Impact of heterogeneous distribution of immunization probability on recurrent epidemic outbreaks

The heterogeneous distribution of immunization probability has been proven to suppress the recurrent epidemic outbreaks effectively, but the reason for this interesting phenomenon is still unclear. To solve this problem, the effects of immunization probability on the maximal infected density and the average infected density are investigated, and it’s found that large immunization probability will depress the maximal infected density sharply. Moreover, it’s proved that small immunization probability is of great importance, which could not only reduce the cost of immunization at low risk but also decrease the outbreak risk of the next year by making the average infected density larger in the current year. Besides, a generalized immunization strategy is presented, which makes the immunization strategy easy to carry out and meanwhile keeps the maximal and the average infected density almost as good as those in the original dynamic immunization strategy. Moreover, the control effects in eight real networks are also investigated, which proves the usefulness of the modified dynamic immunization strategy. Our work proves the usefulness of the heterogeneous distribution of immunization probability and may present theoretical guidance for the government and the public to control the recurrent epidemic outbreaks.