Affiliation:
1. Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah 711 103, India
Abstract
We have considered a tumor growth model with the effect of tumor-immune interaction and chemotherapeutic drug. We have considered two immune
components—helper (resting) T-cells which stimulate CTLs and convert them into
active (hunting) CTL cells and active (hunting) CTL cells which attack, destroy, or
ingest the tumor cells. In our model there are four compartments, namely, tumor
cells, active CTL cells, helper T-cells, and chemotherapeutic drug. We have discussed the behaviour of the solutions of our system. The dynamical behaviour of our
system by analyzing the existence and stability of the system at various equilibrium
points is discussed elaborately. We have set up an optimal control problem relative
to the model so as to minimize the number of tumor cells and the chemotherapeutic drug administration. Here we used a quadratic control to quantify this goal
and have considered the administration of chemotherapy drug as control to reduce
the spread of the disease. The important mathematical findings for the dynamical
behaviour of the tumor-immune model with control are also numerically verified
using MATLAB. Finally, epidemiological implications of our analytical findings are
addressed critically.
Cited by
23 articles.
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