Mathematical Model for the Transmission and Control of Mastitis in Dairy Cows

Abstract

Mastitis in dairy cows is a complex infectious disease that significantly impacts animal health, milk quality, and farm profitability. This study develops and analyzes a deterministic compartmental mathematical model describing the transmission of mastitis among cows and via environmental contamination. The model is formulated using a system of ordinary differential equations that include key biological and management parameters, such as bacterial shedding, recovery, and culling rates. Dimensional consistency and stability analyses were conducted to ensure the model’s validity. The basic reproduction number was calculated, and the equilibrium points were identified and analyzed for both local and global stability. Numerical simulations demonstrate the dynamic behavior of susceptible, infected, and recovered groups, highlighting how infection control depends on changes in shedding and recovery parameters. The model offers a theoretical framework for optimizing mastitis prevention strategies and supports informed decision-making in dairy herd management, as shown through the application of data from a Macedonian dairy farm.