Numerical analysis of polio model: A mathematical approach to epidemiological model using derivative with Mittag–Leffler Kernel.

The goal of this study is to analyze and obtain a new numerical approach to an important mathematical model called polio, which is one of the highly infectious and dangerous diseases challenging many lives in most developing nations, most especially in Africa, Latin America, and Asia. A number of research outputs have proven beyond doubt that modeling with noninteger‐order derivative is much more accurate and reliable when compared with the integer‐order counterparts. In the present case, an extension is given to the polio model by replacing the classical time derivative with the newly defined operator known as the Atangana–Baleanu fractional derivative which has its formulation based on the noble Mittag–Leffler kernel. This derivative has been tested and applied in number of ways to model a range of physical phenomena in science and engineering. The Picard–Lindelöf theorem is applied to determine the condition under which the proposed model has a solution, also to show that the solution exists and unique. Local stability analysis of the disease‐free equilibrium and endemic state is also discussed. A novel approximation based on the Adams–Bashforth method is formulated to numerically approximate the fractional derivative operator. To justify the theoretical findings, some numerical results obtained for different instances of fractional order are presented. [ABSTRACT FROM AUTHOR]