Long-run logistics-based control of non-immunizing infectious diseases

Area of Science:

• Epidemiology
• Operations Research
• Public Health

Background:

• Non-immunizing infectious diseases persist, incurring continuous health and intervention costs.
• Achieving a stable endemic equilibrium is a key long-term policy goal for managing these diseases.

Purpose of the Study:

• To formulate an integrated infinite-horizon SIS-inventory control model for non-immunizing infectious diseases.
• To analyze the impact of controllable replenishment rates on disease dynamics and recovery.
• To establish conditions for stable endemic equilibria under different replenishment regimes.

Main Methods:

• Formulation of an infinite-horizon SIS-inventory control model.
• Application of the Pontryagin Maximum Principle to derive regime-dependent trajectories.
• Analysis of steady-state existence, reachability, and local stability under zero, moderate, and maximum replenishment regimes.

Main Results:

• Zero replenishment leads to persistent infection and fails to reach a disease-free equilibrium.
• Maximum replenishment results in a unique endemic steady state.
• Moderate replenishment can lead to multiple equilibria, indicating complex dynamics.
• Threshold effects demonstrate that inadequate replenishment compromises system stabilization.

Conclusions:

• Inventory control is critical for managing non-immunizing infectious diseases.
• The level of replenishment significantly influences disease persistence and stability.
• Understanding these dynamics provides practical insights for long-term epidemic management strategies.