**2. Epidemiological models**

In 1927 was published for the first time a deterministic model to study the dynamics of virus spread in populations. This was a compartmental model consisting of three compartments (susceptible—infected—removed) [9]. In this work, a theory was developed relating the development of an epidemic to a critical value, later known as the basal reproduction number *R*0.

The modeling of epidemics is associated with the dynamic behavior of processes where populations are studied according to their epidemiological status, these processes are described by differential equations, and the dynamics between their states is given by different parameters such as birth rate, mortality rate, infection, and recovery rate.

The modeling of the spread of epidemics has been the objective of many works [11–15]. These models allow a better understanding of the mechanisms of disease spread and can lead to more effective control strategies.

The scientific literature in epidemiology is quite diverse. Among the most cited models regarding this topic are the models: susceptible—infectious—susceptible (SIS) models [16–19]; susceptible—infected—recovered (SIR) models [20–25]; susceptible —exposed—infected—recovered (SEIR) models [26–28]; susceptible—exposed infected—quarantined—recovered (SEIQR) models; susceptible—exposed—infected —quarantined—recovered—susceptible (SEIQRS) [29]; susceptible—exposed infected—recovered—susceptible—vaccined (SEIRS-V) [30]; susceptible—exposed —infected—susceptible—vaccined (SEIS-V) [31] and others.

As for the way of treating chance, it can be classified into two levels: stocchastic and deterministic. In the first case, the model includes variables, giving a probabilistic distribution to the system, incorporating uncertainty, an intrinsic characteristic of epidemiological systems [32–35]. On the other hand, deterministic models provide the same results every time they are simulated with the same initial conditions [36, 37], being suitable to verify system sensitivity to the variation of the parameters [20, 21, 38].

Adapting the SIR model to computers, a lot of research has contributed to the understanding of virus propagation [26, 28–31, 39, 40] and one of the main goals is to establish effective security strategies [41].

The most explored strategies in cybersecurity are related to the use of antiviral compartments (A) and quarantine (Q). The adaptation of the SIR model gave rise to some robust models, including susceptible—infected—removed—antidotal (SIRA) [21] and susceptible—infected—removed—antidotal (SIQRA) [42].

Following this line, the first analysis of clustered computer networks using an epidemiological model studied the influence between two networks equipped with computers with antivirus and evaluated the dynamics of virus promotion and suggested viral dissemination control strategies.
