Local information based model for epidemic controlling on multiplex networks

Suppressing the outbreak of disease is one of the hottest topics that attracts large amount of related researches to devote themselves into it. In this paper we propose a resource allocation model based on the local information of each healthy nodes to study how we can allocated limited resources optimally in controlling disease spreading. To mimic the processes of resource allocation and disease spreading, we construct a two-layer multiplex network. Based on the modified Susceptible-Infected-Susceptible (SIS) model, we also proposed a resource based model, named rSIS. Through extensive simulations on both random multiplex network and network with edge overlapping, we find that on the random multiplex network, when the bias parameter is positive, there is worst value, at which the disease can not be controlled effectively. Besides, there is only one explosive transition at the threshold. While when the parameter is negative, resources, there is hybrid transition, and the infected density first grows continuously at the first threshold, and then jumps explosively at the second threshold. Next, we studied the case when there is edge overlapping between two layers. We find that when the parameter is positive, with the increase of infection rate, the optimal value changes dynamically. While when the parameter is negative, there is hybrid phase transitions, and resources should be allocated preferentially to the lower infectiousness nodes.