## 2 MSEIR Model  
Many different types of models have been used to capture infectious disease evolution, within a wide range of approaches. From the seminal paper [11] compartment models have been adopted as a well-established methodology even when this kind of model suffers limitations about the kind of phenomena considered in compartment models linked to the fact that most of the mechanisms driving/influencing the progress of an epidemic are unknown. However, in order to show the applicability of the proposed scheme in this paper it is considered a compartmental model in order to obtain simulation results, considering that this network can be parametrized with real-world data from an epidemic scenario. In such cases, the use of the neural identifier is a beneficial methodology to consider all real-world phenomena that are not considered in compartmental models. Compartmental models are generally composed of five compartments labeled with the letters \(M\), \(S\), \(E\), \(I\), and \(R\). The letter \(M\) represents individuals with passive immunity, which is temporary for certain diseases and is acquired by newborns through antibodies transferred from the mother (\(M\)). With the disappearance of these antibodies, the individuals move to the (\(S\)) susceptible class. The compartment \(S\) includes every individual that can be infected. When an individual from the \(S\) class has adequate contact with an infected person (defined as any activity that results in the infection of the susceptible individual) it is moved to the (\(E\)) exposed compartment. In this compartment, the individuals are in the latency phase, i.e., infected but still incapable of transmitting the disease. After this phase, the subject is moved to the (\(I\)) infectious class and is now capable of infecting others. After this period, they are moved to the (\(R\)) recovered compartment, becoming temporarily or permanently immune to the disease. Class \(R\) also includes the individuals that die due to the disease itself [7]. The acronyms used to refer to the different epidemiological models are based on flow patterns between the compartments: SI, SIS, SEI, SEIS, SIR, SIRS, SEIR, SEIRS, MSEIR, MSEIRS, etc. In this work, it is assumed that a recovered individual gains lifelong immunity. The birth and death rates are represented by \(b\) and are assumed to stay constant, keeping the total population (\(N=S+M+E+I+R\)) constant as well, this assumption is made only for academic proposes. The rate \(bS\) increases the number of individuals in the susceptible class \(S\) since newborns from susceptible mothers are also susceptible, these individuals are not a part of the \(M\) class. Evidently, the remaining individuals fall into one of the other remaining classes where, as mentioned before, the class \(M\) is where the passive immunity \(bN-S\) individuals are located. The time it takes for individuals to transition between classes varies for each case, depending on their health conditions and individual life characteristics where \(\delta M\), \(\mu S\), and \(eE\) represent the transfer out of \(M\), \(S\), and \(E\), respectively, and \(\gamma I\) is the rate of recovery from individuals in the infectious class \(I\) as shown in Figure 1.  
According to [12], the dynamic model of the compartmental system MSEIR is defined by the following set of ordinary differential equations  
\[ \begin{split}\dot{M}(t)&=b(N-S(t))-(\delta+b)M(t)\\ \dot{S}(t)&=bS(t)+\delta M(t)-\frac{\beta}{N}S(t)I( t)-bS(t)\\ \dot{E}(t)&=\frac{\beta}{N}S(t)I(t)-(\varepsilon+b) I(t)\\ \dot{I}(t)&=eE(t)-(\gamma+b)I(t)\\ \dot{R}(t)&=\gamma I(t)-bR(t)\end{split}  \tag{1}\]  
Figure 1: Basic elements of the compartmental model in infectious diseases. where, depending on the progression of the disease, time \(t\) can be expressed in hours, days, weeks, months, or years. Furthermore, the value of each parameter of the model is defined by the type of infectious disease that is represented.