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| An Analysis of an SIRS Epidemic Model with General Direct Immunization in Networks |
| ZHANG Fei, WU Qingchu, ZENG Guanghong
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| College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China |
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Abstract We consider an SIRS epidemic model with a general direct immunization rate on networks. By constructing suitable Lyapunov functions, we find that the dynamical behvaior of the model is completely determined by the epidemic threshold λc. When λ≤λc, the disease-free equilibrium is globally asymptotically stable; when λ>λc, the endemic equilibrium is globally asymptotically stable. In addition, we propose a uniform direct immunization and a targeted direct immunization. The results show that under the same average immunization rate s there exists a critical immunization-lost rate δc so that the epidemic threshold of the targeted direct immunization is smaller (larger) than that of the uniform direct immunization if δ<δc(δ>δc).
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Received: 12 October 2015
Published: 24 February 2025
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