Optimal control prevents itself from eradicating stochastic disease epidemics

Area of Science:

• Epidemiology
• Mathematical Biology
• Control Theory

Background:

• Disease management faces resource limitations, driving the need for optimal control strategies.
• Current optimal control often uses deterministic models, which are inaccurate for stochastic, real-world epidemic dynamics, particularly at low infection levels.

Purpose of the Study:

• To evaluate the effectiveness of disease management strategies derived from deterministic optimal control when applied to stochastic epidemic models.
• To identify limitations of current optimal control and model predictive control (MPC) in achieving disease eradication.

Main Methods:

• Comparison of deterministic optimal control solutions against stochastic epidemic models.
• Simulation of spatial disease spread using plant disease examples.
• Evaluation of Model Predictive Control (MPC) performance and comparison with heuristic strategies.

Main Results:

• Deterministic optimal control solutions are suboptimal for stochastic models, especially near eradication.
• Standard optimal control and MPC may underestimate the required control effort for complete disease eradication.
• Heuristic strategies can outperform MPC when sufficient resources are available for eradication.

Conclusions:

• Deterministic models provide a poor approximation for stochastic epidemic control, particularly when aiming for eradication.
• Rethinking optimal control strategies is crucial for effective disease management in realistic, stochastic scenarios.
• Further research into adaptive or heuristic control methods may be necessary for robust epidemic eradication.