Improved polio outbreak prediction using a Caputo fractional-order model with memory effects.

This paper presents a fractional-order mathematical model of the transmission dynamics of poliomyelitis based on the Caputo fractional derivative to address the memory effects present in biological systems. The model sub-divides human population into susceptible, exposed, infected and vaccinated groups and reflects essential processes of the disease progression and control. A strict theoretical examination is conducted, with the calculation of the basic reproduction number [Formula: see text], using next-generation matrix method. The local and global stability of both disease-free and endemic equilibrium points are established. A novel finding is that the fractional order α induces a delay in the epidemic peak and slows the vaccination response, providing a biologically realistic description of polio's slow immune memory. Simulations of the model are conducted to demonstrate model dynamics under varying values of the fractional order and parameters. The results indicate that the rate of transmission and the rate of vaccination have dominant effects on the dynamics of the outbreak. The graphical and tabular comparisons contribute to the reliability and efficiency of the suggested method as well. The proposed framework provides insight into the field of public health planning and helps in the future development of the field of fractional epidemic modeling.