Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.