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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.

We consider continuous-time quantum walks (CTQWs) on modified multilayered spiderwebs (MMSs) and their application to quantum transport. Quantum transport efficiency is determined in terms of the exact and the average return probabilities and it is systematically studied for three kind of MMSs. First, we consider a single layer of modified spiderwebs and we introduce the parameter p, which controls the transition from a pure Cayley tree (p  =  0.0) to a complete spiderweb (p  =  1.0). Topologically, this transition corresponds to adding with probability p more links between nearest neighboring nodes from the same generation, when we start from a Cayley tree. By doing so, we observe an increase in the quantum efficiency and we notice that for all generation numbers its highest value is encountered when only one link is missing from each generation. In the second case we stack more modified spiderwebs on top of each other and interconnect them, obtaining an MMS network. In this case the quantum efficiency is further increased by more than two orders of magnitude. In the third case, we remove some interconnecting links between nearest neighboring layers with probability 1  −  q. For these kind of networks we encounter that the highest quantum efficiency does not correspond to q  =  1.0, but to , more precise when we remove a link between successive layers. For these networks and for a proper choice of parameters the quantum efficiency is further increased by several orders of magnitude.