An SIRS Model of Virus Epidemic on a Computer Network

Recently, intense research has been on how to reduce the spread of virus on a network of computer systems, which involves the mathematical modelling of the spread of virus based on mathematical epidemiological approach. This is necessary because a threshold cannot be discerned from the data generated on the network, rather it requires a mathematical model to analyze and simulate the virus dynamics on the network. It also enables the calculation of the basic reproductive number (R0) which is an important threshold for determining whether the network is at risk or not. In this paper, we adopt the susceptible- infected-recovered-susceptible (SIRS) model to depict the spread of virus on the network. We qualitatively analyze the model and establish that the virus-free state is locally asymptotically stable provided the basic reproduction number is less than unity. We solved the model numerically and simulate the solution for different scenarios on the network. The findings from our simulations are discussed.