On a Mathematical Model Describing Chemotherapeutic Drug Treatment for Tumor Cells
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910010996424704 |
|---|---|
| author | Liu, Xiaoqin Yin, Hong-Ming |
| author_facet | Liu, Xiaoqin Yin, Hong-Ming |
| contents | In this paper, we study a semilinear parabolic PDE system which describes the interaction of normal cells, tumor cells, immune cells, with a chemotherapeutic drug. The model extends the previous model with incorporating strong Allee affects in the normal-tissue and tumor dynamics. Under mild assumptions, we establish global-in-time existence and uniqueness of nonnegative weak solutions and derive L-infinity bounds for all time. We then investigate spatiotemporal dynamics of the model and therapy scheduling using an implicit Crank Nicolson Backward Euler (CNBE) scheme. Simulations in a heterogeneous two-dimensional space-dimensional tissue region with three tumor peaks indicate rapid tumor invasion without treatment and significant tumor suppression under pulsed chemotherapeutic treatment. Moreover, in a fixed total dose delivered within the treatment cycle, while keeping each injection duration fixed, concentrated pulses produce stronger early knock-down of tumor density, while more frequent but gentler pulses achieve comparable control of the tumor invasive front while better preserving normal tissue over a four-week period. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04025 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a Mathematical Model Describing Chemotherapeutic Drug Treatment for Tumor Cells Liu, Xiaoqin Yin, Hong-Ming Analysis of PDEs 35K57, 92C17, 92C50 In this paper, we study a semilinear parabolic PDE system which describes the interaction of normal cells, tumor cells, immune cells, with a chemotherapeutic drug. The model extends the previous model with incorporating strong Allee affects in the normal-tissue and tumor dynamics. Under mild assumptions, we establish global-in-time existence and uniqueness of nonnegative weak solutions and derive L-infinity bounds for all time. We then investigate spatiotemporal dynamics of the model and therapy scheduling using an implicit Crank Nicolson Backward Euler (CNBE) scheme. Simulations in a heterogeneous two-dimensional space-dimensional tissue region with three tumor peaks indicate rapid tumor invasion without treatment and significant tumor suppression under pulsed chemotherapeutic treatment. Moreover, in a fixed total dose delivered within the treatment cycle, while keeping each injection duration fixed, concentrated pulses produce stronger early knock-down of tumor density, while more frequent but gentler pulses achieve comparable control of the tumor invasive front while better preserving normal tissue over a four-week period. |
| title | On a Mathematical Model Describing Chemotherapeutic Drug Treatment for Tumor Cells |
| topic | Analysis of PDEs 35K57, 92C17, 92C50 |
| url | https://arxiv.org/abs/2602.04025 |