Backward bifurcations in dengue transmission dynamics

Area of Science:

• Epidemiology
• Mathematical Biology
• Disease Modeling

Background:

• Dengue transmission dynamics are complex, involving human and mosquito vectors.
• Standard epidemiological models often assume a disease-free equilibrium (DFE) is stable if the basic reproduction number (R(0)) < 1.
• Backward bifurcation can occur, where a stable DFE coexists with a stable endemic equilibrium, challenging control efforts.

Purpose of the Study:

• To develop and analyze a deterministic model for dengue transmission dynamics.
• To investigate the phenomenon of backward bifurcation in dengue models.
• To explore methods for removing backward bifurcation, including the impact of incidence functions and imperfect vaccination.

Main Methods:

• Development of a seven-compartment deterministic model for human and vector dynamics.
• Analysis of local asymptotic stability of the disease-free equilibrium using the basic reproduction number (R(0)).
• Application of center manifold theory and Lyapunov function theory with LaSalle Invariance Principle to analyze model dynamics and bifurcation phenomena.

Main Results:

• The dengue transmission model exhibits backward bifurcation, where R(0) < 1 is insufficient for disease eradication.
• An extended model incorporating an imperfect vaccine also shows backward bifurcation.
• Replacing standard incidence with mass action incidence eliminates backward bifurcation in both models.

Conclusions:

• The standard incidence function in dengue models can induce backward bifurcation, complicating control strategies.
• Mass action incidence offers a more robust approach to dengue control by removing backward bifurcation.
• Effective dengue control requires careful consideration of the incidence function used in mathematical models.