Capturing the interplay between malware and anti-malware in a computer network

Keywords: Mathematical model Computer networks Malware Anti-malware Stability a b s t r a c t In an era with affluence of local area networks, the recurrent attacks of viruses and other malicious objects are undoubtedly an intruding threat. These malicious objects spread quickly through an unprotected network, corrupt the data and harm the nodes. To comprehend this problem and its plausible solutions more thoroughly, we have proposed and analyzed a mathematical model by considering a network in which nodes are either infected or prone to it. It is considered that nodes vulnerable to infection become infected, when attacked by malicious objects present in the network. To minimize the abundance of malicious objects and infected nodes, some anti-malware softwares are installed in the network , which are continuously being updated. On analyzing the proposed model, we obtained two equilibria and a threshold governing the dynamics of malicious objects in a computer network. The characterization of stability behavior of obtained equilibria is also discussed in detail. The numerical simulation illustrates the validity of analytically obtained results. With the evolution of computer networks, the need of protecting files and other information stored on the computers have become imperative. Peer-to-peer file sharing amongst operating systems and other widely distributed network soft-wares provide favorable conditions for malicious attacks. Due to this, the spread of viruses, worms, Trojans and other malicious softwares have increased dramatically in the last decade. Malicious softwares or malwares are the programs written with an intention to cause some kind of damage to computer systems and networks. Computer viruses are most widely recognized class of malware. Once a virus enters any computer or network, it performs two functions: it infects other programs by copying itself and it executes malicious codes those have been included by author in it. These viruses are especially designed to damage the system and their effect can be so extensive that the complete rebuilding of all softwares and data may be required. Due to the swift spreading nature of computer viruses, the damage can multiply in the network topology within a fraction of time. The computer viruses have acquired this name due to their resemblance with the biological viruses. Biological viruses transmit from person-to-person, while computer viruses pass from computer-to-computer. A biological virus is a fragment of DNA inside a protective jacket, which injects its DNA into a cell to reproduce itself. A computer virus does the …