This article presents mathematical models for the error probability of BPSK, QPSK and M-QAM systems, subject to interference caused by a sudden increase in the number of users that access the digital communication system at a given time, the epidemic interference. The rapid increase in the number of users causes a non-stationary traffic in the network, which can be modeled using a stochastic differential approach. The channel outage probability is also computed. The theoretical model is confirmed with results obtained from Monte Carlo simulations.