Recently, there has been great concern about the serious burden and damage caused by malicious objects, such as computer worms, on the Internet. Therefore, the establishment of efficient policies for preventing the propagation of malicious objects becomes an important issue in the operation of computer networks. Because the propagation of malicious code is similar in many aspects to the infectious spread of biological viruses, ordinary-differential-equation-based population models, frequently used in the field of epidemiology, are useful in studying the population change of infectious hosts in computer networks. In this paper, we propose the controlled susceptible-exposed-infectious-removed-antidotal (C-SEIRA) model, an epidemiological population model describing the state transitions of a computer network under malicious code infection. For the proposed model, we derive stability results for the infection-free state and the endemic state. In addition, we apply optimal control theory to the C-SEIRA model with the goal of minimizing the infectious compartment population and the system treatment cost of isolating infectious computers from the network. Simulation results show that the spread of malicious objects can be controlled reasonably well via the optimal control approach.
Ahn, I., Oh, H. C., & Park, J. (2015). Investigation of the C-SEIRA model for controlling malicious code infection in computer networks. Applied Mathematical Modelling, 39(14), 4121–4133. https://doi.org/10.1016/j.apm.2014.12.038