Asian Journal of Pharmaceutical Research and Health Care

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An Analysis of the Dynamics of a Cancerous Tumour Model with Targeted Chemotherapy


Affiliations
1 Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India
 

We have analyzed a model of Lotka-Volterra type interacting between immune cell-tumour cell-normal cells, where control policy is applied in terms of targeted chemotherapy. We determined conditions for the local stability of all the equilibrium points and global stability condition for the tumour free equilibrium point, including the feasibility of the solution. Further, we have discussed the possibility of Hopf bifurcation at each equilibrium point. Numerical simulation was carried out to observe the qualitative behaviour of the system as the control parameter is varied.


Keywords

Global Stability, Hopf Bifurcation, Lotka-Volterra Type, Targeted Chemotherapy.
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  • An Analysis of the Dynamics of a Cancerous Tumour Model with Targeted Chemotherapy

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Authors

Anusmita Das
Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India
Ranu Paul
Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India
Kaushik Dehingia
Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India
Hemanta Kumar Sarmah
Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, India

Abstract


We have analyzed a model of Lotka-Volterra type interacting between immune cell-tumour cell-normal cells, where control policy is applied in terms of targeted chemotherapy. We determined conditions for the local stability of all the equilibrium points and global stability condition for the tumour free equilibrium point, including the feasibility of the solution. Further, we have discussed the possibility of Hopf bifurcation at each equilibrium point. Numerical simulation was carried out to observe the qualitative behaviour of the system as the control parameter is varied.


Keywords


Global Stability, Hopf Bifurcation, Lotka-Volterra Type, Targeted Chemotherapy.

References





DOI: https://doi.org/10.18311/ajprhc%2F2020%2F25431