Fractional order for the transmission dynamics of coffee berry diseases (CBD)

Abstract

Abstract Coffee berry diseases (CBD) pose significant threats to coffee production worldwide, affecting the livelihoods of millions of farmers and the global coffee market. Fractional calculus provides a powerful framework for describing non-local and memory-dependent phenomena, making it suitable for modelling the long-range interactions inherent in CBD spread. This study aims to formulate and analyse fractional order model for CBD transmission dynamics in the sense of Atangana–Baleanu–Caputo. Fixed point theorems were utilised to test the existence and uniqueness of the model’s solutions using fractional order. The basic reproduction number was calculated utilising the next-generation matrix. The model has locally asymptotically stable equilibrium positions (disease-free and endemic). Furthermore, the Lyapunov function was used to conduct a global stability analysis of the equilibrium locations. A numerical simulation of the CBD model was created using the fractional Adam–Bashforth–Moulton approach to validate the analytical findings. Our findings contribute to the development of more accurate predictive models and inform the design of targeted interventions to mitigate the impact of CBD on coffee production systems.