Description of variables.

This study presents a novel non-autonomous mathematical model to explore the intricate relationship between temperature and desert locust population dynamics, considering the influence of both solitarious and gregarious phases across all life stages. The model incorporates temperature-dependent parameters for key biological processes, including egg development, hopper growth, adult maturation, and reproduction. Theoretical analysis reveals the model’s capacity for complex dynamical behaviors, such as multiple stable states and backward bifurcations, suggesting the potential for sudden and unpredictable population shifts. Sensitivity analysis identifies temperature-related parameters as critical drivers of population fluctuations, highlighting the importance of accurate temperature predictions for effective management. Numerical simulations demonstrate the significant impact of temperature on population growth, with optimal conditions promoting rapid development and increased survival, while extreme temperatures can hinder population growth and trigger phase transitions. By providing a deeper understanding of temperature-driven population shifts, this model enhances the ability to predict locust outbreaks, optimize control strategies, and reduce the socio-economic and ecological impacts of locust invasions.