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Published on: September 19, 2017
Bifurcation analysis of an SIS epidemic reaction-diffusion model with maturation delay and nonlinear birth
Qianqian Sun1, Chunjin Wei1, Junjie Wei2
1School of Science, Jimei University, Xiamen, Fujian 361021, PR China.
Abstract:
In this paper, we investigate the dynamics of SIS epidemic reaction-diffusion model with maturation delay and nonlinear birth. The stability of disease free equilibrium (DFE) and endemic equilibrium (EE) is determined by analyzing the distribution of the eigenvalues. Based on this investigation, a bifurcation set in the parameter plane is constructed, revealing how the system's behavior evolves with varying parameters. Furthermore, we obtain some local Hopf bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Finally, numerical simulations are conducted to validate the theoretical results and further illustrate the dynamic behavior of the model.
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