Dynamical analysis of healthcare policy effects in an integrated economic-epidemiological model

We study the static and dynamical properties of a model that describes the interaction between the economic and epidemiological domains. The epidemiological sphere is represented by a susceptible-infected-susceptible model, while the economic domain consists of an overlapping generations model in which the workers correspond to the non infected population of adults. The productivity of the firms and the propensity to save for retirement of the households are negatively affected by the disease spread. A capital tax is levied and the collected resources are used to curb the spread of the outbreak. We show that multiple endemic steady states can arise from the interaction between the two domains, and different stable endemic attractors can coexist with the stable disease free steady state. We study analytically and numerically the complex dynamics and the evolution of the basins of attraction in the case of multistability. We show that the effect of taxation can be beneficial both from the epidemiological and the economic points of view, as it can give rise to new steady states characterized by reduced shares of infected people and increased capital level, it can simplify the dynamical behaviors and reduce the size of the basins of attraction of those outcomes in which large shares of infected people and low capital levels are observed.