Analysis of optimal lockdown in integral economic–epidemic model

Abstract

We analyze the optimal lockdown in an economic–epidemic model with realistic infectiveness distribution. The model is described by Volterra integral equations and accurately depicts the COVID-19 infectivity pattern from clinical data. A maximum principle is derived, and a qualitative dynamic analysis of the optimal lockdown problem is provided over finite and infinite horizons. We analytically prove and economically justify the possibility of an endemic scenario when the infection rate begins to climb after the lockdown ends.

Covid-19 and mobility: determinant or consequence?

“…We first develop a theoretical epidemiological framework in which the spread of the epidemic rises with mobility, which can be constrained by the government but is also expected to react negatively to the rise in the infection rate. More specifically, we consider a compartmental epidemiological model that features the dynamics of SARS-Cov-2 and extends previous works of Arino et al (2006), (Augeraud-Véron, 2020), Liu et al (2020a), Liu et al (2020b), Aubert and and complement recent researches that introduce mobility in economic-epidemic models (such as La Torre et al (2022), Makris (2021), Goenka et al (2022), Hritonenko and Yatsenko (2022) and Fabbri et al (2023)). Our model allows us to disentangle the short-run and long-run interactions between mobility and the infection/death rates.…”

Optimal vaccination in a SIRS epidemic model

“…Modeling a social planner's actions usually results into the introduction of control variables in the dynamics of the considered compartmental epidemic model. For example, the transmission rate becomes a control variable in the generalized SIR models considered in Hritonenko and Yatsenko (2022), Kruse and Strack (2020) and Miclo et al (2020), and a controlled state-variable in the stochastic version of Federico and Ferrari (2021). More in detail, Kruse and Strack (2020) introduces an additional parameter in the dynamics, which is then used by the social planner in order to control the rate at which the disease is transmitted; that parameter is meant to capture the policymakers' measures, such as social distancing, but also lockdown of businesses, schools, universities and other institutions.…”

Epidemics, vaccines, and health policy

“…The next two studies are of a macroeconomic nature and make use of overlapping generations general equilibrium settings. As such, they join a number of articles published in the previous Special Issue on the same general topic, namely Gori et al (2022), La Torre et al (2022; as well as studies that evaluate the performance of specific policies aiming at epidemic control, such as Iverson et al (2022), Gallic et al (2022), Hellmann andThiele (2022), and Hritonenko and Yatsenko (2022). Davin et al (2023) develop the first dynamic (overlapping-generations [OLG]) general equilibrium model where fully specified epidemic infection dynamics intersect with a pollution health externality to jointly determine long-term health and economic outcomes.…”

“…The next two studies are of a macroeconomic nature and make use of overlapping generations general equilibrium settings. As such, they join a number of articles published in the previous Special Issue on the same general topic, namely Gori et al (2022), La Torre et al (2022); as well as studies that evaluate the performance of specific policies aiming at epidemic control, such as Iverson et al (2022), Gallic et al (2022), Hellmann and Thiele (2022), and Hritonenko and Yatsenko (2022).…”