The mathematical analysis of blood’s non-Newtonian behavior in the presence of drug nanoparticles and microbes with magnetic and thermal radiation effects is the focus of the current article. The response surface methodology (RSM) is used to conduct a sensitivity study of the bioconvection impacts on the heat and mass transmission rate of the unsteady magnetohydrodynamic blood flow. The physical laws governing unsteady blood flow over stretching blood vessels are mathematically represented as a system of partial differential equations, which are numerically solved using the Fourth Order Runge–Kutta Method in conjunction with the Shooting Technique. Following an analysis of the numerical data, statistical conclusions are drawn on the heat and mass transfer rates. The impact of Brownian motion and thermophoresis factors is discovered to increase blood temperature. Additionally, at the largest Brownian motion factor and maximum thermophoresis effect, the largest heat transfer rate occurs. It is also observed that the lowest mass transfer rates are generated by higher radiation parameter and chemical reaction parameter values. The findings of the study show potential for important applications in therapeutic hypothermia, magnetic therapy, and targeted drug delivery.