A Filippov tumor-immune system with antigenicity

Hengjie Peng; Changcheng Xiang; Hengjie Peng; Changcheng Xiang

doi:10.3934/math.20231004

AIMS Mathematics

2023, Volume 8, Issue 8: 19699-19718. doi: 10.3934/math.20231004

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A Filippov tumor-immune system with antigenicity

Hengjie Peng ,
Changcheng Xiang ^,

School of Mathematics and Statistics, Hubei Minzu University, Enshi, Hubei, 445000, China

Received: 27 March 2023 Revised: 08 May 2023 Accepted: 19 May 2023 Published: 12 June 2023
MSC : 34C25, 34D20

A threshold strategy model is proposed to demonstrate the extinction of tumor load and the mobilization of immune cells. Using Filippov system theory, we consider global dynamics and sliding bifurcation analysis. It was found that an effective model of cell targeted therapy captures more complex kinetics and that the kinetic behavior of the Filippov system changes as the threshold is altered, including limit cycle and some of the previously described sliding bifurcations. The analysis showed that abnormal changes in patients' tumor cells could be detected in time by using tumor cell-directed therapy appropriately. Under certain initial conditions, exceeding a certain level of tumor load (depending on the patient) leads to different tumor cell changes, that is, different post-treatment effects. Therefore, the optimal control policy for tumor cell-directed therapy should be individualized by considering individual patient data.
- Filippov system,
- tumor-immune model,
- threshold strategy,
- global dynamic,
- sliding bifurcation
Citation: Hengjie Peng, Changcheng Xiang. A Filippov tumor-immune system with antigenicity[J]. AIMS Mathematics, 2023, 8(8): 19699-19718. doi: 10.3934/math.20231004

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Abstract

A threshold strategy model is proposed to demonstrate the extinction of tumor load and the mobilization of immune cells. Using Filippov system theory, we consider global dynamics and sliding bifurcation analysis. It was found that an effective model of cell targeted therapy captures more complex kinetics and that the kinetic behavior of the Filippov system changes as the threshold is altered, including limit cycle and some of the previously described sliding bifurcations. The analysis showed that abnormal changes in patients' tumor cells could be detected in time by using tumor cell-directed therapy appropriately. Under certain initial conditions, exceeding a certain level of tumor load (depending on the patient) leads to different tumor cell changes, that is, different post-treatment effects. Therefore, the optimal control policy for tumor cell-directed therapy should be individualized by considering individual patient data.

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