Mathematical analysis and simulation of an ABC fractional Zika virus model with natural transform and stability assessment

This work introduces an Atangana-Baleanu Caputo (ABC) fractional model for the transmission dynamics of the Zika virus. A novel Natural Transform approach is employed to obtain an approximate analytical solution and to examine the stability and uniqueness of the system. The positivity and boundedness of the ABC fractional model are established, and the equilibrium points as well as the basic reproduction number are derived. The existence and uniqueness of solutions are further analyzed using the Lipschitz condition. Moreover, Routh-Hurwitz and Lyapunov stability analyses are applied to determine the local and global stability of the equilibrium states. To enhance model robustness, the Markov Chain Monte Carlo (MCMC) method is utilized for parameter estimation. Finally, the Adams-Moulton method is implemented to obtain numerical approximations, and simulations are carried out to predict the controllability of pandemic spread. All numerical simulations and parameter estimations were implemented using computational algorithms, highlighting the role of ICT tools in analyzing and predicting the dynamics of fractional epidemic.