一类具有接种的确定性和随机性分数阶传染病模型。

A Class of Deterministic and Stochastic Fractional Epidemic Models with Vaccination.

机构信息

School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, Xinjiang 830000, China.

出版信息

Comput Math Methods Med. 2022 Aug 16;2022:1797258. doi: 10.1155/2022/1797258. eCollection 2022.

DOI:10.1155/2022/1797258

PMID:36017144

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9398855/

Abstract

In this paper, a class of fractional deterministic and stochastic susceptible-infected-removed- susceptible (SIRS) epidemic models with vaccination is proposed. For the fractional deterministic SIRS epidemic model, the existence of solution and the stability of equilibrium points are analyzed by using dynamic method. Then, the appropriate controls are established to effectively control the disease and eliminate it. On this basis, the fractional stochastic SIRS epidemic model with vaccination is further considered, and a numerical approximation method is proposed. The correctness of the conclusion is verified by numerical simulation.

摘要

本文提出了一类具有接种的分数阶确定性和随机 SIRS 传染病模型。对于分数阶确定性 SIRS 传染病模型，利用动态方法分析了解的存在性和平衡点的稳定性。然后，建立了适当的控制措施来有效控制疾病并将其消除。在此基础上，进一步考虑了具有接种的分数阶随机 SIRS 传染病模型，并提出了一种数值逼近方法。通过数值模拟验证了结论的正确性。