Optimal Control and Cost-Effectiveness Analysis of a Mathematical Model for Mastitis Dynamics in Dairy Cows

Mastitis remains one of the most important infectious diseases affecting dairy cows, with substantial consequences for animal health, milk production, and farm profitability. In this study, we extend a nonlinear SIRS–P compartmental model for mastitis transmission in dairy cows by incorporating sensitivity analysis, optimal control, and cost-effectiveness analysis. The model consists of susceptible, infected, and recovered cow populations together with an environmental pathogen compartment, and accounts for direct cow-to-cow transmission, indirect transmission through environmental contamination, recovery, recurrence of infection, recruitment, and culling. A sensitivity analysis of the basic reproduction number R0 is performed to identify the parameters that most strongly influence mastitis transmission. An optimal control problem is then formulated using time-dependent controls that reduce direct transmission, reduce environmental contamination, and enhance recovery. Pontryagin’s Maximum Principle is applied to derive the optimality system, which is solved numerically using the forward–backward sweep method. Seven intervention strategies are compared through numerical simulations and cost-effectiveness analysis using ACER and ICER. The results indicate that the fully integrated strategy S7, which combines prevention and screening, environmental sanitation, and treatment, provides the largest overall disease reduction. However, Strategy S1, based on direct transmission reduction, offers the most cost-effective allocation of resources for reducing the mastitis infection burden.