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Mathematical Modeling Approach to Hepatitis B virus with Vaccination and optimal control

Saif Ullah, Muhammad Altaf Khan, Muhammad Farooq


Infectious diseases produce many deaths throughout the world and Hepatitis B is one of them, which mainly causes lever infection. In this work, a mathematical model of Hepatitis B with vaccination is investigated. Initially the model is constructed without control and the mathematical results are presented. The without control model is stable locally and globally whenever the threshold. Then, we construct model with controls and investigate their mathematical results. The numerical results are presented by choosing appropriate set of control and presented the graphical results. The graphical results for each set of controls suggest the possible elimination of the disease from the population but the most powerful strategy is considered to be the activation of all controls at the same time.


Hepatitis B, Stability results, Optimal control, Vaccination, Numerical results.

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