Abstract
The concept of information science is inevitable in the human development as science and technology has become the driving force of all economics. The connection of one human being during epidemics is vital and can be studied using mathematical principles. In this study, a well-recognized model of computer virus by Piqueira et al. (J Comput Sci 1:31−34, 2005) and Piqueira and Araujo (Appl Math Comput 2(213):355−360, 2009) is investigated through the Caputo and beta-derivatives. A less detail of stability analysis was discussed on the extended model. The analytical solution of the extended model was solved via the Laplace perturbation method and the homotopy decomposition technique. The sequential summary of each of iteration method for the extend model was presented. Using the parameters in Piqueira and Araujo (Appl Math Comput 2(213):355−360, 2009), some numerical simulation results are presented.
Highlights
The idea of computer virus came into being around 1980 and has continued threatening the society
In 2001, for example, the cost associated with computer virus was estimated to be 10.7 United State dollars for only the first quarter [1]
A comprehensive understanding of computer virus dynamics has become inevitable to researchers considering the role played by this wonderful device
Summary
The idea of computer virus came into being around 1980 and has continued threatening the society. The fractional order, is an indispensable tool for numerical simulations, and a local derivative with fractional order is presented in this study to model the propagation of computer virus in a network. This provides the invariance of as to be determined. Analysis of approximate solutions One of the most challenging tasks in non-linear fractional differential equation systems is probably how to obtain exact analytical solutions This accounts for the reasons why in recent times, a lot of attention has been devoted in the quest for obtaining techniques that can ensure asymptotic solutions in such situations.
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