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首页> 外文期刊>Applied Mathematical Modelling >A time-delayed SVEIR model for imperfect vaccine with a generalized nonmonotone incidence and application to measles
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A time-delayed SVEIR model for imperfect vaccine with a generalized nonmonotone incidence and application to measles

机译：具有通用非单调发病率的不完美疫苗的时间延迟SVEIR模型及麻疹施用

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摘要

In this paper, we investigate the effects of the latent period on the dynamics of infectious disease with an imperfect vaccine. We assume a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population when the number of infectious individuals increases. After we propose the model, we provide the well-posedness property by verifying the non-negativity and boundedness of the models solutions. Then, we calculate the effective reproduction number R_E. The threshold dynamics of the system is obtained with respect to R_E. We discuss the global stability of the disease-free equilibrium when R_E < 1 and explore the system persistence when R_E > 1. Moreover, we prove the coexistence of an endemic equilibrium when the system persists. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to: (ⅰ) implement a case study regarding the measles disease transmission in the United States from 1963 to 2016; (ⅱ) study the local and global sensitivity of R_E with respect to the model parameters; (ⅲ) discuss the stability of endemic equilibrium; and (ⅳ) explore the sensitivity of the proposed model solutions with respect to the main parameters.
机译：在本文中，我们研究了潜在疫苗对传染病动态的影响。我们假设当传染性人数增加时，具有非单调性财产的一般发病率函数，以解释易感人群中的心理效应。在我们提出该模型后，我们通过验证模型解决方案的非消极性和界限提供良好的良好性质。然后，我们计算有效的再现号码R_E。关于R_E获得系统的阈值动态。我们讨论了r_e <1时探讨了无疾病平衡的全球稳定性，并在r_e> 1时探索系统持久性。此外，当系统持续存在时，我们证明了流行均衡的共存。然后，我们讨论消除疾病所需的关键疫苗接种覆盖率。提供了数值模拟：（Ⅰ）在1963年至2016年，实施了美国麻疹疾病传播的案例研究; （Ⅱ）研究R_E关于模型参数的局部和全局敏感性; （Ⅲ）讨论流行均衡的稳定性; （ⅳ）探讨所提出的模型解决方案对主要参数的灵敏度。

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