Open AccessA Within-host Tuberculosis Model Using Optimal Control
Author(s) -
Yudi Ari Adi
Publication year - 2021
Publication title -
jtam (jurnal teori dan aplikasi matematika)
Language(s) - English
Resource type - Journals
eISSN - 2614-1175
pISSN - 2597-7512
DOI - 10.31764/jtam.v5i1.3813
Subject(s) - pontryagin's minimum principle , vaccination , tuberculosis , optimal control , maximum principle , mycobacterium tuberculosis , transmission (telecommunications) , hamiltonian (control theory) , mathematical optimization , mathematics , immunology , control theory (sociology) , computer science , medicine , control (management) , artificial intelligence , pathology , telecommunications
In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis. We considered an in-host tuberculosis model that described the interaction between Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal control is applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula is obtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results. The results suggest that control or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large. In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis.We considered an in-host tuberculosis model that described the interaction between macrophages Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal controlis applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula isobtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results.The results suggest thatcontrol or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large.