Codimension-one bifurcation and stability analysis in an immunosuppressive infection model

Area of Science:

• Mathematical Biology
• Epidemiology
• Dynamical Systems Theory

Background:

• Infectious diseases like HIV and hepatitis pose significant global health challenges, necessitating robust mathematical models for analysis.
• Understanding the parametric behavior of these disease models is crucial for predicting and controlling outbreaks.

Purpose of the Study:

• To investigate the stability and codimension-one bifurcation points of differential equation systems for HIV and hepatitis.
• To analyze the impact of time delays on the dynamical behavior of these infectious disease models.

Main Methods:

• Analysis of differential equations systems representing HIV and hepatitis.
• Application of stability theory and codimension-one bifurcation analysis.
• Utilizing center manifold theory to analyze the delayed differential equation model.

Main Results:

• The study demonstrates that variations in model parameters alter the dynamical behavior of HIV and hepatitis models.
• In the absence of a delay parameter, the models exhibit saddle-node and transcritical bifurcations.
• The presence of a delay parameter leads to a saddle-node bifurcation in the investigated model.

Conclusions:

• Mathematical models, both with and without time delays, are essential for understanding the complex dynamics of infectious diseases like HIV and hepatitis.
• Bifurcation analysis provides critical insights into potential shifts in disease behavior as parameters change, informing public health strategies.