A bifurcation and sensitivity analysis of fractional order deafness model incorporating genetic factors

Abstract

This study presents a comprehensive analysis of a novel fractional-order mathematical model addressing the spread of deafness influenced by genetic factors. The model incorporates Caputo fractional derivatives, accounting for memory and hereditary properties, to provide a more realistic depiction of disease progression. The system of equations models transitions between compartments based on genetic transmission, recovery, and demographic factors. To solve the model, the Laplace Residual Power Series (LRPS) method is employed, offering a semi-analytical approximation of the system’s behavior over time. Power series expansions for each compartment provide insights into the temporal dynamics of the model under fractional-order influence. A comparison between the standard Residual Power Series (RPS) and LRPS methods is conducted to evaluate their accuracy and efficiency. Results demonstrate that the LRPS method outperforms the RPS method in terms of convergence and solution accuracy. Specifically, the LRPS method exhibits faster convergence to the true solution with a significantly lower absolute error, making it more reliable for solving fractional-order models. The absolute error between the LRPS and exact solutions decreases more rapidly, showcasing superior accuracy, particularly at higher fractional orders. Convergence analysis reveals that the LRPS method converges more quickly than the RPS method, especially as the fractional-order parameter increases. The study highlights the importance of incorporating fractional calculus in modeling hereditary diseases, providing valuable insights into disease dynamics. By identifying critical thresholds and sensitive parameters, the model can inform effective control strategies and improve our understanding of disease spread, offering more accurate predictions for future interventions. This work underscores the potential of fractional-order modeling in capturing the complexities of genetic diseases like deafness and enhances the accuracy of simulation results.