Fast and slow dynamics of malaria model with relapse

Area of Science:

• Mathematical Epidemiology
• Disease Dynamics Modeling

Background:

• Malaria remains a significant global health challenge, necessitating robust mathematical models for understanding transmission dynamics.
• Relapse in malaria cases adds complexity to disease modeling, requiring specific analytical approaches.

Purpose of the Study:

• To develop and analyze two mathematical models of malaria incorporating relapse.
• To investigate the impact of constant and variable vector population sizes on malaria persistence and equilibrium states.

Main Methods:

• Application of geometric singular perturbation theory for analyzing model dynamics.
• Utilizing the next-generation matrix method to derive the basic reproduction number.
• Analysis of global stability for disease-free and endemic equilibria.

Main Results:

• Complete dynamic analyses were performed for models with constant vector populations.
• The basic reproduction number and stability of equilibria were determined for both constant and variable vector population scenarios.
• Conditions for the uniform persistence of malaria were established.

Conclusions:

• The study provides a comprehensive mathematical framework for understanding malaria with relapse.
• Both constant and variable vector populations significantly influence malaria's epidemiological outcomes.
• The models offer insights into disease control strategies by identifying key stability and persistence parameters.