Epidemic spreading with nonlinear infectivity in weighted scale-free networks

TL;DR

This paper explores how nonlinear infectivity and weighted connections in scale-free networks influence epidemic thresholds and spreading dynamics, revealing adjustable thresholds and sensitivity differences between infectivity and weight exponents.

Contribution

It introduces a combined analytical model with infectivity and weight exponents, analyzing their effects on epidemic thresholds and prevalence in weighted scale-free networks.

Findings

Adjustable epidemic threshold through exponents $oldsymbol{ extalpha}$ and $oldsymbol{eta}$

Exponential growth of steady epidemic prevalence in early stages

Higher sensitivity of $oldsymbol{ extalpha}$ compared to $oldsymbol{eta}$ in epidemic dynamics

Abstract

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.