Dynamical graphs for the SI epidemiological model

TL;DR

This paper models the SI epidemiological process using dynamical graphs to analyze how individual behavior and network structure influence disease spread and the formation of subgraphs, with implications for understanding epidemic dynamics.

Contribution

It introduces a dynamical graph model with a single parameter for rewiring probability, linking individual avoidance actions to disease transmission and network evolution.

Findings

Dynamical behavior impacts subgraph evolution.

Connectivity degree influences disease spread and subgraph formation.

Model captures effects of individual actions on epidemic dynamics.

Abstract

In this paper we study the susceptible-infectious (SI) epidemiological model using dynamical graphs. Dynamical structures have been recently applied in many areas including complex systems. Dynamical structures include the mutual interaction between the structure topology and the characteristics of its members. Dynamical graphs applied to epidemics consider generally that the nodes are individuals and the links represent different classes of relationships between individuals with the potential to transmit the disease. The main aim in this article is to study the evolution of the SI epidemiological model and the creation of subgraphs due to the dynamic behavior of the individuals trying to avoid the contagious of the disease. The proposed dynamical graph model uses a single parameter which reflects the probability of rewire that represent actions to avoid the disease. This parameter includes also information regarding the infectivity of the disease. The numerical simulations using Monte Carlo method show that the dynamical behavior of individuals affects the evolution of the subgraphs. Furthermore, it is shown that the connectivity degree of the graphs can change the arise of subgraphs and the asymptotic state of the infectious diseases.