A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model

This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2022-07, Vol.24 (7), p.949
Main Authors: Khan, Muhammad Salman, Samreen, Maria, Khan, Muhammad Asif, De la Sen, Manuel
Format: Article
Language:English
Subjects:
Andronov–Hopf bifurcation
boundedness
Cancer therapies
Chemotherapy
Cytotoxicity
Discrete time systems
existence
Hopf bifurcation
Immune system
immunogenic tumors model
Immunotherapy
linearized stability
Mathematical models
nonstandard difference scheme
Tumors
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Summary:This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown that a continuous system experiences Hopf bifurcation at one and only one positive fixed point, whereas its discrete-time counterpart experiences Neimark-Sacker bifurcation at one and only one positive fixed point. It is shown that there is no chance of period-doubling bifurcation in our discrete-time system. Additionally, numerical simulations are carried out in support of our theoretical discussion.
ISSN:1099-4300
1099-4300
DOI:10.3390/e24070949