Unveiling epidemic spreading and control on networks with self-recovery and social support

Given the inherent complexities of individual recovery, self-recovery stems from the individual themselves, whereas social support originates from their susceptible surroundings. Utilizing the quenched mean-field method, two distinct analytical models are developed. The condition for an epidemic outbreak is established through a comprehensive analysis of stability and bifurcation. Continuous-time simulations confirm the predictive capability of these models in terms of spreading behavior. Our findings indicate that both self-recovery and social support can decrease the likelihood of an epidemic outbreak. Further simulations imply that self-recovery can eradicate the explosive transition in scale-free networks, but only dampen its magnitude in random regular networks. These insights could have profound implications for governmental strategies in increasing its publicity efforts for epidemic control.