Abstract
We analyze the role of disease containment policy in the form of treatment in a stochastic economic-epidemiological framework in which the probability of the occurrence of random shocks is state-dependent, namely it is related to the level of disease prevalence. Random shocks are associated with the diffusion of a new strain of the disease which affects both the number of infectives and the growth rate of infection, and the probability of such shocks realization may be either increasing or decreasing in the number of infectives. We determine the optimal policy and the steady state of such a stochastic framework, which is characterized by an invariant measure supported on strictly positive prevalence levels, suggesting that complete eradication is never a possible long run outcome where instead endemicity will prevail. Our results show that: (i) independently of the features of the state-dependent probabilities, treatment allows to shift leftward the support of the invariant measure; and (ii) the features of the state-dependent probabilities affect the shape and spread of the distribution of disease prevalence over its support, allowing for a steady state outcome characterized by a distribution alternatively highly concentrated over low prevalence levels or more spread out over a larger range of prevalence (possibly higher) levels.
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Acknowledgements
We are indebted to two anonymous referees for their constructive comments on an earlier draft. All remaining errors and omissions are our own sole responsibility. Simone Marsiglio acknowledges financial support from the University of Pisa under the “PRA—Progetti di Ricerca di Ateneo” (Institutional Research Grants)—Project No. PRA_2020_79 “Sustainable development: economic, environmental and social issues”. The research of FM is partially supported by NSERC 2019:05237. The usual disclaimer applies.
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La Torre, D., Marsiglio, S., Mendivil, F. et al. Stochastic disease spreading and containment policies under state-dependent probabilities. Econ Theory 77, 127–168 (2024). https://doi.org/10.1007/s00199-023-01496-y
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DOI: https://doi.org/10.1007/s00199-023-01496-y