Fig. 5.

The effects of the correlated individual degree and recovery rate. We show $R_0$ and $R\left(\infty \right)$ (red circles) as the function of $Corr\left(k^2,{\gamma }^{-1}\right)$, and the results are obtained by 500 independent realizations for each value of $Corr\left(k^2,{\gamma }^{-1}\right)$. Here, $n=100$, individual susceptibility is set as a constant value $\beta =0.0556$, and the degree of individuals follows power-law distribution with $\mu =2.5$ and $M=100$. On the left, individual course of disease follows Poisson distribution with $\langle {\gamma }^{-1}\rangle =6.5000$, $Var\left({\gamma }^{-1}\right)=5.5000$; on the right it follows power-law distribution with $\langle {\gamma }^{-1}\rangle =6.5000$, $Var\left({\gamma }^{-1}\right)=173.2610$. For comparison, we also compute $R_0$ and $R\left(\infty \right)$ (blue squares) when the degree and recovery rate are independent correspondingly.