  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.
