Fig. 4.

The effects of the correlated individual degree and susceptibility. We show $R_0$ and $R\left(\infty \right)$ (red circles) as the function of $Corr\left(k^2,\beta \right)$, and the results are obtained by 500 independent realizations for each value of $Corr\left(k^2,\beta \right)$. Here, $m=100$, the course of disease of all individuals is set as a constant value ${\gamma }^{-1}=6.5000$, and individual degree follows power-law distribution with exponent $\mu =2.5$ and $M=100$. On the left, the susceptibility follows Poisson distribution with $\langle \beta \rangle =0.0556$, $Var\left(\beta \right)=5.6\times {10}^{-4}$; on the right it follows power-law distribution with $\langle \beta \rangle =0.0556$, $Var\left(\beta \right)=0.0177$. For comparison, we also compute $R_0$ and $R\left(\infty \right)$ (blue squares) when the degree and susceptibility are independent correspondingly.