Bifurcation and Basin-Mediated Hysteresis in the Oviposition Strategy of a Seasonal Aedes aegypti Population Model

The Aedes aegypti mosquito exhibits a critical behavioral adaptation through its oviposition strategy, laying eggs in dry and wet environments just above the water level, allowing eggs to resist desiccation and hatch only when submerged by rain. To investigate this mechanism, we developed a nonlinear dynamic model incorporating climate-driven parameters affecting egg hatching and adult emergence. Theoretical analysis revealed an imperfect pitchfork bifurcation giving rise to a phenomenon we term basin-mediated hysteresis. Unlike classical hysteresis, which relies on coexisting stable states, this mechanism results from the progressive collapse of the extinction basin boundary. As the control parameter approaches its critical value, the basin of attraction of the trivial equilibrium shrinks. Once the population establishes itself above the threshold, returning the parameter below unity does not restore extinction, leading to an irreversible transition governing population persistence. The model was validated using field data from mosquito traps in a Brazilian city, showing strong agreement with observed seasonal patterns of female captures. Parameters were optimized using the Differential Evolution algorithm, yielding high correlation between model and field data. The results demonstrate that the dual oviposition strategy underlies population persistence and seasonal peaks, providing information for planning interventions amid global arbovirus expansion.