In this paper, we have developed a compartmental e-Epidemic SIJR (Susceptible-Infectious-Highly Infectious-Recovered) model of viruses in a computer network with natural death (that is, crashing of nodes due to the reason other than the attack of viruses). The local asymptotically stability of the system has been discussed using the Jacobian and the explicit formula for basic reproduction number has been derived. Numerical methods and MATLAB are employed to solve and simulate the system of equations developed and analysis of the model gives remarkable exposure.