Optimal control of vancomycin-resistant enterococci using preventive care and treatment of infections

• We present a mathematical model for VRE spread in a hospital ICU.
• Controls are included for VRE preventive care and treatment of VRE infections.
• The basic reproductive number is calculated for different levels of controls.
• Optimal controls for minimizing VRE-related deaths and total cost are found.
• Results show optimal balance of controls depends on relative costs of controls.

The rising prevalence of vancomycin-resistant enterococci (VRE) is a major health problem in intensive care units (ICU) because of its association with increased mortality and high health care costs. We present a mathematical framework for determining cost-effective strategies for prevention and treatment of VRE in the ICU. A system of five ordinary differential equations describes the movement of ICU patients in and out of five VRE-related states. Two control variables representing the prevention and treatment of VRE are incorporated into the system. The basic reproductive number is derived and calculated for different levels of the two controls. An optimal control problem is formulated to minimize VRE-related deaths and costs associated with prevention and treatment controls over a finite time period. Numerical solutions illustrate optimal single and dual allocations of the controls for various cost values. Results show that preventive care has the greatest impact in reducing the basic reproductive number, while treatment of VRE infections has the most impact on reducing VRE-related deaths.