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| Dynamics Analysis of a SVEIQR Epidemic Model with Reaction-diffusion |
| WANG Haixia, LU Yanling, MENG Ziyi
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| School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China |
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Abstract In order to more accurately predict the spread trend of infectious diseases and seek the best strategy to control the development of diseases. In this paper, a spatial diffusion SVEIQR epidemic model with a saturated incidence rate and temporary immunity is presented. We define the basic reproduction number R0 and establish the threshold criteria for the global dynamics. By constructing a Lyapunov function, we ascertain that the disease-free equilibrium point is globally asymptotically stable when R0<1, and when R0>1, the endemic equilibrium point exhibits the same property. Finally, the correctness of the theoretical derivation was verified by numerical simulation and it was found that the diffusion effect will not fundamentally change the global threshold stability of the epidemic model. However, a large diffusion coefficient will accelerate the spread of the epidemic and thus accelerate the speed of the epidemic to reach a stable state.
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Published: 15 September 2026
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