Zhimin Han, Yi Wang, Shan Gao, Guiquan Sun, Hao Wang
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Unlike the typical positive correlation between <math><msub><mi>R</mi> <mn>0</mn></msub> </math> and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, <math><msub><mi>R</mi> <mn>0</mn></msub> </math> does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . We further demonstrate that network contacts within communities have a greater effect on <math><msub><mi>R</mi> <mn>0</mn></msub> </math> than casual contacts between communities. 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To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number <math><msub><mi>R</mi> <mn>0</mn></msub> </math> , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between <math><msub><mi>R</mi> <mn>0</mn></msub> </math> and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, <math><msub><mi>R</mi> <mn>0</mn></msub> </math> does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase <math><msub><mi>R</mi> <mn>0</mn></msub> </math> . We further demonstrate that network contacts within communities have a greater effect on <math><msub><mi>R</mi> <mn>0</mn></msub> </math> than casual contacts between communities. 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引用次数: 0
摘要
社区之间通常不是孤立的,而是非对称互动的,这使得传染病可以在同一社区内和不同社区之间传播。为了揭示非对称互动和接触异质性对疾病传播的影响,我们建立了一个双社群 SIR 流行病模型,其中每个社群都有自己的接触结构,而社群之间的交流则通过临时通勤者进行。我们推导出了基本繁殖数 R 0 的显式公式,给出了最终流行病规模 z 的隐式公式,并分析了它们之间的关系。与经典的 SIR 模型中 R 0 和 z 之间典型的正相关关系不同,我们发现偏离同质种群的模型中对应的 R 0 和 z 之间存在负相关关系。此外,我们还研究了非对称耦合机制对 R 0 的影响。结果表明,在社区内易感个体流动受限的情况下,R 0 并不遵循简单的单调关系,这表明易感个体流动的不规则减少可能会增加 R 0。我们进一步证明,与社区之间的偶然接触相比,社区内的网络接触对 R 0 的影响更大。最后,我们建立了一个不限制易感个体流动的流行病模型,数值模拟结果表明,社区间人流的增加会导致更大的 R 0。
Final epidemic size of a two-community SIR model with asymmetric coupling.
Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase . We further demonstrate that network contacts within communities have a greater effect on than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger .
期刊介绍:
The Journal of Mathematical Biology focuses on mathematical biology - work that uses mathematical approaches to gain biological understanding or explain biological phenomena.
Areas of biology covered include, but are not restricted to, cell biology, physiology, development, neurobiology, genetics and population genetics, population biology, ecology, behavioural biology, evolution, epidemiology, immunology, molecular biology, biofluids, DNA and protein structure and function. All mathematical approaches including computational and visualization approaches are appropriate.