The Language of Epidemic

Infectious diseases are transmitted from one person to another and spread throughout a network under certain conditions. Considering an example of propagation, we explain how to define an automaton on the network according to the propagation steps and the conditions under which the epidemic is transmitted. We call this automaton forcing automaton. Also, we call the language of this automaton an epidemic language. We describe how forcing automata and epidemic languages allow us to have a more accurate analysis of propagation in reality. Furthermore, we show that by knowing the epidemic language, it is possible to compare the spread of an epidemic in different networks. Finally, we present an algorithm that can predict a network in which the epidemic spreads, by only knowing its epidemic language.