Abstract
In this article, a dynamical model with advection-diffusion, elucidating the transmission process of disease infection type computer virus, is studied. Such kind of systems help to alleviate the effects of virus by prior predictions described in the model. The existence and uniqueness of the solutions of the system is investigated. A solution space (Banach space) is considered to make the possibility of existence of the solutions of proposed system. A closed and convex subset is defined in the Banach space, in which the solutions of the coupled system are optimized. The essential explicit estimates for the solutions are also calculated for the corresponding auxiliary data. Moreover, a non-standard finite difference scheme is applied to find the approximate solution of the prescribed problem. For the validity of the proposed scheme, the possession of some important structural properties by the applied numerical technique are presented. These structural properties are consistency and stability. To prove the numerical stability, Von-Neumann criteria is adopted. In the study of such population dynamics type models, positivity is one of the most important physical properties of the numerical scheme that must be preserved. To prove the positivity of the numerical method, a reliable result is established. The validation of the present study is shown by illustrating an example. The behaviors of the state variables are described by plotting the graphs of the associated example.