Dynamical analysis of an OLG model with interacting epidemiological and environmental domains

We study a model encompassing economic, epidemiological and environmental domains, which feature reciprocal interactions. The economy is described by an overlapping generations model in which productivity and agents’ preferences are affected by the epidemiological situation. The evolution of an epidemic is represented through a susceptible-infected-susceptible model, in which the disease spread depends on the pollution level and can be reduced through the government expenditure. The pollution level increases during the production process and can be reduced by allocating resources to its abatement. Resources are collected through the capital taxation and the regulator must decide how to share them between healthcare and environmental protection. For the resulting model, we show the possible existence of a unique steady state, either characterized by the presence of epidemics or disease-free. We study its comparative statics depending on the policy parameter regulating the share of resources that is devoted to improve the epidemiological situation with respect to the environmental one. We investigate the emergence of dynamics non convergent toward the equilibrium, with possible complex and quasi-periodic trajectories.