Noémi Nagy | Searcharxiv

arXiv2025

On the accuracy of population level approximation of network processes

The individual-based model of simple contagion processes is considered on regular graphs. This model explicitly incorporates the adjacency matrix of the network enabling us to study the effect of network structure on the dynamic of the propagation process. While the asymptotic behaviour of the model is well known, the transient behaviour has been less studied. Our goal in this paper is to give a theoretical estimate on the accuracy of the one-dimensional population-level approximation. This is carried out for arbitrary simple contagion processes and regular Turán graphs. Numerical evidence is shown that the theoretical estimate is rather sharp for dense graphs.

physics.soc-ph↗

arXiv2018

Detailed analytic study of the compact pairwise model for SIS epidemic propagation on networks

The global behaviour of the compact pairwise approximation of SIS epidemic propagation on networks is studied. It is shown that the system can be reduced to two equations enabling us to carry out a detailed study of the dynamic properties of the solutions. It is proved that transcritical bifurcation occurs in the system at $τ= τ_c = \frac{γn}{\langle n^{2}\rangle-n}$, where $τ$ and $γ$ are infection and recovery rates, respectively, $n$ is the average degree of the network and $\langle n^{2}\rangle$ is the second moment of the degree distribution. For subcritical values of $τ$ the disease-free steady state is stable, while for supercritical values a unique stable endemic equilibrium appears. We also prove that for subcritical values of $τ$ the disease-free steady state is globally stable under certain assumptions on the graph that cover a wide class of networks.

math.DS↗