In medical field, \({\text{Ag + TiO}}_{{2}} {\text{/blood}}\) hybrid nanofluids have a wide range of applications like improvement of coatings on medical devices to prevent infections, drug delivery systems, where these fluids transport therapeutic agents through the bloodstream with greater efficiency and targeted delivery. Considering these vital applications, this study investigates the thermo-rheological properties of an incompressible three-dimensional Casson hybrid nanofluid flow between two rotating and stretching disks. The space between both the disks is filled with variable porous medium, where the disks are gyrating with different spinning rates and angular velocities. The nanofluid comprises of \({\text{TiO}}_{{2}}\) and \({\text{Ag}}\) nanoparticles mixed in blood. The modeled equations have converted to dimension-free form by implementing suitable variables and have then evaluated by ANN. It has been noticed in this work that, with growth in variable porous space factor, the concentration of nanoparticles and Reynolds number, there is a reduction in the azimuthal velocity component. Radial velocity depicts twofold behavior with an upsurge in nanoparticles number; near the lower plate, it is declined while close to the upper plate it is augmented. Thermal profiles escalated with growth in concentration of nanoparticles and Eckert number. The optimal performance of the model has noticed at epochs 87, 268, 245, 150, 300, 152, 150, 260, 150 and 260. The percentage-wise comparison shows that hybrid nanoparticles augment the heat transfer rate by 8.90%.
