Mortality containment vs. Economics Opening: Optimal policies in a SEIARD model

Area of Science:

• Epidemiology
• Public Health Policy
• Mathematical Modeling

Background:

• The classic SIR model provides a foundation for understanding infectious disease dynamics.
• Economic impacts of public health interventions require integrated modeling approaches.
• Social planners face trade-offs between mortality reduction and economic output (GDP).

Purpose of the Study:

• To develop and analyze a SEAIRD (Susceptible-Exposed-Asymptomatic-Infectious-Recovered-Deceased) model incorporating policy controls.
• To investigate the optimal control strategies for a social planner balancing health and economic objectives.
• To explore the impact of realistic policy limitations, such as implementation lags and restricted policy flexibility.

Main Methods:

• Extension of the traditional SIR compartmental model to a SEAIRD framework.
• Incorporation of a social planner's objective function considering the value of statistical life (PVSL) and GDP.
• Analysis of optimal control strategies under constraints on policy implementation and duration.

Main Results:

• The model captures the joint dynamics of infection spread and economic performance.
• Demonstration of optimal policy existence within the constrained control set.
• Identification of a critical threshold in the PVSL, triggering a shift from laissez-faire to significant lockdown policies.
• Simulation of infection and economic outcomes across different confinement scenarios (single or multiple episodes).

Conclusions:

• Constrained optimization reveals complex optimal strategies for public health interventions.
• The PVSL is a critical determinant of policy stringency, explaining potential policy conflicts.
• Realistic implementation frictions and policy flexibility limitations significantly shape optimal control outcomes.