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

TL;DR

This paper presents a game-theoretic model showing how household decision-making influences mosquito population oscillations, revealing conditions for stable states and sustained cycles driven by perceived risk and behavioral feedback.

Contribution

It introduces a novel game-theoretic framework linking household behavior to mosquito dynamics, including analysis of equilibrium stability and oscillatory regimes.

Findings

Identification of four stable equilibria including full control and no control states

Existence of a partial engagement equilibrium influenced by perceived risk

Conditions for Hopf bifurcation leading to sustained oscillations

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.