**1. Introduction**

Computer viruses emerged as programs capable of harming the functioning of a machine. Initially, the damage was minor as well as its proliferation capacity. With the increasing access to communication networks, the great development of hardware and software, and the inclusion of these services as an essential part of daily life, computer viruses have become a threat [1, 2].

Virus program codes are complex and easy to replicate, and detection and removal by antivirus programs are difficult [3]. Some feats of these viral programs are the

ability to acquire bank passwords, personal data, and confidential information [4], which can cause immeasurable damage [5].

The increase in the use of mobile devices combined with the increasing access to wireless Internet facilitated the execution of many daily tasks such as accessing e-mail, electronic transactions of various natures and created opportunities for the advent of the Internet of Things (IoT), and connecting sensors and actuators to allow different types of objects to establish connections to the Internet, including home appliances, cars, and even industrial equipment. Therefore, these items are able to collect and transmit data from the cloud, contributing to a digital transformation in the world, and can provide several improvements in human life [6].

Consequently, understanding the spread of viruses in computer networks has become fundamental for the establishment of strategies to control and mitigate the spread of viruses. To improve the security and reliability of networks, a new branch of study, known as cybersecurity, has contributed to guide control strategies in order to minimize losses and one of its approaches is to build mathematical models.

One of the areas of cybersecurity is related to the study of the propagation of viruses in computer networks. Many ways of approaching the problem have been relevant to the understanding of the dissemination of malware, including the mathematical approach.

The mathematical study of computer viruses has an inspiration in biology and can be understood at two levels: microscopic and macroscopic [2, 7]. The tools used to develop antivirus programs, which are programs capable of detecting threats and preventing damage to machines, are concentrated at the microscopic level. In addition, the propagation of viruses in the network can be mitigated by the action of antivirus and quarantines proposed by the software when detecting some unexpected action [8].

The macroscopic level was developed from the classical model of disease propagation whose dynamics indicate the possibility of infection [9] and favor the orientation of strategies to control dissemination. The classic epidemiological model, proposed by Kermack and McKendrick, suggests the division of the population into compartments containing the group of susceptible (S), infected (I), and removed (R), giving rise to the SIR model, whose dynamics and parameters indicate strategies for control [9, 10].

Inspired by the above-mentioned works and based on the compartment level SIR model, this chapter considers the review of relationship between networks and the influence of the biolocical compartmental models for cybersecurity. Different from the conventional compartimental level models, this study shows the issue of how the association of two compartmental models occurs and indicates future prospects.

This work reviews the develop and analyze a model of virus propagation in two independent populations where those who ware infected from one population can come into contact with those who are susceptible from the other, to analyze the effects that one infected population can cause on the other. For this, two clusters were created and each cluster represents a population, both exposed to the same virus and represented by a model with antoidotal compartment. To represent the interaction between the two populations, a new connection between the sets was created and represents the capacity of an infected person come into contact with a susceptible one from the other, and this interaction will be modulated by a parameter.

The remaining chapter is ordered as follows: In the next section, a review of epidemiological models is presented with applications in computers, in section 3, hypothesis and equations are presented for the model with antidotal compartment, and the cluster model is presented, followed by the conclusion.
