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Dehingia, Kaushik
- An Analysis of the Dynamics of a Cancerous Tumour Model with Targeted Chemotherapy
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PDF Views:100
Authors
Affiliations
1 Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, IN
1 Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, IN
Source
Asian Journal of Pharmaceutical Research and Health Care, Vol 12, No 3 (2020), Pagination: 130-140Abstract
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.Full Text
References
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- A Study on an HIV Pathogenesis Model with Different Growth rates of Uninfected and Infected CD4+T cells
Abstract Views :290 |
PDF Views:118
Authors
Affiliations
1 Department of Mathematics, Barnagar College, Sorbhog – 781317, Barpeta, Assam, IN
2 Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, IN
1 Department of Mathematics, Barnagar College, Sorbhog – 781317, Barpeta, Assam, IN
2 Department of Mathematics, Gauhati University, Guwahati – 781014, Assam, IN
Source
Asian Journal of Pharmaceutical Research and Health Care, Vol 12, No 4 (2020), Pagination: 198-212Abstract
The objective of this paper is to discuss the dynamics of an HIV pathogenesis model with full logistic target cell growth of uninfected T cells and cure rate of infected T cells. Local and global dynamics of both infection-free and infected equilibrium points are rigorously established. It is found that if basic reproduction number R0≤1, the infection is cleared from T cells and if R0>1, the HIV infection persists. Also, we have carried out numerical simulations to verify the results. The existence of non-trivial periodic solution is also studied by means of numerical simulation. Therefore, we find a parameter region where infected equilibrium point is globally stable to make the model biologically significant. From the overall study, it is found that proliferation of T cells cannot be ignored during the study of HIV dynamics for better results and we can focus on a treatment policy which can control the parameters of the model in such a way that the basic reproduction number remains less than or equal to one.
Keywords
HIV, Local and Global Stability, Periodic Solution, Treatment2010 AMS classification: 34A34, 34D23, 37C25
Full Text
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