Mathematical Model of Computer Viruses Spread on a Closed Network

Abstract

We consider a system with a population divided into compartments: strongly protected computers (S), weakly protected computers (W), infected computers (I), susceptible removable devices (Rₛ ), and infected removable devices ( Rᵢ). Given the dynamics between these compartments, we develop a mathematical model to study the effect of external removable devices on a system with both protected and unprotected computers (heterogeneous immunity). Considering certain factors such as infection rates, the rate at which removable devices are used, and the probability that infected devices connect with vulnerable computers, we form a system of differential equations that will predict the behavior of the virus. With our model, we determine the general form of the basic reproduction number to study the system and analyze its behavior under different parameters. It was found that increasing the parameters associated with installation of antivirus software and recovery of infected removable devices decreased the amount of infection present in the final equilibrium, and sufficient increase in these parameters yielded the virus free equilibrium. Conversely, decrease in the parameters associated with expiration of antivirus software and the infection of removable devices decreased the infection present in the equilibrium, with sufficient decrease giving the virus free equilibrium. We conclude that careful monitoring of antivirus software is the most effective method of virus elimination after a system has been infected, but management of removable devices is critically important in controlling virus spread. Adherence to these principles could protect the systems of individuals, corporations, and governments and prevent massive damages.