Nonlinear dynamics of Nosema ceranae and the fragile resilience of honeybee colonies under environmental strain.

The health and sustainability of honeybee populations are essential for global food production and ecological balance. More than one-third of agricultural crops depend on pollination, making honeybees indispensable to the global economy. However, colonies worldwide are increasingly threatened by the gut parasite Nosema ceranae, whose recurrent outbreaks cause severe productivity losses and economic damage to the apicultural and agricultural sectors. Despite its prevalence, the nonlinear mechanisms responsible for the persistence and resurgence of Nosema ceranae remain poorly understood. This study aims to develop a mathematical model that interpret the complex epidemiological behaviour of Nosema ceranae under realistic biological conditions, specifically focusing on renewal of colony-level susceptibility and the strained resources available for control and management. A nonlinear Susceptible-Infected-Recovered-Susceptible (SIRS) model incorporating renewal of colony-level susceptibility and resource saturation is formulated and analysed using stability theory and numerical bifurcation techniques. Analytical derivations identify the conditions for transcritical and Hopf bifurcations, while numerical continuation analysis and time series simulations validate the theoretical predictions and reveal the rich dynamical structure. The analysis uncovers two critical thresholds governing colony dynamics. A forward (transcritical) bifurcation marks the transition from disease eradication to endemic persistence, while a Hopf bifurcation arising from resource limitations induces sustained oscillations representing recurrent infection waves. The coexistence of stable equilibria and periodic orbits highlights bistability, indicating that small perturbations or change in control interventions can trigger large amplitude outbreaks. These nonlinear feedbacks provide a mechanistic explanation for the cyclical prevalence of Nosema ceranae observed in distinct colonies. The proposed framework establishes, for the first time, how the interplay between partial recovery and limited resource availability can drive complex epidemic patterns in honeybee colonies. Beyond its theoretical contribution, the study provides actionable insight for the agriculture industry: efficient allocation of control resources and timely interventions are essential to prevent recurrent epidemics that threaten pollination services and agricultural productivity. The results bridge mathematical modelling and ecological management, offering a predictive foundation for mitigating the economic and environmental impact of Nosema ceranae on global food security.