Predictive modeling of fractional plankton-assisted cholera propagation dynamics using Bayesian regularized deep cascaded exogenous neural networks

Cholera infectious disease spread through water sanitation containing zooplankton carrying Vibrio Cholerae is a significant global threat, underscoring the urgent need for effective prevention through mathematical simulation regimes. In this study, novel quad-layered deep cascaded feed-forward nonlinear autoregressive exogenous (CFNARX) neural networks optimized with Bayesian regularization (BR) technique are employed to model fractional plankton-assisted cholera propagation (FPCP) system declaring the transmission of Vibrio Cholerae infested on zooplanktons into sanitation system of human society. The fractional differential epidemiological model incorporating density of phytoplankton, density of Vibrio Cholerae infected on zooplankton, number of infected human population with cholerae, number of recovered human population from cholerae, total number of human population and concentration of free-living Vibrio Cholerae exacted by a fractional Adams-Bashforth-Moulton predictor-corrected method across sundry scenarios comprising different fractional order values. The synthetic datasets are partitioned into training and testing sub-sets to model intricate dynamics of FPCP by means of a novel CFNARX-BR computing paradigm. The adept aptitudes of designed neural networks are assessed on diverse FPCP system scenarios using mean squared error (MSE) converging patterns, error-input correlations and error auto-correlation analytics, error regression analysis, time-series response plots, and error histogram studies. The forecasted outcomes of CFNARX-BR paradigm are compared with reference numerical outcomes through comparison charts and absolute error analysis. The minute deviations of CFNARX-BR outcomes reflected by MSE, ranging from 10⁻¹¹ to 10⁻¹², across all complex FPCP system cases affirming the robustness of the devised intelligent computing schematic. Furthermore, the absolute error analysis reveals minute deviations of the order 10⁻⁵ to 10⁻⁷, thereby reflecting the adept utilization of an efficient neurocomputing technique to model the fractional ecological-epidemiological differential models.