Exploring the dynamical bifurcation and stability analysis of Nipah virus; novel perspectives utilizing fractional calculus

A zoonotic virus called the Nipah virus (NV) can create deadly illness epidemics in humans. The animal host repository for NV is the fruit bat, sometimes referred to as the flying fox. It has been documented to infect pigs, which are regarded as intermediary carriers. Scientists’ interest in infectious disease modeling has surged because non-integer-order derivatives work so well. In this work, we present a model of NV infection propagation that accounts for both the disappearance of antibodies in rehabilitated people and all human-to-host animal propagation. Taking into consideration the fractal-fractional operator in the generalized Mittag–Leffler kernel sense, we contemplated the numerical solutions for the proposed model via the Lagrange interpolation polynomial technique. Several qualitative aspects of the NV model, such as positive bounded solution, disease-free equilibrium, and the basic reproduction number ( \({R}_{0}\) $R_0$ ), are presented with a graphic illustration to demonstrate the effectiveness of the system parameters. To establish efficient time-dependent oversight, sensitive evaluation of the framework’s components is also carried out. Besides that, the local and global stability at the disease-free equilibrium point is provided in detail. Meanwhile, a fractional bifurcation framework is developed according to the sensitivity indices, and numerical simulations are used to identify the most efficient prevention approach. The mathematical mechanism of the NV model is characterized by the Atangana-Baleanu fractal-fractional differential operators, which are newly described as fractal-fractional differential operators. Three approaches were taken to examine the numerical behavior of the NV: (i) varying both the fractal dimension ( \(\eta\) $\eta$ ) and the fractional order ( \(\omega\) $\omega$ ); (ii) varying \(\omega\) $\omega$ while maintaining \(\eta\) $\eta$ constant; and (iii) varying \(\eta\) $\eta$ while maintaining \(\alpha\) $\alpha$ constant. We analyzed simulation findings and visualizations of the above system using Python for numerical modeling, determining that the newly created Atangana-Baleanu fractal-fractional differential operators yield superior outcomes in comparison to the classical framework.