An infectious disease epidemic model with migration and stochastic transmission in deterministic and stochastic environments

Healthcare analytics (New York, N.Y.) Pub Date : 2024-04-24 DOI:10.1016/j.health.2024.100337

Mohammed Salman , Prativa Sahoo , Anushaya Mohapatra , Sanjay Kumar Mohanty , Libin Rong

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Abstract

Understanding population migration is essential for controlling highly infectious diseases. This paper studies the global dynamics of an infectious disease epidemic model incorporating population migration and a stochastic transmission rate. Our findings demonstrate that in deterministic and stochastic environments, the models exhibit global Lyapunov stability near the disease-free equilibrium point, determined by a threshold parameter. Furthermore, we analyze the effect of migration on infectious diseases. We discover that the number of infections and the peak value of the infection curve increase with a higher level of population migration. These results are supported by numerical illustrations that hold epidemiological relevance. Additionally, the disease-free equilibrium of the associated time delay model is linearly asymptotically stable, and the endemic equilibrium exhibits more bifurcation for larger time delay values.

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在确定性和随机环境中带有迁移和随机传播的传染病流行模型

了解人口迁移对控制高度传染性疾病至关重要。本文研究了包含人口迁移和随机传播率的传染病流行模型的全局动态。我们的研究结果表明，在确定性和随机环境中，模型在由阈值参数决定的无疾病平衡点附近表现出全局李亚普诺夫稳定性。此外，我们还分析了移民对传染病的影响。我们发现，随着人口迁移水平的提高，感染数量和感染曲线的峰值也会增加。这些结果得到了与流行病学相关的数字说明的支持。此外，相关时间延迟模型的无疾病均衡是线性渐近稳定的，而流行均衡在时间延迟值越大时越容易出现分叉。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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