A reaction-diffusion malaria model with incubation period in the vector population

Area of Science:

• Epidemiology
• Mathematical Biology
• Parasitology

Background:

• Malaria remains a significant global health threat, affecting over two billion people annually.
• Understanding the spatial dynamics and parasite development within mosquitoes is crucial for effective malaria control.

Purpose of the Study:

• To investigate the impact of spatial heterogeneity and the extrinsic incubation period (EIP) on malaria epidemiology.
• To develop a mathematical model for analyzing malaria transmission dynamics.

Main Methods:

• A nonlocal and time-delayed reaction-diffusion model was proposed.
• The basic reproduction ratio (R₀) was defined and analyzed as a threshold parameter.
• Numerical simulations were conducted to compare spatially averaged and heterogeneous models.

Main Results:

• The basic reproduction ratio (R₀) was identified as a critical threshold for malaria spread.
• A condition for disease stabilization at a positive steady state was established for spatially independent parameters.
• Spatially averaged models were found to potentially underestimate malaria risk compared to heterogeneous models.

Conclusions:

• Spatial heterogeneity and EIP are critical factors influencing malaria epidemiology.
• The proposed heterogeneous model provides a more accurate assessment of malaria risk.
• The framework can guide the spatial allocation of malaria control resources.