Efficiency of quarantine and self-protection processes in epidemic spreading control on scale-free networks

One of the most effective mechanisms to contain the spread of an infectious disease through a population is the implementation of quarantine policies. However, its efficiency is affected by different aspects, for example, the structure of the underlining social network where highly connected individuals are more likely to become infected; therefore, the speed of the transmission of the decease is directly determined by the degree distribution of the network. Another aspect that influences the effectiveness of the quarantine is the self-protection processes of the individuals in the population, that is, they try to avoid contact with potentially infected individuals. In this paper, we investigate the efficiency of quarantine and self-protection processes in preventing the spreading of infectious diseases over complex networks with a power-law degree distribution [ P(k)∼k^-ν] for different ν values. We propose two alternative scale-free models that result in power-law degree distributions above and below the exponent ν = 3 associated with the conventional Barabási-Albert model. Our results show that the exponent ν determines the effectiveness of these policies in controlling the spreading process. More precisely, we show that for the ν exponent below three, the quarantine mechanism loses effectiveness. However, the efficiency is improved if the quarantine is jointly implemented with a self-protection process driving the number of infected individuals significantly lower.