Optimal Control Strategy on Mathematical Model for the Dynamics of Mastitis

Authors

Basem Abu Izneid, Department of Electrical Engineering, College of Engineering, University of Business and Technology, Jeddah, 21448, Saudi ArabiaFollow
Eshetu Dadi Gurmu, Department of Mathematics, Salale University, Fitche, EthiopiaFollow
Legesse Lemecha Obsu, Department of Applied Mathematics, Adama Science and Technology University, Adama, EthiopiaFollow
Abdisa Shiferaw Melese, Department of Applied Mathematics, Adama Science and Technology University, Adama, EthiopiaFollow
Mohammad Kanan, Department of Industrial Engineering, College of Engineering, University of Business and Technology, Jeddah, 21448, Saudi ArabiaFollow
Ahmad Al-Qerem, Department of Computer Science, Faculty of Information Technology, Zarqa University, Zarqa, JordanFollow

Author Country (or Countries)

Saudi Arabia

Abstract

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170418

Recommended Citation

Abu Izneid, Basem; Dadi Gurmu, Eshetu; Lemecha Obsu, Legesse; Shiferaw Melese, Abdisa; Kanan, Mohammad; and Al-Qerem, Ahmad (2023) "Optimal Control Strategy on Mathematical Model for the Dynamics of Mastitis," Applied Mathematics & Information Sciences: Vol. 17: Iss. 4, Article 18.
DOI: http://dx.doi.org/10.18576/amis/170418
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss4/18