Epidemic spreading with nonlinear infectivity in weighted scale-free networks

In this paper, we investigate the epidemic spreading for SIR model in weighted scale-free networks with nonlinear infectivity, where the transmission rate in our analytical model is weighted. Concretely, we introduce the infectivity exponent $\alpha$ and the weight exponent $\beta$ into the analytical SIR model, then examine the combination effects of $\alpha$ and $\beta$ on the epidemic threshold and phase transition. We show that one can adjust the values of $\alpha$ and $\beta$ to rebuild the epidemic threshold to a finite value, and it is observed that the steady epidemic prevalence $R$ grows in an exponential form in the early stage, then follows hierarchical dynamics. Furthermore, we find $\alpha$ is more sensitive than $\beta$ in the transformation of the epidemic threshold and epidemic prevalence, which might deliver some useful information or new insights in the epidemic spreading and the correlative immunization schemes.