# Optimal Treatment Strategy for Cancer Based on Mathematical Modeling and Impulse Control Theory

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Model and Its Theoretical Analysis

#### 2.1. A Competition Model for Sensitive and Resistant Cells with Impulsive Effects

#### 2.2. Preliminaries

**Theorem**

**1.**

**Proof.**

#### 2.3. Theoretical Analysis

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

## 3. Optimal Control Strategies

#### 3.1. Optimal Pulse Time and Dose

**Theorem**

**4.**

**Proof.**

#### 3.2. The Optimal Dosage at a Fixed Time

#### 3.3. Optimal Pulse Time and Constant Drug Dose

## 4. Numerical Simulation

#### 4.1. The Optimal Dosage at a Fixed Time

#### 4.2. Optimal Pulse Time and Constant Drug Dose

#### 4.3. Optimal Pulse Time and Dose

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Luo, W.; Tan, X.; Shen, J.
Optimal Treatment Strategy for Cancer Based on Mathematical Modeling and Impulse Control Theory. *Axioms* **2023**, *12*, 916.
https://doi.org/10.3390/axioms12100916

**AMA Style**

Luo W, Tan X, Shen J.
Optimal Treatment Strategy for Cancer Based on Mathematical Modeling and Impulse Control Theory. *Axioms*. 2023; 12(10):916.
https://doi.org/10.3390/axioms12100916

**Chicago/Turabian Style**

Luo, Wenhui, Xuewen Tan, and Juan Shen.
2023. "Optimal Treatment Strategy for Cancer Based on Mathematical Modeling and Impulse Control Theory" *Axioms* 12, no. 10: 916.
https://doi.org/10.3390/axioms12100916