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

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.

Summary points

• In this paper, from the perspective of stability analysis of equilibrium states, it is revealed that the stabilities of the free-disease and disease hand, foot and mouth disease equilibrium states differ in terms of returning to their original states.

• Through an examination of the nonlinearity factor in transmission, it is discovered that nonlinearity plays a crucial role in reinstating the original equilibrium states when using conditional nonlinear optimal perturbation-type and linear singular vector-type initial perturbations.

• Our results imply that it is important to consider nonlinear physical processes if one wants to be more prepared to forecast disease outbreaks, persistence and even seasonal characteristics.

Keywords: :

• CNOP method
• hand, foot and mouth disease
• HFMD
• nonlinear character
• stability

Author contributions

G Sun and X Liu conceptualized the work. G Sun and X Liu wrote the paper. X Liu made the figures and tables. L Lin checked the details of the article, and X Gao and Y Li and S Teng organized the content of specific references.

Financial disclosure

Grants from the Innovative Development Program for Young Pediatricians of Professional Committee on Children's Health and Pharmaceutical Research of Chinese Association of Traditional Chinese Medicine (EKQNJJ-2023-12), the National Natural Science Foundation of China (Nos. 82004422), and the Research Program of Dongfang Hospital, Beijing University of Chinese Medicine (2023-DFJY-071) provided funding for this research. The authors have no other relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript apart from those disclosed.

Competing interests disclosure

The authors have no competing interests or relevant affiliations with any organization or entity with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.

Writing disclosure

No writing assistance was utilized in the production of this manuscript.

Additional information

Funding

Grants from the Innovative Development Program for Young Pediatricians of Professional Committee on Children's Health and Pharmaceutical Research of Chinese Association of Traditional Chinese Medicine (EKQNJJ-2023-12), the National Natural Science Foundation of China (Nos. 82004422), and the Research Program of Dongfang Hospital, Beijing University of Chinese Medicine (2023-DFJY-071) provided funding for this research.