| Volume 14, Number 4, 2024, Pages - DOI：10.11948/JAAC-2023-0376 |
| Dynamics of an epidemic model with relapse and delay |
| Jian Liu,Qian Ding,Hongpeng Guo,Bo Zheng |
| Keywords:Delay relapse stability persistence Hopf bifurcation. |
| 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. |
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