Optimal reduced-mixing for an SIS infectious-disease model

Area of Science:

• Epidemiology
• Mathematical Modeling
• Economic Analysis

Background:

• Disease outbreaks significantly impact economic productivity.
• Managing population mixing is a key strategy to control disease spread.
• Balancing economic revenue with disease-related costs is crucial during outbreaks.

Purpose of the Study:

• To determine the optimal reduced-mixing strategy that maximizes economic output during an epidemic.
• To analyze the economic implications of disease spread under varying mixing levels.
• To identify the conditions under which reduced mixing is most economically beneficial.

Main Methods:

• Formulation of an optimal-control problem to maximize net economic output (revenue minus costs).
• Utilizing Susceptible-Infectious-Susceptible (SIS) disease dynamics model.
• Application of Pontryagin's maximum principle to derive a closed-form solution.
• Sensitivity analysis using parameters for *Staphylococcus aureus* in dairy cows.

Main Results:

• A closed-form solution for the optimal mixing strategy was derived.
• Less mixing is economically preferable under specific conditions: high transmission rates, low recovery rates, and when disease costs significantly exceed revenue.
• The study provides a framework for optimizing disease control strategies for economic benefit.

Conclusions:

• Reduced population mixing can be an effective strategy to maximize economic output during disease outbreaks.
• The optimal level of mixing is contingent on epidemiological parameters and economic factors.
• Findings are applicable to managing diseases in various populations, including livestock.