Bifurcation analysis of a two-infection transmission model with explicit vector dynamics

Area of Science:

• Epidemiology
• Mathematical Biology
• Vector-Borne Diseases

Background:

• Dengue fever presents a significant global public health challenge, necessitating accurate transmission modeling.
• Previous models often implicitly accounted for vector dynamics, potentially limiting a full understanding of disease spread.
• Explicitly incorporating vector population dynamics is key to refining dengue transmission patterns and control strategies.

Purpose of the Study:

• To introduce and analyze the SIRSIR-UV model, which explicitly includes vector population dynamics.
• To investigate the influence of explicit vector dynamics on dengue transmission patterns.
• To compare the findings with existing models that use implicit vector dynamics.

Main Methods:

• Utilized nonlinear dynamics and bifurcation theory to analyze the SIRSIR-UV model.
• Derived analytical conditions for transcritical and tangent bifurcations.
• Employed center manifold theory for backward bifurcation and computed Hopf and global homoclinic bifurcation curves.

Main Results:

• Demonstrated that seasonal variations in vector populations can induce chaotic behavior in disease transmission.
• Characterized the complex dynamics of the SIRSIR-UV model, highlighting the impact of explicit vector dynamics.
• Found that the bifurcation structures of the SIRSIR-UV model are consistent with the simpler SIRSIR model.

Conclusions:

• Explicit vector dynamics in dengue models, while complex, yield results comparable to models with implicit vector dynamics.
• Simplifying assumptions regarding vector dynamics can effectively capture essential disease transmission characteristics.
• This finding has significant implications for developing more manageable yet accurate mathematical models for vector-borne diseases.