Interactions between different diseases may change their dynamics. Thus, these interactions represent a source of uncertainty in the modeling of empirical data when the symptoms of both infections are hard to distinguish. We recall previously proposed models of interacting infections, generalizing them to non-symmetric scenarios, showing that both cooperative and competitive interactions lead to synchronization of the maximum fraction of infected individuals in their dynamics. We exemplify this framework with a model coupling the dynamics of COVID-19 and seasonal influenza, simulating cooperation, competition, and asymmetric interactions. We find that the coupling synchronizes both infections, with a stronger influence on the dynamics of influenza.