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 by a susceptible-infected-susceptible model, in which disease spread depends on the pollution level and can be reduced through 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 the comparative statics with respect to the policy parameter that governs the share of resources devoted to improving the epidemiological situation relative to environmental protection. We investigate the emergence of dynamics that do not converge to equilibrium, including complex and quasi-periodic trajectories.