Mechanisms to decrease the diseases spreading on generalized scale-free networks

Abstract

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.

Quantum transport on multilayer generalized scale-free networks

“…All other L-values give the same value of t eq for both kind of networks. Thus, the equilibrium time is independent of D, equation (12), or the presence of intralayer loops. MGSFNs with the same size and variable number of layers have the equilibrium time t eq ∝ L δ , where δ ≈ 2.…”

“…The presence of loops increases the total number of links and the sum of all eigenvalues increases [83]. Thus, in figure 2(d) we display the eigenvalues normalized by D, which is proportional to the number of links, see equation (12). By employing a similar procedure as in equation ( 14) D is determined analytically also for the B.-A.…”

“…scale-free networks give values around 3. Remarkably, for all multilayer networks β of the exponential decay equals D, equation (12), which for our MGSFNs is given by equation ( 13) and for B.-A. model by equation (17).…”

“…The solution to many problems in these areas is found by implementing a classical Random Walk (RW) [1][2][3][4][5]. The RW model was able to explain some peculiar behaviors related to the configurational properties of polymers [6], kinetic chemical reactions [4,7], diffusion [8,9], or disease or virus spreading [10][11][12], to name only a few. However, other phenomena are better understood only when a quantum mechanical variant of the RW, the Quantum Walk (QW), is considered.…”

Heterogeneity is a key factor describing the initial outbreak of COVID-19

“…The majority of them have focused on scale-free networks as an alternative contact structure for more realistic social contact patterns. A scale-free network epidemic model was proposed to explore the impact of social distancing and isolation strategies by varying the power-law exponent and the minimum and maximum degrees in the scale-free network [11] . Empirical evidence of SSEs was investigated in SARS-CoV, MERS-CoV, and COVID-19.…”