Applied Mathematics & Information Sciences

Author Country (or Countries)

Saudi Arabia


Inthisstudy,anonlinearmathematicalmodelforthetransmissiondynamicsofmastitisdiseasesisformulatedandanalyzed. The local and global stability analysis of mastitis-free equilibrium and endemic equilibrium is obtained using the stability theory of differential equation. It was established that the mastitis-free equilibrium is locally stable if the basic reproduction number is less than unity. The endemic equilibrium, which exists only when the basic reproduction number is greater than unity, is globally asymptotically stable. Sensitivity analysis of the reproduction number suggested that the concentration of bacteria in the environment has a high impact on the dynamics of mastitis. Furthermore, an optimal control problem is formulated by applying Pontryagin’s minimum principle with three control strategies, namely, prevention strategy, screening strategy, and treatment strategy. Therefore, based on optimal control problem simulation results and analysis of cost-effectiveness prevention strategy is the most effective and least costly to eradicate the transmission of mastitis from the cattle.

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