Optimal control and cost-effectiveness analysis of Fasciola hepatica model

Abstract

A deterministic model with an optimal control framework is formulated to analyse the cost-effectiveness of intervention measures used to control Fasciola hepatica in cattle populations. Using the Volterra-Lyapunov stability method, it is noted that the model is globally stable at the endemic equilibrium point. The Pontryagin maximum principle has been applied to determine optimal disease control conditions, including strategies such as pasture management, treatment of infected cattle, and molluscicide use. Numerical simulations for the optimum problem show that double and triple controls have significant effects on reducing disease transmission. The results indicate that for optimal impact, the molluscicide control parameter should always be at its highest possible value. The incremental cost-effectiveness ratio (ICER) analysis of strategies to reduce the disease shows that pasture management combined with molluscicide use will be the most effective and least expensive option. The molluscicide intervention rate should always be at its maximum value for better control of the disease. Educational programs for proper pasture management conditions and sufficient use of molluscicides can significantly reduce the spread of Fasciola hepatica among cattle and humans.

Keywords

• Optimal control
• Volterra–Lyapunov stability
• Global stability
• Pontryagin maximum principle
• Cost-effectiveness