\beta$, $\gamma$, and the initial value of $i$ and $s$, we can numerical calculate the $s$, and $i$ as a function of $t$. Here is a typical result:
The epidemic spreading gradually progresses to a stable fraction of infected nodes in the end. My question what decides the time to progress to the stable state? That is how the epidemic parameters affect the length of $Ts$.
It would be create if there is an analytical equation for $Ts$. If it is not possible, it would be help as well if you could talk about how $Ts$ changes with other epidemic parameters.