Impact of contact rate on epidemic spreading in complex networks

Contact reduction is an effective strategy to mitigate the spreading of epidemic. However, the existing reaction-diffusion equations for infectious disease are unable to characterize this effect. Thus, we here propose an extended susceptible-infected-recovered model by incorporating contact rate into the standard SIR model, and concentrate on investigating its impact on epidemic transmission. We analytically derive the epidemic thresholds on homogeneous and heterogeneous networks, respectively. The effects of contact rate on spreading speed, scale and outbreak threshold are explored on ER and SF networks. Simulations results show that epidemic dissemination is significantly mitigated when contact rate is reduced. Importantly, epidemic spreads faster on heterogeneous networks while broader on homogeneous networks, and the outbreak thresholds of the former are smaller.