流行病模型
最优控制
传输(电信)
扩散
反应扩散系统
图灵
传输速率
数学优化
控制(管理)
生物系统
计算机科学
数学
应用数学
生物
热力学
物理
人工智能
数学分析
环境卫生
人口
医学
电信
程序设计语言
作者
Liangliang Chang,Shupeng Gao,Zhen Wang
标识
DOI:10.1016/j.jtbi.2022.111003
摘要
Patterns arising from the reaction-diffusion epidemic model provide insightful aspects into the transmission of infectious diseases. For a classic SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates. A quantitative indicator, "normal serious prevalent area (NSPA)", is introduced to characterize the relationship between patterns and the extent of the epidemic. The extent of epidemic is positively correlated to NSPA. To effectively reduce NSPA of patterns under the large transmission rates, taken removed (recovery or isolation) rate as a control parameter, we consider the mathematical formulation and numerical solution of an optimal control problem for the SIR reaction-diffusion model. Numerical experiments demonstrate the effectiveness of our method in terms of control effect, control precision and control cost.
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