PDF(Pubmed)
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.
摘要：
我们分析了疾病遏制政策在随机经济流行病学框架中以治疗形式的作用，在该框架中，随机冲击发生的概率与状态有关，即与疾病的流行程度有关。随机冲击与新的疾病菌株的扩散有关，该菌株会影响感染物的数量和感染的增长率，这种冲击实现的可能性可能在感染的数量上增加或减少。我们确定了这样一个随机框架的最优策略和稳态，其特点是在严格的积极流行水平上支持不变的措施，这表明，完全根除从来都不是一个可能的长期结果，而地方性将占上风。我们的结果表明：(I)独立于状态相关概率的特征，治疗允许向左移动不变测量的支持;和（ii）状态相关概率的特征影响的形状和分布的疾病患病率在其支持，允许稳态结局，其特征是分布高度集中在低患病率水平上，或者更分散在更大范围的患病率（可能更高）水平上。
