A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account

I. Khaloufi, M. Lafif, Y. Benfatah, H. Laarabi, J. Bouyaghroumni, M. Rachik
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引用次数: 5

Abstract

A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed. Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause. We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures. The Pontryagin's maximum principle is used to describe the optimal controls, and an iterative approach is used to solve the optimality system. Finally, numerical simulations are carried out in MATLAB to verify the theoretical analysis.
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考虑到人体免疫力的传染病传播的连续SIR数学模型
提出了一种基于免疫标准的传染病传染数学模型,该模型考虑了人群分层。我们的目标是证明这一想法在预防不同流行病方面的有效性,并减少这些疾病造成的重大财政和人力成本。我们确定了基本繁殖率,并利用该繁殖率检验了自由平衡点的稳定性,提出了两种控制措施。采用庞特里亚金极大值原理描述最优控制,并采用迭代法求解最优性系统。最后,在MATLAB中进行数值仿真,验证理论分析的正确性。
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来源期刊
Mathematical Modeling and Computing
Mathematical Modeling and Computing Computer Science-Computational Theory and Mathematics
CiteScore
1.60
自引率
0.00%
发文量
54
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