Stochastic disease spreading and containment policies under state-dependent probabilities

Davide Torre (), Simone Marsiglio, Franklin Mendivil () and Fabio Privileggi
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Davide Torre: SKEMA Business School and Université Côte d’Azur, Sophia Antipolis Campus
Franklin Mendivil: Acadia University

Economic Theory, 2024, vol. 77, issue 1, No 5, 127-168

Abstract: 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.

Keywords: Economic epidemiology; Invariant distribution; Optimal policy; State-dependent probability (search for similar items in EconPapers)
JEL-codes: C60 H50 I10 (search for similar items in EconPapers)
Date: 2024
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Working Paper: Stochastic Disease Spreading and Containment Policies under State-Dependent Probabilities (2022)
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DOI: 10.1007/s00199-023-01496-y

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