From static thresholds to dynamic waves: How biological memory destabilizes malaria transmission Potential

The basic reproduction number R ₀ is central to malaria epidemiology, yet it is typically treated as a static quantity derived under memoryless assumptions for mosquito demography. In natural systems, however, mosquito populations are shaped by delayed processes such as larval development and density-dependent feedback, introducing biological memory into vector dynamics. We develop a minimal delay-based framework that incorporates this memory into the Ross–Macdonald model by describing adult mosquito abundance with a retarded differential equation. This formulation induces a time-dependent transmission potential R ₀ ( t ). Using complex analysis and the argument principle, we derive an explicit stability threshold , which separates stable from oscillatory transmission regimes. Near this threshold, delayed feedback produces slow relaxation times and sustained transient oscillations, implying that transmission potential may vary intrinsically even in the absence of external forcing. To account for ecological variability, we extend this deterministic condition into a probabilistic framework and define the stability probability as . Numerical simulations and global sensitivity analysis show that recruitment and developmental delays are the primary drivers of instability, while adult mortality has a weaker stabilizing effect. These results indicate that malaria interventions may influence not only the magnitude of malaria transmission but also its dynamical stability. By linking delay dynamics, transmission theory, and uncertainty quantification, this framework provides a basis for stability-aware modeling and interpretation of malaria transmission under ecological variability.