Global Stability of a Time-delayed Malaria Model with Standard Incidence Rate

Area of Science:

• Mathematical epidemiology
• Dynamical systems theory
• Disease modeling

Background:

• Malaria remains a significant global health challenge, necessitating robust mathematical models for understanding transmission dynamics.
• Delay differential equations (DDEs) are essential for capturing the complexities of disease transmission, including incubation periods and variable infectiousness.

Purpose of the Study:

• To propose and analyze a four-dimensional DDEs model for malaria transmission with a standard incidence rate.
• To determine the global stability of the model's equilibria in relation to the basic reproduction number (R0).

Main Methods:

• Utilizing the limiting system of the proposed DDEs model.
• Applying Lyapunov's direct method to establish global asymptotic stability (GAS) and global attractivity (GA).
• Employing specific analysis techniques to prove weak persistence for model equilibria.

Main Results:

• The disease-free equilibrium (E0) is globally asymptotically stable when R0 < 1.
• The disease-free equilibrium (E0) is globally attractive when R0 = 1.
• The endemic equilibrium (E*) is globally asymptotically stable, and E0 is unstable when R0 > 1.

Conclusions:

• The basic reproduction number (R0) is a critical threshold parameter determining the long-term malaria persistence and eradication.
• The proposed DDEs model provides a rigorous framework for analyzing malaria dynamics and stability.
• The findings offer valuable insights for public health interventions and disease control strategies.