Mathematical Model Of The Transmission Dynamics Of Tuberculosis With Optimal Control Strategies

Abstract

This Thesis Focused On A Mathematical Model Of The Transmission Dynamics Of Tuberculosis With Optimal Control To Assess The Dynamics Of Tuberculosis Infection In East Shewa Zone. The Existence And Stability Of The Disease-Free And Endemic Equilibria Of The Model Were Performed. Both Local And Global Stability Of The Disease-Free And The Endemic Equilibrium Are Determined. Sensitivity Indices Of R0 With Respect To The Model Parameters Are Performed To Reveal The Transmission Dynamics Of Tuberculosis. Then The Optimal Control Strategy Is Found By Minimizing The Number Of Exposed And Infected Individual Population With Tuberculosis Taking Into Account The Cost Of Implementation. The Existence Of Optimal Controls Is Established With The Help Of Pontryagin?��?S Maximum Principle. The Model Is Then ???Tted With Cumulative Cases Of Infected Tuberculosis Real Data From East Shewa Zone Health O???Ce From 2010 To 2019 Years. In Addition, Di??��Erent Simulation Cases Were Comparatively Performed To Obtain The Best Control Strategies. In General, The Numerical Simulation Results Demonstrate Good Agreement With Our Analytical Results. The Simulation Results Also Clearly Shown That The Epidemic Of Tuberculosis Can Be Minimized By Preventing The Failure Of Treatment In Active Tuberculosis Individuals Through Continuous Supervision And Helping Patients During Treatment Period With Optimal Implementation Cost. F