Oscillatory Regimes in a Game-Theoretic Model for Mosquito Population Dynamics under Breeding Site Control

Abstract

Mosquito-borne diseases remain a major public-health threat, and the effective control of mosquito populations requires sustained household participation in removing breeding sites. While environmental drivers of mosquito oscillations have been extensively studied, the influence of spontaneous household decision-making on the dynamics of mosquito populations remains poorly understood. We introduce a game-theoretic model in which the fraction of households performing breeding site control evolves through imitation dynamics driven by perceived risks. Household behavior regulates the carrying capacity of the aquatic mosquito stage, creating a feedback between control actions and mosquito population growth. For a simplified model with constant payoffs, we characterize four locally stable equilibria, corresponding to full or no household control and the presence or absence of mosquito populations. When the perceived risk of not controlling breeding sites depends on mosquito prevalence, the system admits an additional equilibrium with partial household engagement. We derive conditions under which this equilibrium undergoes a Hopf bifurcation, yielding sustained oscillations arising solely from the interaction between mosquito abundance and household behavior. Numerical simulations and parameter explorations further describe the amplitude and phase properties of these oscillatory regimes.