The recent COVID-19 crisis has revealed the urgent need to study the impact of an infectious disease on market economies and provide adequate policy recommendations. The present paper studies the optimal lockdown policy in a dynamic general equilibrium model where households are altruistic and they care about the share of infected individuals. The spread of the disease is modeled here using SIS dynamics, which implies that recovery does not confer immunity. To avoid non-convexity issues, we assume that the lockdown is constant in time. This strong assumption allows us to provide analytical solutions. We find that the zero lockdown is efficient when agents do not care about the share of infected, while a positive lockdown is recommended beyond a critical level of altruism. Moreover, the lockdown intensity increases in the degree of altruism. Our robust analytical results are illustrated by numerical simulations, which show, in particular, that the optimal lockdown never trespasses 60% and that eradication is not always optimal.

最近的COVID-19危机表明，迫切需要研究传染病对市场经济的影响并提供适当的政策建议。本文研究了动态一般均衡模型中的最优锁定策略，该模型中的家庭是无私的，他们关心被感染个体的份额。此处使用SIS动态模型对疾病的传播进行建模，这表明恢复并不赋予免疫力。为了避免出现非凸性问题，我们假设锁定在时间上是恒定的。这个强有力的假设使我们能够提供分析解决方案。我们发现，当代理不关心感染份额时，零锁定是有效的，而建议在利他主义的临界水平之外进行正锁定。而且，锁定强度在利他程度上增加。