In this talk, we will introduce a dissipative version of the contact process with mean-field interaction admitting a simple epidemiological interpretation. In particular, we will focus on the thermodynamic limit of the process, providing a law of large numbers (propagation of chaos) and a central limit theorem for the corresponding normal fluctuations.
These results reveal that it is the noise,  which is only present in the finite-size system and is internal to the system, that induces persistent oscillatory behaviors reminiscent of the emergence of pandemic waves in real epidemics.