Periodic solutions in a tumor-immune competition system with time-delay and chemotherapy effects
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| author | Amster, Pablo Rivera, Andrés Arredondo, John A. |
| author_facet | Amster, Pablo Rivera, Andrés Arredondo, John A. |
| contents | The main purpose of this paper is to analyze the dynamics of the system of time-delay differential equations (DDEs) \begin{equation*} \begin{split} \dot{T}(t)&=T(t) f(t,T(t))-γE(t)T(t),\\ \dot{E}(t)&=σ+ \frac{pE(t)T(t-τ_1)}{g+a T(t-τ_1)}-\frac{mE(t)T(t-τ_2)}{g+a T(t-τ_2)}-ηE(t), \end{split} \end{equation*} where $T=T(t)$ and $E=E(t)$ represent the concentrations of tumor and effector cells at the time $t$. The coefficients $σ$, $μ$, $γ$, and $η$ are all positive, and $f(t, T)$ represents the relative growth rate of tumor cells, corresponding to a generalized logistic growth function that describes periodic time chemotherapeutic effects. The parameter $τ_1 \in \mathbb{R}_{\ge 0}$ is the response time delay of the immune system (mediated by effector cells) to an invasion of tumor cells, while $τ_2 \in \mathbb{R}_{\ge 0}$ represents the time delay of tumor cells in response to the appearance of effector cells. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_11135 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodic solutions in a tumor-immune competition system with time-delay and chemotherapy effects Amster, Pablo Rivera, Andrés Arredondo, John A. Dynamical Systems 92B05, 92D25, 37M25, 34C23 The main purpose of this paper is to analyze the dynamics of the system of time-delay differential equations (DDEs) \begin{equation*} \begin{split} \dot{T}(t)&=T(t) f(t,T(t))-γE(t)T(t),\\ \dot{E}(t)&=σ+ \frac{pE(t)T(t-τ_1)}{g+a T(t-τ_1)}-\frac{mE(t)T(t-τ_2)}{g+a T(t-τ_2)}-ηE(t), \end{split} \end{equation*} where $T=T(t)$ and $E=E(t)$ represent the concentrations of tumor and effector cells at the time $t$. The coefficients $σ$, $μ$, $γ$, and $η$ are all positive, and $f(t, T)$ represents the relative growth rate of tumor cells, corresponding to a generalized logistic growth function that describes periodic time chemotherapeutic effects. The parameter $τ_1 \in \mathbb{R}_{\ge 0}$ is the response time delay of the immune system (mediated by effector cells) to an invasion of tumor cells, while $τ_2 \in \mathbb{R}_{\ge 0}$ represents the time delay of tumor cells in response to the appearance of effector cells. |
| title | Periodic solutions in a tumor-immune competition system with time-delay and chemotherapy effects |
| topic | Dynamical Systems 92B05, 92D25, 37M25, 34C23 |
| url | https://arxiv.org/abs/2510.11135 |