Nonlocal and nonsingular kernel-based fractional dynamics of infectious disease with waning immunity

The burden of infections is a critical public health issue, and addressing it requires a multifaceted approach involving healthcare systems, governments, and communities. In this work, the dynamics of Japanese encephalitis (JE) is constructed with waning immunity using the Atangana-Baleanu fractional derivative. We introduce the fundamental theory related to the proposed fractional operator for the evaluation of the dynamics. The recommended model of the infection is examined for the essential results and the endemic indicator \(\mathcal{R}_0\) is determined with the help of next generation matrix approach. The existence and uniqueness of the solution of fractional-order system are evaluated via fixed point theory. Moreover, a newly developed numerical method is applied to iteratively solve our fractional-order model. Numerical simulations suggest that the management strategies are productive in reducing the prevalence of JE in humans, mosquitoes, and pigs. The fractional-order derivative provides more precise and realistic insights into the dynamics of JE, as evidenced by numerical findings that demonstrate the impact of various input factors on infection dynamics. Our research underscores the role of different factors of the recommended system for the management and control of the infection.