Modeling and numerical analysis of fractional order hepatitis B virus model with harmonic mean type incidence rate

A Numerical Study Based on Haar Wavelet Collocation Methods of Fractional-Order Antidotal Computer Virus Model

Computer networks can be alerted to possible viruses by using kill signals, which reduces the risk of virus spreading. To analyze the effect of kill signal nodes on virus propagation, we use a fractional-order SIRA model using Caputo derivatives. In our model, we show how a computer virus spreads in a vulnerable system and how it is countered by an antidote. Using the Caputo operator, we fractionalized the model after examining it in deterministic form. The fixed point theory of Schauder and Banach is applied to the model under consideration to determine whether there exists at least one solution and whether the solution is unique. In order to calculate the approximate solution to the model, a general numerical algorithm is established primarily based on Haar collocations and Broyden’s method. In addition to being mathematically fast, the proposed method is also straightforward and applicable to different mathematical models.

Modeling and numerical analysis of a fractional order model for dual variants of SARS-CoV-2☆

This paper considers the novel fractional-order operator developed by Atangana-Baleanu for transmission dynamics of the SARS-CoV-2 epidemic. Assuming the importance of the non-local Atangana-Baleanu fractional-order approach, the transmission mechanism of SARS-CoV-2 has been investigated while taking into account different phases of infection and various transmission routes of the disease. To conduct the proposed study, first of all, we shall formulate the model by using the classical operator of ordinary derivatives. We utilize the fractional order derivative and the model will be extended to a model containing fractional order derivatives. The operator being used is the fractional differential operator and has fractional order Φ1. The model is analyzed further and some basic aspects of the model are investigated besides calculating the basic reproduction number and the possible equilibria of the proposed model. The equilibria of the model are examined for stability purposes and necessary conditions for stability are obtained. Stability is also necessary in terms of numerical setup. The theory of non-linear functional analysis is employed and Ulam-Hyers’s stability of the model is presented. The approach of newton’s polynomial is considered and a new numerical scheme is developed which helped in presenting an iterative process for the proposed ABC system. Based on this scheme, sample curves are obtained for various values of Φ1 and a pattern is derived between the dynamics of the infection and the order of the derivative. Further simulations are presented which show the cruciality and importance of various parameters and the impact of such parameters on the dynamics and control of the disease is presented. The findings of this study will also provide strong conceptual insights into the mechanisms of contagious diseases, assisting global professionals in developing control policies.