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A dengue epidemic model highlighting vertical-sexual transmission and impulsive control strategies

机译：登革热疫情模型突出垂直性传播和冲动控制策略

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摘要

Together with emerging infectious diseases, dengue fever continues to ravage tropical and subtropical countries amidst weak health systems. Vertical and sexual transmission have been shown to exhibit synergism in the endemic maintenance during inter-epidemics. This work presents a SISUV model modulating horizontal transmission, also vertical and sexual transmission in mosquitoes. Mendel's law applied to non-genetic reproduction is the key tool in the model derivation. Our finding on time scale separation reveals that certain solution trajectories approach a slow manifold before advancing toward the critical manifold and finally confining to a stable equilibrium. Equilibria in the critical manifold disclose a supercritical bifurcation around the threshold of the basic reproductive number, where the latter is shown to exhibit high sensitivity to the vertical transmission. Further extension of the model includes seasonal effects inspired by periodically varying meteorological factors. We then study how awareness campaigns and pesticide spraying contribute to compromising the disease spread, brought within toward-realistic impulsive mechanisms. The final format of the model is then numerically analyzed via path-following methods for hybrid dynamical systems, which allows to gain deeper insight into the effect of key model parameters on the system behavior. Furthermore, the proposed control scheme is optimized for efficient use of limited resources, in terms of reduction of the dengue spread among the population.
机译：与新兴的传染病一起，登革热仍在疲软的健康系统中继续蹂躏热带和亚热带国家。垂直和性传播已被证明在交叉间流行病期间在流行性维持中表现出协同作用。这项工作提出了一种SISUV模型调制水平传输，也是蚊子中的垂直和性传播。孟德尔的法律适用于非遗传繁殖是模型推导中的关键工具。我们对时间尺度分离的发现表明，某些解决方案轨迹在推进临界歧管之前接近慢歧管，并最终限于稳定的平衡。关键歧管中的均衡公开了围绕基本生殖数的阈值的超临界分叉，其中后者被示出对垂直传输表现出高灵敏度。该模型的进一步扩展包括通过定期不同的气象因素激发的季节性效果。然后，我们研究了意识运动和农药喷涂如何促使疾病扩散的促进，以实现 - 实际的冲动机制。然后，通过用于混合动态系统的路径跟踪方法，对模型的最终格式进行数值分析，这允许深入了解关键模型参数对系统行为的影响。此外，就拟议的控制方案优化了有效利用有限资源，就群体中的登革扬传播的减少而言。

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  • 来源
    《Applied Mathematical Modelling》 |2021年第7期|279-296|共18页
  • 作者

    Karunia Putra Wijaya; Joseph Paez Chavez; Thomas Goetz;

  • 作者单位

    Mathematical Institute University of Koblenz-Landau Universitatstr.1 Koblenz D-56070 Germany;

    Mathematical Institute University of Koblenz-Landau Universitatstr.1 Koblenz D-56070 Germany Center for Applied Dynamical Systems and Computational Methods (CADSCOM) Faculty of Natural Sciences and Mathematics Escuela Superior Politecnica del Litoral P.O. Box 09-01-5863 Guayaquil Ecuador;

    Mathematical Institute University of Koblenz-Landau Universitatstr.1 Koblenz D-56070 Germany;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Dengue; Vertical transmission; Sexual transmission; Time scale separation; Impulsive control;

    机译：登革热;垂直变速器;性传播;时间尺度分离;冲动控制;

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