Role of nonlinear transmission term in stability of hand, foot and mouth disease dynamics

Xiaofang Liu, Lvping Lin, Xu Gao, Yuping Li, Shangyu Teng, Guodong Sun
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Abstract

Aim: This study focuses on the nonlinear characteristics of two linearly stable equilibrium states within a theoretical hand, foot and mouth disease (HFMD) dynamics model. Methods: The conditional nonlinear optimal perturbation method, the Lyapunov method and the linear singular vector method are employed. Results: By utilizing the conditional nonlinear optimal perturbation method, it is determined that the two linearly stable equilibrium states (namely the free disease and disease HFMD states) also exhibit nonlinear stability. It is found that the stabilities of the free disease and disease HFMD equilibrium states differ in terms of returning to their original states. Conclusion: It is discovered that nonlinearity plays a crucial role in reinstating the original equilibrium states.
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非线性传播项在手足口病动态稳定性中的作用
目的:本研究主要探讨手足口病(HFMD)理论动态模型中两个线性稳定平衡状态的非线性特征。研究方法采用条件非线性最优扰动法、Lyapunov 法和线性奇异向量法。结果:通过利用条件非线性最优扰动法,确定了两个线性稳定的平衡状态(即无疾病状态和手足口病疾病状态)也表现出非线性稳定性。研究发现,自由疾病状态和疾病手足口病平衡状态在返回原始状态方面的稳定性有所不同。结论研究发现,非线性在恢复原始平衡状态方面起着至关重要的作用。
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