Optimal Personalized Therapies in Colon Cancer Induced Immune Response using a Fokker‐Planck Framework

Roy, Souvik; Pal, Suvra

doi:10.1002/9781119896715.ch3

Cited by 1 publication

(2 citation statements)

References 29 publications

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“…We provide a theoretical analysis of the NE and SE for the differential game (AS). In [35][36][37][38], there are analogous findings for other NE and SE differential games and optimal control problems. First, we prove that the ODE system (2.5) has positive solutions.…”

Section: Theory Of the Evolutionary Differential Gamementioning

confidence: 53%

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An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer

Alajmi,

Roy

2024

R. Soc. Open Sci.

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This work presents a new framework for a competitive evolutionary game between monoclonal antibodies and signalling pathways in oesophageal cancer. The framework is based on a novel dynamical model that takes into account the dynamic progression of signalling pathways, resistance mechanisms and monoclonal antibody therapies. This game involves a scenario in which signalling pathways and monoclonal antibodies are the players competing against each other, where monoclonal antibodies use Brentuximab and Pembrolizumab dosages as strategies to counter the evolutionary resistance strategy implemented by the signalling pathways. Their interactions are described by the dynamical model, which serves as the game’s playground. The analysis and computation of two game-theoretic strategies, Stackelberg and Nash equilibria, are conducted within this framework to ascertain the most favourable outcome for the patient. By comparing Stackelberg equilibria with Nash equilibria, numerical experiments show that the Stackelberg equilibria are superior for treating signalling pathways and are critical for the success of monoclonal antibodies in improving oesophageal cancer patient outcomes.

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Section: Theory Of the Evolutionary Differential Gamementioning

confidence: 53%

“…With this preparation, we are now ready to state and prove the main results of the existence of Nash and Stackelberg equilibria. The proofs use similar arguments given in [35][36][37][38]. ∎ Theorem 4.3.…”

Section: Let U Cmentioning

confidence: 96%

An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer

Alajmi,

Roy

2024

R. Soc. Open Sci.

View full text Add to dashboard Cite

show abstract

Optimal Personalized Therapies in Colon Cancer Induced Immune Response using a Fokker‐Planck Framework

Cited by 1 publication

References 29 publications

An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer

An evolutionary differential game for regulating the role of monoclonal antibodies in treating signalling pathways in oesophageal cancer

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