The complex interplay between {COVID}-19 and economic activity

We introduce a dynamical system to model the complex interaction between COVID-19 and economic activity. The model introduces some novelties not accounted by SIR-like models. The equilibrium of the system is an unstable focus, with fluctuations having increasing size and periodicity. Numerical simulations of the model produce waves which reproduce the pandemic dynamics. In observing the stylized facts linking economics and pandemic and stating related reasonable assumptions, we obtain a Lotka-Volterra co-dynamics. This outcome is confirmed by extensive simulations. The outcomes obtained qualitatively replicate some important stylized facts deepening the knowledge about the role of some parameters in their origin and eventually in their shaping.