Reaction–diffusion systems are mathematical models which link to several physical phenomena. The most common is the change in space and time of the meditation of one or more materials. Reaction–diffusion modeling is a substantial role in the modeling of computer propagation like infectious diseases. We investigated the transmission dynamics of the computer virus in which connected to each other through network globally. The current study devoted to the structure

Computer viruses are automated programs that, against the users’ wish, make copies of themselves to spread to new targets and as a result infect the computers [_{1}I_{2}QR model in which they examine types of malware acquired based on infection symptoms treatment. In 2016, Xu et al. [

with initial conditions

and homogenous Neumann boundary conditions. Where

The model

where,

Divide

Take

Similarly we have from

where

This section is concerned about the verification of the proposed scheme to be consistent. For this,

By putting all these definitions’ in

Similarly we can check for

Hence our proposed scheme is consistent and first order accurate in time and second order accurate in space.

In this section, we will use von Neumann stability criteria to show our proposed implicit scheme from

And

Put all these terms in

where

After proper calculation and rearranging terms, we have

Take absolute value on both sides, we have the following inequality,

By using similar process for

and

Inequalities from

If

The off-diagonal and diagonal entries of

Thus

This implies

Suppose that

Also

⇒ R.H.S of

So

Hence our proposed implicit scheme preserve positivity.

In this section, we demonstrate a numerical example and simulations for the application of proposed structure preserving technique. For this we consider the following initial conditions,

First we discuss the simulations of proposed structure preserving method at CVF point. For the CVF point we take the following values of parameters involved in the model so that the value of

Now we present the simulations of proposed structure preserving method at CVE point. For the CVE point we use the following values of parameters involved in the model so that the value of

In this paper, we propose an extended reaction–diffusion epidemic model of computer virus dynamics for the numerical investigation. An efficient and reliable numerical technique is designed which preserves the stability of equilibria and positivity of the approximation. The stability, consistency, and positivity of the proposed algorithm are shown mathematically and are validated graphically with the help of a numerical example. The proposed algorithm can be used for the solution of reaction–diffusion models like predator-prey models, chemical reaction models and infectious disease models. In future work, we shall extend the modeling of a computer virus in the computer population in the well-known notations like fractional and stochastic fractional-order derivatives [

The authors are grateful to anonymous referees. Also, thankful to the Vice-Chancellor of University of the Lahore, National College of Business Administration and Economics Lahore and University of Central Punjab Lahore, for providing an excellent research environment and facilities.