Effective medium estimate of spreading growth in random networks with L\'{e}vy flights

The spreading of epidemic in random spatial metapopulation networks with power-law decaying connectivity is investigated. We perform numerical simulations of reaction-diffusion processes with two compartments on the simplest one-dimensional ring topology of metapopulation graphs and use the effective medium approximation to estimate the spreading velocity of the infection, which we find to grow exponentially in time. We also provide an upper bound for the diameter of the infected populations. Our study outlines a direct and simple approach to estimate possible outbreaks of epidemic spreading in very general mobility patterns.