The effect of incidence function in backward bifurcation for malaria model with temporary immunity

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• Malaria remains a significant global health challenge.
• Mathematical models are crucial for understanding malaria transmission dynamics.
• Backward bifurcation can hinder disease eradication efforts.

Purpose of the Study:

• To investigate the impact of incidence functions on backward bifurcation in malaria models.
• To compare malaria models with standard and nonlinear incidence rates.
• To identify conditions for effective malaria control.

Main Methods:

• Qualitative analysis of two mathematical malaria models.
• Analysis of the basic reproduction number (R0).
• Sensitivity analysis of model parameters.

Main Results:

• The standard incidence model exhibits backward bifurcation when R0 < 1, challenging control.
• The nonlinear incidence model avoids backward bifurcation, ensuring stability when R0 < 1.
• Both models show a globally asymptotically stable endemic equilibrium when R0 > 1 under specific conditions.

Conclusions:

• The choice of incidence function critically affects malaria model stability and control strategies.
• Nonlinear incidence functions offer a more robust framework for malaria elimination.
• Sensitivity analysis highlights key parameters for targeted malaria interventions.