一类传染病模型解的存在性和迭代算法
Existence and Iterative Algorithms of Solutions for a Class of Epidemic Model
DOI: 10.12677/aam.2024.138359, PDF,   
作者: 石丽莉：成都纺织高等专科学校，人文与通识教育学院，四川 成都
关键词: 非自治SIRS模型；迭代算法；存在唯一性；误差估计；Non-Autonomous SIRS Model； Iterative Algorithm； Existence and Uniqueness； Error Estimations
摘要: 通过研究非自治传染病SIRS模型解的存在性和建立迭代算法，分析模型的特殊性质，引入特殊性质的函数，将模型转换为积分系统，并构造所需的迭代序列，证明这个序列收敛于模型的解。可以证明，在一定时间内，SIRS模型具有唯一解，解和近似解之间能进行误差估计。该算法克服模型中非线性项可取负值和不满足Lipschitz条件的困难，证明了SIRS模型解存在，且可使用迭代算法求出和进行误差估计。
Abstract: This paper studies the existence and iterative algorithms of solutions to the SIRS model of non- autonomous infectious diseases. By analyzing the special properties of the model and introducing the function with special properties, the SIRS model is changed to an integral system, and the required iterative sequence is constructed. It is proved that this sequence converges to the solution of the model. It is proved that the SIRS model has a unique solution within a certain period of time, and the error estimations between the exact solution and the approximate solution are established. By overcoming the difficulties that the nonlinear terms in the model may take negative values and do not satisfy the Lipschitz condition, it is proved that the solution of the SIRS model can be obtained by an iterative method, and the error estimation can be performed.
文章引用：石丽莉. 一类传染病模型解的存在性和迭代算法[J]. 应用数学进展, 2024, 13(8): 3769-3777. https://doi.org/10.12677/aam.2024.138359

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