EXPLORING THE IMPACT OF DIFFUSION AND CHEMOTAXIS IN SPATIAL PATTERNS IN A MALARIA EPIDEMIC PDE MODEL: A TURING ANALYSIS

Abstract

The Ross model has been pivotal in studying malaria transmission dynamics, yet its limitations in describing parasite dispersal and other crucial factors hinder comprehensive control strategies. In this paper, we introduce a partial differential equations (PDE) modeling framework that extends the Ross model with enhanced features, addressing aspects like parasite dispersal and attractiveness to humans.

Our research investigates the influence of diffusion and chemotaxis within the PDE model on spatial patterns in malaria transmission. Employing Turing analysis, we explore the impact of chemotactic movement on the emergence of spatial structures. We hypothesize that for stable eigenvalues in well-mixed conditions, there is a pattern formation for an eigenvalue that has positive real part in the presence of diffusion and chemotaxis for several allowable frequencies in a given domain.

This interdisciplinary study integrates mathematical modeling, biological insights, and computational methods, offering a nuanced understanding of the interplay between chemotaxis and diffusion in malaria propagation. The findings contribute valuable insights for designing targeted interventions and advancing our comprehension of malaria dynamics.