La Torre Davide, Marsiglio Simone, Mendivil Franklin, Privileggi Fabio
SKEMA Business School and Université Côte d'Azur, Sophia Antipolis Campus, Sophia Antipolis, France.
Department of Economics and Management, University of Pisa, Pisa, Italy.
Econ Theory. 2023 Apr 12:1-42. doi: 10.1007/s00199-023-01496-y.
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.
我们在一个随机经济 - 流行病学框架中分析以治疗形式存在的疾病控制政策的作用，在该框架中，随机冲击发生的概率取决于状态，即它与疾病流行程度相关。随机冲击与一种新的疾病毒株的传播有关，这会影响感染者数量和感染增长率，并且这种冲击实现的概率在感染者数量上可能是递增或递减的。我们确定了这样一个随机框架的最优政策和稳态，其特征是在严格正的流行水平上有一个不变测度，这表明完全根除在长期内永远不可能实现，相反地方病状态将占主导。我们的结果表明：（i）无论状态依赖概率的特征如何，治疗都能使不变测度的支撑向左移动；（ii）状态依赖概率的特征会影响疾病流行程度分布在其支撑上的形状和范围，从而允许出现一种稳态结果，其特征是分布要么高度集中在低流行水平，要么在更大范围的流行（可能更高）水平上更分散。
