Fast Diffusion of a Mutant in Controlled Evolutionary Dynamics^*

We present a novel approach to model the diffusion of a mutant in a geographical network. This is a key issue in the control of epidemics, since many diseases are transmitted by intermediate hosts that could be substituted with genetically modified organisms (GMOs) with a mutation that prevents them from spreading the pathogen. The main strength of our model lies in making analytically tractable the estimation of the expected time needed for the mutant to replace the native species all over the geographical network. Our main results consist in providing an upper-bound and two lower-bounds on this quantity, depending on the network topology. Their use is presented through some simple examples, for which Monte Carlo simulations corroborate our analytical results. Finally, we propose a non-trivial feedback control policy that, using little knowledge of the network topology and of the evolution of the dynamics, allows to substantially speed up the diffusion process.