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

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.