Dynamical graphs for the SI epidemiological model

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. MSC classes: 62P10 60J10