具有社会距离习惯和公众意识的分数阶猴痘流行模型动力学及最优控制

Raqqasyi Rahmatullah Musafir, Agus Suryanto, Isnani Darti, Trisilowati
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引用次数: 0

摘要

在本文中,我们提出了一个包含社会距离习惯和公众意识的分数阶猴痘流行模型。该模型包括增加一个保护隔间和饱和传输速率。我们对所提出的模型的参数进行幂次缩放以确保维度的一致性。我们研究了解的存在性、唯一性、非负性和有界性。该模型具有无猴痘、人类地方病和地方病的平衡点,这些平衡点取决于导数的阶数。根据基本复制数,分析了各平衡点的局部和全局存在性和稳定性。此外,模型的基本再现数还取决于导数的阶数。用实际数据进行了实例研究,结果表明分数阶模型在校正和预测方面优于一阶模型。数值模拟证实了各平衡点相对于指定参数值的稳定性。数值模拟还表明,保持社交距离的习惯可以在早期减少猴痘病例,但不会显著改变基本繁殖数量。同时,公众意识可以大大改变基本繁殖数,将地方病状况转变为无病状态,尽管其对早期病例减少的影响并不显著。我们还在该模型中实现了媒介扑杀和疫苗接种的最优控制策略。我们解决了最优控制问题,仿真结果表明,与单独实现控制相比,两种控制组合产生的成本最小且效果更好。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamics and optimal control of fractional-order monkeypox epidemic model with social distancing habits and public awareness
In this article, we propose a fractional-order monkeypox epidemic model incorporating social distancing habits and public awareness. The model includes the addition of a protected compartment and a saturated transmission rate. We implement a power rescaling for the parameters of the proposed model to ensure dimensional consistency. We have investigated the existence, uniqueness, nonnegativity, and boundedness of the solution. The model features monkeypox-free, human-endemic, and endemic equilibrium points, which depend on the order of derivative. The existence and stability of each equilibrium point have been analyzed locally and globally, depending on the basic reproduction number. Moreover, the basic reproduction number of the model also depends on the order of derivative. We carried out a case study using real data showing that the fractional-order model performs better than the first-order model in calibration and forecasting. Numerical simulations confirm the stability properties of each equilibrium point with respect to the specified parameter values. Numerical simulations also demonstrate that the social distancing habits can reduce monkeypox cases in the early stages, but do not significantly alter the basic reproduction number. Meanwhile, public awareness can substantially modify the basic reproduction number, shifting the endemic condition towards a disease-free state, although its impact on case reduction in the early period is not significant. We also implemented optimal control strategies for vector culling and vaccination in the proposed model. We have solved the optimal control problem, and the simulation results show that the combination of both controls yields the minimum cost with better effectiveness compared to the controls implemented separately.
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