Infectious diseases and economic growth

Aditya Goenka, Lin Liu, Manh-Hung Nguyen

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


This paper develops a framework to study the economic impact of infectious diseases by integrating epidemiological dynamics into a neo-classical growth model. There is a two way interaction between the economy and the disease: the incidence of the disease affects labor supply, and investment in health capital can affect the incidence and recuperation from the disease. Thus, both the disease incidence and the income levels are endogenous. The disease dynamics make the control problem non-convex thus usual optimal control results do not apply. We establish existence of an optimal solution, continuity of state variables, show directly that the Hamiltonian inequality holds thus establishing optimality of interior paths that satisfy necessary conditions, and of the steady states. There are multiple steady states and the local dynamics of the model are fully characterized. A disease-free steady state always exists, but it could be unstable. A disease-endemic steady state may exist, in which the optimal health expenditure can be positive or zero depending on the parameters of the model. The interaction of the disease and economic variables is non-linear and can be non-monotonic.
Original languageEnglish
Pages (from-to)34-53
Number of pages20
JournalJournal of Mathematical Economics
Early online date16 Oct 2013
Publication statusPublished - 1 Jan 2014


  • Epidemiology
  • Infectious diseases
  • Existence of equilibrium
  • Sufficiency in non-convex dynamic problems
  • Health expenditure
  • Economic growth


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