DYNAMICS OF AN EPIDEMIC MODEL WITH RELAPSE AND DELAY

Jian Liu; Qian Ding; Hongpeng Guo; Bo Zheng

doi:10.11948/20230376

2024 Volume 14 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(4): 2317-2336

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Jian Liu, Qian Ding, Hongpeng Guo, Bo Zheng. DYNAMICS OF AN EPIDEMIC MODEL WITH RELAPSE AND DELAY[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2317-2336. doi: 10.11948/20230376

Citation:

Jian Liu, Qian Ding, Hongpeng Guo, Bo Zheng. DYNAMICS OF AN EPIDEMIC MODEL WITH RELAPSE AND DELAY[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2317-2336. doi: 10.11948/20230376

DYNAMICS OF AN EPIDEMIC MODEL WITH RELAPSE AND DELAY

1.
College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, Guangdong 510006, China
2.
School of Mathematics and Information Science, Xiangnan University, Chenzhou, Hunan 423000, China
3.
College of Science, Hunan City University, Yiyang, Hunan 413000, China

Author Bio: Email: liujian2679@163.com(J. Liu); Email: dqian@hncu.edu.cn(Q. Ding); Email: zhengbo611@outlook.com(B. Zheng)
Corresponding author: Email: ghp8013@gzhu.edu.cn (H. Guo)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos: 11971127, 12371484, 12301621, 12171110)

Abstract

Abstract

In this paper, we consider a new epidemiological model with delay and relapse phenomena. Firstly, a basic reproduction number $ R_0 $ is identified, which serves as a threshold parameter for the stability of the equilibria of the model. Then, beginning with the delay-free model, the global asymptotic stability of the equilibria is obtained through the construction of suitable Lyapunov functions. For the delay model, the stability of the positive equilibrium and the existence of the local Hopf bifurcation are discussed. Furthermore, the application of the normal form theory and center manifold theorem is used to determine the direction and stability of these Hopf bifurcations. Finally, we shed light on corresponding biological implications from a numerical perspective. It turns out that time delay affects the stability of the positive equilibrium, leading to the occurrence of periodic oscillations and disease recurrence.
- Delay /
- relapse /
- stability /
- persistence /
- hopf bifurcation
MSC: 92D30, 34D23, 34K20

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References

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