The current investigation explains the chemical reaction and bioconvection process for an inclined magnetized Cross nanofluid over an inclined cylinder using a spectral relaxation approach. Additionally, the facts concerning swimming gyrotactic microorganisms, non-uniform thermal conductivity, and variable decrease or increase in heat sources are taken together. Each profile is checked for inclined and orthogonal magnetic impact. Appropriate transformations made for conversion of nonlinear PDEs into systems of ODEs. For obtaining numerical results, a spectral relaxation approach is utilized, and graphs are plotted with each physical parameter attached. It is well established that the temperature field intensifies owing to an amplification of thermal conduction and Brownian diffusivity phenomena. The heat transfer rate amplifies owing to a magnification in magnetic parameter and thermal conductivity, but the velocity field diminishes as a result of magnification in the Weissenberg number and power law index. Amplification in the reaction rate constant parameter diminishes the concentration field. Activation energy is the key factor responsible for magnification in the concentration field. Furthermore, smooth agreement is found during comparison with the existing literature. Statistical analysis is also conducted for physical quantities.

The current work aims to design a computational framework based on artificial neural networks (ANNs) and the optimization procedures of global and local search approach to solve the nonlinear dynamics of the spread of COVID-19, i.e., the SEIR-NDC model. The combination of the Genetic algorithm (GA) and active-set approach (ASA), i.e., GA-ASA, works as a global-local search scheme to solve the SEIR-NDC model. An error-based fitness function is optimized through the hybrid combination of the GA-ASA by using the differential SEIR-NDC model and its initial conditions. The numerical performances of the SEIR-NDC nonlinear model are presented through the procedures of ANNs along with GA-ASA by taking ten neurons. The correctness of the designed scheme is observed by comparing the obtained results based on the SEIR-NDC model and the reference Adams method. The absolute error performances are performed in suitable ranges for each dynamic of the SEIR-NDC model. The statistical analysis is provided to authenticate the reliability of the proposed scheme. Moreover, performance indices graphs and convergence measures are provided to authenticate the exactness and constancy of the proposed stochastic scheme.