Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

Abstract

This research aims to understand the fractional order dynamics of the deadly Nipah virus (NiV) disease. We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system. We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem. By utilizing the Newtonian polynomials interpolation technique, we recall a powerful algorithm to interpret the numerical findings for the aforesaid model. Here, we remark that the said viral infection is caused by an RNA type virus which can transmit from animals and also from an infected person to person. Fruits bats which are also known as flying foxes are one of the sources of transmission of NiV disease. Here in this work, we investigate its transmission mechanism through some new concepts of fractional calculus for further analysis and prediction. We present the approximate results for different compartments using different fractional orders. By using the piecewise derivative concept, we detect the crossover or multi-steps behavior in the transmission dynamics of the mentioned disease. Therefore, the considered form of the derivative is used to deal with problems exhibiting crossover behaviors.