Dynamical aspects of poliomyelitis disease via non-singular fractional differential equations: mathematical and biological aspects

Global public health continues to be significantly threatened by infectious diseases, demanding the creation of reliable mathematical models for their investigation and management. Despite being on the verge of eradication, the polio virus is nevertheless a subject of worry owing to its possible return. In this study, the fractional differential equations with the Mittag-Leffler kernel are used as a modeling tool to investigate the polio virus epidemic disease. The non-local and memory-dependent aspects of the Polio virus transmission mechanism are captured by the Mittag-Leffler kernel. In comparison to conventional integer-order models, the resultant system of fractional differential equations offers a more realistic depiction of the dynamics of the epidemic. The results of this study shed light on the crucial elements driving the polio virus epidemic’s development and management, providing insightful information for public health measures. Analytical results establish the existence, uniqueness, and Hyers-Ulam stability of solutions, while numerical simulations confirm that fractional models outperform classical approaches in predicting epidemic trends. Furthermore, this research highlights the importance of fractional calculus in simulating and understanding the dynamics of infectious diseases, emphasizing the improved accuracy and practicality of fractional differential equations with the Mittag-Leffler kernel in epidemiological studies. These findings advance our knowledge of epidemic modeling and control, and they may also have implications for the control of other infectious diseases.