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Pollution effects on disease transmission and economic stability


  • Stefano BOSI


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.

Suggested Citation

  • Stefano BOSI & David DESMARCHELIER, 2018. "Pollution effects on disease transmission and economic stability," Working Papers of BETA 2018-11, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
  • Handle: RePEc:ulp:sbbeta:2018-11

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    SIS model; Ramsey model; pollution; transcritical bifurcation; Hopf bifurcation; Gavrilov-Guckenheimer bifurcation.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth

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