scholarly journals Dynamical Analysis of the Delayed Immune Response to Cancer

2021 ◽  
pp. 104282
Author(s):  
Khaled A. Al-Utaibi ◽  
Ayesha Sohail ◽  
Zhenhua Yu ◽  
Robia Arif ◽  
Alessandro Nutini ◽  
...  
2019 ◽  
Vol 29 (03) ◽  
pp. 1950031 ◽  
Author(s):  
Ángel G. Cervantes-Pérez ◽  
Eric Ávila-Vales

This paper considers a general virus dynamics model with cell-mediated immune response and direct cell-to-cell infection modes. The model incorporates two types of intracellular distributed time delays and a discrete delay in the CTL immune response. Under certain conditions, the model exhibits a global threshold dynamics with respect to two parameters: the basic reproduction number and the reproduction number of immune response. We use suitable Lyapunov functionals and apply Lasalle’s invariance principle to establish the global asymptotic stability of the two boundary equilibria. We also perform a bifurcation analysis for the positive equilibrium to show that the time delays may lead to sustained oscillations. To determine the direction of the Hopf bifurcation and the stability of the periodic solutions, the method of multiple time scales is applied. Finally, we carry out numerical simulations to illustrate our results.


1978 ◽  
Vol 87 (1) ◽  
pp. 138-141 ◽  
Author(s):  
Charles J. Krause ◽  
John O. Nysather

It is apparent that development of consistently effective methods of immunotherapy must await a more thorough understanding of the immune response to cancer. However, even those forms of immunotherapy which have been developed to date indicate a tremendous potential. It appears that immunotherapy may be most useful as an adjuvant to established forms of treatment. Surgery, radiation therapy and/or chemotherapy are used to remove all of the gross tumor, with immune therapy then employed to destroy the small foci of tumor which remain. As methods are developed which are effective in counteracting the immunosuppression of tumors, other means of immunotherapy may be found which are capable of destroying tumor cells while not affecting the adjacent normal tissue. Thus, the future of immune therapy holds great promise. As more is learned about the immune response to cancer, advances in therapy will certainly follow.


2012 ◽  
Vol 8 (5) ◽  
pp. 401-403 ◽  
Author(s):  
Allison Nelson ◽  
Sajitha Nair ◽  
Srinivas Nagaraj

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