# Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Model Formulation

## 3. Equilibrium and Basic Reproductive Number

**Theorem**

**1.**

## 4. Global Stability of Equilibriums

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Theorem**

**5.**

**Proof.**

## 5. The Numerical Simulation

## 6. Discussions

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Variational curves of $S,$ I, and R with time t when ${R}_{1}=11.4706>1$ for the same initial values and parameters of Figure 2 except $\delta =p=0$.

**Figure 4.**Variational curves of $S,$ $I,$ Q, and R with time t when ${R}_{2}=11.47>1$ for the same initial values and parameters of Figure 2 except $p=q=0$.

**Figure 5.**Variational curves of $S,$ I, and R with time t when ${R}_{3}=5.0649>1$ for the same initial values and parameters of Figure 2 except $q=\delta =0$.

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**MDPI and ACS Style**

Ma, Y.; Liu, J.-B.; Li, H.
Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies. *Mathematics* **2018**, *6*, 328.
https://doi.org/10.3390/math6120328

**AMA Style**

Ma Y, Liu J-B, Li H.
Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies. *Mathematics*. 2018; 6(12):328.
https://doi.org/10.3390/math6120328

**Chicago/Turabian Style**

Ma, Yanli, Jia-Bao Liu, and Haixia Li.
2018. "Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies" *Mathematics* 6, no. 12: 328.
https://doi.org/10.3390/math6120328