A general forward neural network was adapted for a simulation of viral epidemics. This involves the introduction of a strongly dependence upon history, upon the cumulated values of the corresponding neuron (individual) activations (states of infection) specifying the activation (health) states of the contaminated individuals, represented by the activated neurons and the dynamic parameters of the neural network: the matrix of the synaptic connection and the vector of the activation thresholds (corresponding to the matrix of the viral transfers between the various individuals and to the vector of the minimal individual contamination doses of virus). The recurrence relations and the learning procedures were also adapted to these processes. This methodology was used for the study of the micropopulational spreading of viral epidemics in various epidemiological situations.