  The manner epidemics occurs in a social network depends on various elements,
with two of the most influential being the relationships among individuals in
the population and the mechanism of transmission. In this paper, we assume that
the social network has a homogeneous random topology of Erd\"os-R\'enyi type.
Regarding the contagion process, we assume that the probability of infection is
proportional to the proportion of infected neighbours.
  We consider a constant population, whose individuals are the nodes of the
social network, formed by two variable subpopulations: Susceptible and Infected
(SI model). We simulate the epidemics on this random network and study whether
the average dynamics can be described using a mean field approach in terms of
Differential Equations, employing the law of mass action. We show that a
macroscopic description could be applied for low average connectivity,
adjusting the value of the contagion rate in a precise function. This
dependence is illustrated by calculating the transient times for each
connectivity.
  This study contributes valuable insights into the interplay between network
connectivity, contagion dynamics, and the applicability of mean-field
approximations. The delineation of critical thresholds and the distinctive
behaviour at lower connectivity enable a deeper understanding of epidemic
dynamics.
