Pollution effects on disease transmission and economic stability

In this article, we embed a model of disease spread into a Ramsey model. A stock of pollution, viewed as a productive externality, affects both the disease transmission and the consumption demand. An ecofriendly government levies a proportional Pigouvian tax on production to depollute. We show the coexistence of two steady states in the long run: a disease-free and an endemic steady state. At the endemic steady state, a higher green-tax rate always reduces the pollution level. In the short run, we show the existence of limit cycles (through a Hopf bifurcation) as well as more complex dynamics of codimension two (a Gavrilov-Guckenheimer bifurcation). We complete the study with a numerical illustration of these bifurcations and a new facet of the Green Paradox: a higher tax rate can allow more scope for cycles by lowering the critical aversion to pollution and, thus, contribute to destabilize the economy and promote intergenerational inequalities.