Optimal Local Control Strategy for the Spreading of Epidemic in Two-Dimensional Kleinberg Networks

In this paper we study the spreading of epidemic and its optimal control strategy in two-dimensional Kleinberg networks. We propose a local control strategy based on the Manhattan distance to inhibit the spreading of epidemic in Kleinberg networks, and then study the effect of this strategy on the cost function of total system (defined as the sum of the density of infection and the density of cured individuals). We find that, when the number of long-distance edges and the transmission rate are in a certain range, there will be an optimal control radius that makes the cost function of total system be minimum. When the control radius is smaller than the optimal radius, the epidemic cannot be effectively controlled, leading to the outbreak of epidemic. However, when the control radius is larger than the optimal radius, the cost of controlling is very high though the epidemic can be controlled. Meanwhile, we also show that the optimal control radius is influenced by the transmission rate and the parameter depicting the Kleinberg network.