Modelling and Analysis of Vaccination Effects on Hand, Foot, and Mouth Disease Transmission Dynamics

In this study, the transmission dynamics of hand, foot, and mouth disease (HFMD), incorporating vaccination, were comprehensively assessed.A Susceptible-Vaccinated-Exposed-Infectious-Recovered (SVEIR) model was formulated and its stability was evaluated in relation to disease-free and endemic equilibrium points.The fundamental reproduction number, R0, was derived utilizing the Next-Generation Matrix method.This work demonstrates the local and global asymptotic stability of both disease-free and endemic equilibria under defined conditions.The local stability of the disease-free equilibrium set was ascertained via the Jacobian matrix method, contingent upon certain prerequisites.Conversely, the stability of the endemic equilibrium set was affirmed using the Routh-Hurwitz criteria.In the context of global stability, a Lyapunov function was employed to establish the disease-free equilibrium case, demonstrating that the equilibrium E0 is globally asymptotically stable within region Ω.Stability of the endemic equilibrium set for the susceptible and infected compartments was exhibited using Dulac's criteria.Additionally, a sensitivity analysis was performed, revealing a significant correlation of the basic reproduction number to specific parameters, namely A, β1, β2, β3, β4, and ρ.This analysis indicates that these aforementioned parameters have a substantial influence on HFMD propagation.The analytical findings were corroborated through numerical simulations which further reinforced the validity of the model.This work presents a profound exploration of HFMD transmission dynamics, offering valuable insights for the development of efficacious control strategies.