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

Mosquito-borne diseases remain a major public health threat, and the control of mosquito populations depends on 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 mosquito dynamics remains poorly understood. We introduce a game-theoretic model in which the proportion of households performing breeding site control evolves through imitation dynamics, driven by perceived risks that can depend on mosquito prevalence. We assume that 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 confirm our analytical results by delineating the parametric regions of local stability for each steady state. Parameter explorations of the oscillatory regime further reveal that larger basic offspring numbers produce oscillations of higher amplitude and shorter period, while the perceived risk ratio modulates these trends and drives the amplitude to vanish near the Hopf boundaries. Our study demonstrates that spontaneous household decision-making alone can generate nontrivial dynamics in mosquito populations, offering insights into the interplay between risk perception and vector ecology. From a public health perspective, recurrent peaks in mosquito abundance may translate into periodic surges in cases, and effective interventions may therefore target the perceived risks that drive household participation in controlling breeding sites.