Backward Bifurcation Phenomena of Dengue Transmission in the Presence of Re-Infection and Imperfect Vaccine

Abstract

The transmission dynamics of the dengue disease with imperfect vaccination and re-infection are being considered & analyzed. The model exhibits backward bifurcation when the basic reproduction number (R₀) is less than 1. However, using the Lyapunov function as well as the LaSalle Invariance Principle, it is demonstrated that with perfect vaccination and no re-infection, the DFE point is globally asymptotically stable. If R₀ > 1, there exists a distinct endemic equilibrium that is locally asymptotically stable. Numerical results of the model, using relevant parameter values, indicate that the increasing rate of vaccination waning resulted in the increase of infected individuals. Further numerical results suggest that the disease will continue in the community in the presence of re-infection. It also suggests that the dengue virus can be controlled effectively using the perfect vaccine.

J. Bangladesh Math. Soc. 45.1 (2025) 16–31