Global dynamics of an age-structured malaria model with prevention

Area of Science:

• Epidemiology
• Mathematical Biology
• Disease Modeling

Background:

• Malaria remains a significant global health challenge.
• Existing models often lack detailed age-structured dynamics.
• Understanding transmission dynamics is crucial for effective control strategies.

Purpose of the Study:

• To develop a novel age-structured mathematical model for malaria transmission.
• To analyze the global dynamics and persistence of malaria.
• To identify key factors influencing disease spread using the basic reproduction number (R₀).

Main Methods:

• Formulation of a new age-structured malaria compartmental model.
• Analysis of the model's global attractor and uniform persistence.
• Derivation and analysis of the basic reproduction number (R₀).
• Numerical simulations to validate theoretical findings.

Main Results:

• The model exhibits a compact global attractor and uniform persistence under certain conditions.
• The basic reproduction number (R₀) was derived.
• Global dynamics are completely determined by R₀: R₀ < 1 implies a globally asymptotically stable disease-free equilibrium, while R₀ > 1 indicates a unique, globally attracting endemic equilibrium.

Conclusions:

• The age-structured model provides a comprehensive framework for understanding malaria dynamics.
• The basic reproduction number (R₀) is a critical threshold for malaria control.
• The findings support targeted interventions based on age-specific transmission patterns.