Epidemic SIR model on a face-to-face interaction network: new mobility induced phase transitions

In this work, we study the epidemic SIR model on a system which takes into consideration face-to-face interaction networks. This approach has been used as prototype to describe people interactions in different kinds of social organizations and, here, it is considered by means of three features of human interactions: the mobility, the duration of the interaction among people, and the dependence of the number of interactions of each person on the time evolution of the system. For this purpose, the initial configuration of the system is set as a regular square lattice where the nodes are the individuals which, in turn, are able to move in a random walk along the network. So, the connectivity among the individuals evolve with time and is defined by the positions of the individuals at each iteration. In a time unit, each individual is able move up to a distance $v$ creating different networks along the time evolution of the system. In addition, the individuals are interacting with each other only if they are within the interaction distance $\delta$ and, in this case, they are considered as neighbors. If a given individual is interacting with other ones, he performs the random walk with a diffusion probability $\omega$. Otherwise, the diffusion occurs with probability 1. The study was carried out through non-equilibrium Monte Carlo Simulations and we take into account the asynchronous updating scheme. The results show that, for a given $v>0$, there exist a critical line in the $(c, \delta)$ space, where $c$ is the immunization rate. We also obtain the dynamic critical exponent $\theta$ for some points belonging to this line and show that this model does not belong to the directed percolation universality class.