In this work, an epidemiological model is constructed based on a target problem that consists of a chemical reaction on a lattice. We choose the generalized scale-free network to be the underlying lattice. Susceptible individuals become the targets of random walkers (infectious individuals) that are moving over the network. The time behavior of the susceptible individuals' survival is analyzed using parameters like the connectivity γ of the network and the minimum (Kmin) and maximum (Kmax) allowed degrees, which control the influence of social distancing and isolation or spatial restrictions. In all cases, we found power-law behaviors, whose exponents are strongly influenced by the parameter γ and to a lesser extent by Kmax and Kmin, in this order. The number of infected individuals diminished more efficiently by changing the parameter γ, which controls the topology of the scale-free networks. A similar efficiency is also reached by varying Kmax to extremely low values, i.e., the number of contacts of each individual is drastically diminished.