Global stability mathematical analysis for virus transmission model with latent age structure.
Global stability mathematical analysis for virus transmission model with latent age structure.
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DOI：
10.3934/mbe.2022154
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发表时间：
2022-01
期刊：
影响因子：
--
通讯作者：
Shanjing Ren;Lingling Li
中科院分区：
文献类型：
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作者：
Shanjing Ren;Lingling Li
背景与目的数学模型是控制和预防疾病传播的重要方法。根据疾病传播的特点，有必要在传染病模型中加入快过程和慢过程，从而更有效地反映传染病的传播机制。方法建立了一个具有快进和慢进的年龄结构传染病模型。在种群规模不变的假设下，利用微分方程的稳定性理论分析了模型的动态性质。结果计算出了非常重要的阈值R0。若R01，则用Lyapunov函数证明地方病平衡点是全局稳定的。通过对基本繁殖数进行更深入的分析，得出传染病慢进率越大，阈值结果越少。此外，我们还提供了一些数值模拟来验证我们的结果。结论疫苗不能提供终身免疫，但可以降低感染者的死亡率。通过接种疫苗，患者进入缓慢进展的比率增加，门槛相应降低。因此，接种疫苗可以有效控制冠状病毒的传播。通过数学模型预测的理论发病率可以为预防和控制疫情的传播提供依据。
BACKGROUND AND OBJECTIVE Mathematical model is a very important method for the control and prevention of disease transmissing. Based on the communication characteristics of diseases, it is necesssery to add fast and slow process into the model of infectious diseases, which more effectively shows the transmission mechanism of infectious diseases. METHODS This paper proposes an age structure epidemic model with fast and slow progression. We analyze the model's dynamic properties by using the stability theory of differential equation under the assumption of constant population size. RESULTS The very important threshold R0 was calculated. If R01, the Lyapunov function is used to show that endemic equilibrium is globally stable. Through more in-depth analysis for basic reproduction number, we obtain the greater the rate of slow progression of an infectious disease, the fewer the threshold results. In addition, we also provided some numerical simulations to prove our result. CONCLUSIONS Vaccines do not provide lifelong immunity, but can reduce the mortality of those infected. By vaccinating, the rate of patients entering slow progression increases and the threshold is correspondingly reduced. Therefore, vaccination can effectively control the transmission of Coronavirus. The theoretical incidence predicted by mathematical model can provide evidence for prevention and controlling the spread of the epidemic.