## 2 Material and Methods
### Epidemiological Model: SEPAI3R3O  
The literature has extensively discussed the use of compartmental models for studying infectious diseases. The SEIR model, for example, divides the population into susceptible, exposed, infectious, and recovered compartments. Each of these compartments is modelled using a set of differential equations. The model assumes that the population is divided into four groups, represented by the letters in the model name:  
* Susceptible (S): People who have not yet been exposed to the virus but are susceptible to contracting it. * Exposed (E): Individuals who have been in contact with the virus and are carrying the infection but have not yet reached the stage where they can transmit the virus to others. At this stage, they do not show symptoms and are not contagious. * Infectious (I): People who are infected and are infectious. These people show symptoms and can infect susceptible individuals if they contact them. * Recovered (R): People who no longer have the virus (either because they have recovered or have died) cannot be infected again. In the SEIR model, controlling how these groups interact is possible and specifying the average transition time between groups. It is necessary to define entry and exit rates for all these groups, which control how an individual moves from one group to another. As these groups (i.e., stages of the disease/compartments) follow the order of the model (S \(\rightarrow\) E \(\rightarrow\) I \(\rightarrow\) R), the exit rate of the previous group is used as the entry rate for the new group. In the case of the susceptible (S) group, there is no entry rate, as this model assumes that no one can be re-infected. The spread of the virus and the exit rate are controlled by the number of contacts that infected individuals have with susceptible individuals. This is the same rate that defines the entry of new people into the exposed (E) group who have been contaminated but are not yet infectious. The time in this group refersto the disease's incubation period, and the exit refers to the transition to the infectious group who can transmit the disease to susceptible individuals and usually show symptoms. In the infectious (I) group, the exit rate is controlled by the recovery or death rate; this is commonly known as the case fatality rate (CFR), which is the ratio of deaths caused by the disease to the number of infected people. For the infectious group, it is also necessary to model a contamination rate of susceptible individuals by the infectious ones; the number of new people exposed to the virus also depends on the expected number of new infections generated by an infectious person. This rate is called the primary reproduction number (R0). The recovered (R) group only has an entry rate, as this model considers that there is nowhere else to go once in this group. In this article, we apply a variation of this model that we call SEPAI3R3O. The numbers added to each compartment indicate that the groups are subdivided into more subgroups; in particular, in this model, we use Exposed (E), Pre-symptomatic (P), Asymptomatic (A), three groups of Infectious (I), and three groups of Recovered (R), in addition to adding a new group called O which represents the deceased. Separating the deceased as a new group is a practice used in other adapted models, as detailed in Section 3, as recovery and death are opposite outcomes for the infected, in addition to the need for analytical interest in both cases. The model includes the possibility that exposed individuals who have not yet developed symptoms can transmit the virus (\"pre-symptomatic transmission\"). To model this situation, we added the P class (without symptoms but can transmit). Another common condition is the presence of people who contract the virus but do not show symptoms, for which the A class (asymptomatic individuals) was included.