Investigation of ABPV predict dynamics infection in honeybee colony production: Soft patterns multiscale modeling with fractional approach

In this study, we present a nonlinear fractional order for a SIR-Ross-MacDonald model for the Acute Bee Paralysis Virus (ABPV) infection of a honeybee colony transmitted by parasitic varroa mites. We use advanced analysis to address positivity, boundedness, and the existence of a single solution. Sensitivity analysis is used to show how the model responds to parameter changes, and local and global stability evaluations are used to better understand the model's behavior under constrained conditions. In addition, we investigated the model's chaotic behavior and used phase portraits. Simulations are built to investigate the global influence of parameters on the levels of deriving conditions under which the bee colony can defend itself against an ABPV epidemic, and system solutions are numerically generated using a Newton polynomial-based method for the effects of four different seasons. The numerical simulations depict the actual epidemic behavior in various seasons for control measures, ignoring the effects of relapse and saturation index. Simulation results reveal that the fractional order model effectively predicts population dynamics in long-term interactions between vectors and hosts, allowing for effective control of varroa-mite-carrying virus transmission in honeybees.