Joint economic and epidemiological modelling of alternative pandemic response strategies

Technical Summary: Joint Economic and Epidemiological Modelling of Alternative Pandemic Response Strategies

Problem Statement
Emerging pandemics present policymakers with high-stakes decisions under conditions of uncertainty and limited data. These decisions require trade-offs between the health impacts of the disease and the economic costs of control measures. While mathematical models have traditionally focused on direct health outcomes (e.g., infection peaks, mortality), they often neglect the economic costs of control measures (Public Health and Social Measures, or PHSMs) and the behavioral responses of the population. Existing literature has largely focused on optimizing mitigation strategies (reaching herd immunity) or minimizing infections subject to constraints, with comparatively little attention paid to comparing the aggregate costs of mitigation versus suppression and elimination strategies across varying epidemiological and economic parameters.

Methodology
The authors propose a novel mathematical framework that integrates epidemiological transmission dynamics with economic cost functions to compare three distinct response strategies: mitigation, suppression, and elimination.

1. Transmission Model:
   The core epidemiological component is a compartment-based SIR model (Susceptible $S$, Infectious $I$) in a closed, homogeneous population of size $N$. The force of infection is modulated by an activity level $a(t) \in [0, 1]$, where $a(t)=1$ represents baseline activity. The model employs "quadratic matching," where the force of infection is proportional to $a(t)^2$, reflecting the product of activity levels of both susceptible and infectious individuals.

2. Cost Function:
   The framework defines a total cost function comprising:

   • Infection Costs ($k$): A per-capita cost associated with infection, encompassing mortality, morbidity, healthcare costs, and lost earnings.
   • Control Costs: The cost of reducing activity, modeled as a convex function $c_1(1-a(t)) + c_2(1-a(t))^2$, representing the increasing marginal cost of stricter restrictions.
   • Specific Strategy Costs:
     • Border Control ($b$): A fixed daily cost for maintaining strict border controls in an elimination strategy.
     • Outbreak Control: Costs associated with detecting and eliminating sporadic border-related outbreaks using Test-Trace-Isolate (TTI) measures and temporary community restrictions.

3. Strategy Formulations:

   • Centralised Mitigation: An optimal control problem where a central planner minimizes the aggregate cost over an infinite time horizon. The solution requires the population to eventually reach the herd immunity threshold.
   • Decentralised Mitigation: A game-theoretic approach (Nash equilibrium) where self-interested individuals minimize their own costs. This captures the endogenous behavioral response (voluntary social distancing) in the absence of central mandates.
   • Suppression: A strategy maintaining the effective reproduction number ($R_{eff}$) at or below 1 via sustained community controls and TTI measures until a vaccine/therapy becomes available at time $T$.
   • Elimination: A strategy relying on strict border controls to minimize imported infections, with community controls applied only to eliminate detected border-related outbreaks. The model assumes outbreaks occur with frequency $r$ and are detected after time $t_{det}$.

4. Parameterization:
   The framework is anchored using data from New Zealand's response to the 2020 Covid-19 pandemic. Parameters include estimated costs of PHSMs (derived from New Zealand Treasury data), border closure costs, and infection costs (estimated via revealed preference from South Korean data and bottom-up health/economic calculations). Simulations explore a range of basic reproduction numbers ($R_0$) and infection costs ($k$).

Key Contributions

• Unified Framework: The paper introduces a comparative framework that explicitly calculates the aggregate economic and health costs of mitigation, suppression, and elimination, allowing for direct trade-off analysis.
• Endogenous Behavioral Response: The model explicitly quantifies the "decentralised" response, demonstrating how rational individual behavior (without central mandates) differs from the "socially optimal" centralised solution.
• Threshold Analysis: The study identifies specific thresholds in parameter space (specifically $R_0$ and $k$) that determine the most cost-effective strategy.
• Time Horizon Dependency: The framework highlights that the optimal strategy is contingent on the time horizon ($T$) until an effective vaccine or therapy becomes available.

Results
The simulations, visualized across various scenarios of transmissibility ($R_0$) and infection severity/cost ($k$), yield the following findings:

• Low Severity/Low Cost ($k$): Mitigation is generally the most cost-effective strategy. When the cost per infection is low, the economic burden of strict controls outweighs the health benefits. In extreme cases (low $k$, high $R_0$), neither centralised nor decentralised mitigation results in any activity reduction.
• High Severity/High Cost ($k$):
  • Low $R_0$: Suppression is most cost-effective. A modest reduction in activity combined with TTI measures can maintain $R_{eff} \leq 1$ at a lower cost than elimination.
  • High $R_0$: Elimination becomes more cost-effective than suppression. When $R_0$ is high, the cost of maintaining community suppression to keep $R_{eff} \leq 1$ exceeds the cost of border controls and sporadic outbreak management.
• Decentralised vs. Centralised: The decentralised (Nash equilibrium) response consistently results in higher aggregate costs and lower activity reduction than the centralised optimal solution, as individuals do not account for the externalities of their behavior on the epidemic dynamics.
• New Zealand Case Study: Using parameter estimates for SARS-CoV-2 in New Zealand (2020), the model places the scenario close to or above the threshold where elimination is predicted to be more cost-effective than mitigation. This aligns with the historical observation that New Zealand's elimination strategy minimized health impacts while allowing for shorter periods of strict lockdown compared to other jurisdictions.
• Sensitivity: The cost-effectiveness of elimination is highly sensitive to the frequency of border-related outbreaks ($r$), the time to detection ($t_{det}$), and the effectiveness of TTI measures ($\alpha$). Improved surveillance and border control reduce the cost of elimination.

Significance and Claims
The authors position this framework as a decision-support tool rather than a definitive predictor of optimal policy. The paper claims the following significance:

• Adaptability: The model uses a relatively small number of parameters that can be rapidly estimated for novel pathogens, making it suitable for early-stage pandemic planning.
• Nuanced Rationale: By quantifying the marginal net benefit of intervention against a no-intervention benchmark (accounting for endogenous behavior), the framework provides a more nuanced rationale for implementing PHSMs.
• Strategic Guidance: It elucidates how the choice of strategy depends on the interplay between disease transmissibility, severity, economic costs, and the expected time to medical countermeasures.
• Limitations and Future Work: The authors modestly acknowledge that the model simplifies complex realities, such as population heterogeneity, stochastic outbreak dynamics, and the social/psychological impacts of prolonged restrictions. They note that the model assumes a homogeneous population and does not account for global pathogen control or the evolution of variants. Future work is proposed to incorporate population stratification and more detailed behavioral dynamics.

In conclusion, the paper argues that while no single strategy is universally optimal, this framework offers a structured method to evaluate the trade-offs between health and economic outcomes, helping policymakers navigate the complex landscape of pandemic response strategies.