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考虑疫苗接种和失效的COVID-19传播模型的动力学分析
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Abstract:
疫苗接种是一种控制疫情传播的有效措施。但是随着毒株的变异出现了一个新的问题–免疫逃亡。免疫逃亡会使我们接种的疫苗失去作用，再次面临被感染的风险。重症治疗是应对COVID-19疫情的重要环节，不仅决定了患者的康复率和死亡率，还直接影响了疫情的传播速度和范围。因此本文构建了一个具疫苗失效以及重症住院治疗的COVID-19传播动力学模型，计算了模型的控制再生数，证明了模型无COVID-19平衡点和COVID-19平衡点存在性条件，并进行数值模拟验证了理论结果。
Vaccination is an effective measure to control the spread of epidemics. However, as strains of the virus mutate, a new problem arises-immune escape. Immune escape renders the vaccine ineffective and puts us at risk of being infected again. Critical care is an important part of the response to COVID-19 epidemic, which not only determines the recovery rate and mortality rate of patients, but also directly affects the speed and scope of the epidemic. In this paper, we constructed a model of COVID-19 transmission dynamics with vaccine failure and intensive care hospitalisation, calculated the control regeneration number of the model, proved that the model has no COVID-19 equilibrium point and the existence condition of COVID-19 equilibrium point, and conducted numerical simulations to verify the theoretical results.
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