# An Integrated Neural Network and SEIR Model to Predict COVID-19
## 3 Methodology  
### SEIR Model  
We used the well-known SEIR compartmental model because of the uncertainty due to incomplete identification of the infected population. Similarly, E, I, and R denote the population figures in the exposed, infected, and recovered or removed compartments, respectively. The architecture of the SEIR model is shown in Figure 1.  
\(\beta\) denotes the transmission rate, which is also known as the infection rate. The onset rate \(\varepsilon\) is the inverse of the incubation period, and \(\gamma\) denotes the removal rate, which is the inverse of the infection period. The following differential equations are used to change the status of each compartment at time \(t\) (\(t>0\)). \[\frac{dS}{dt}=-\beta S(t)I(t) \tag{1}\]  
\[\frac{dE}{dt}=\beta S(t)I(t)-\varepsilon E(t) \tag{2}\]  
\[\frac{dI}{dt}=\varepsilon E(t)-\gamma I(t) \tag{3}\]  
\[\frac{dR}{dt}=\gamma I(t) \tag{4}\]  
In the above equations, \(dS/dt\) denotes the number of infected patients changed in the susceptible compartment. Similarly, \(dE/dt\), \(dl/dt\), and \(dR/dt\) denote the change in the \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt} p{142.3 pt} p{142.3 pt}} \hline \hline
**Ref. No.** & **Description** & **Model** & **Limitation** \\ \hline
[11] & Forecasted the latest pandemic situation of COVID-19 inside and outside of China until 7 March 2020. & Time varying SIR & Applicable only in China. \\ \hline
[12] & Introduced a new parameter named testing rates accompanying transmission rate and transition rate. The outcome of this experiment suggests that there is a strong benefit in tracing and moving tests. & Fractional type SEIR & Cannot predict the number of quarantined persons in a day. \\ \hline
[13] & Predicted the disability-adjusted life years (DALYs) of Iran. The result shows that the total DALYs among women and men are 861 years/100,000 and 1082/100,000, respectively. & Extended SEIR & Cannot suggest an end date to the pandemic. \\ \hline
[14] & Assessed the impact of non-pharmaceutical interventions during this pandemic & Modified SEIR & Cannot analyze the impact of a lockdown in any area. \\ \hline
[15] & Considered the exponential phases of this disease in Italy, France, China, Switzerland, Spain, the UK, New York State, and Germany. The range was estimated as 4.7 to 11.4, which was higher than previous estimates. & SEIR & Cannot calculate results for specific parts of a country. \\ \hline
[18] & The removed compartment was extended using two new compartments: death and cured. The model parameters was estimated depending on the issued data of China. & Improved SEIR & Applicable only in China. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 1: SEIR (Susceptible, Exposed, Infected, Removed) model. exposed, infected, and removed compartments, respectively. The number of infective persons who are diagnosed at time t can be identified using the following equation that was proposed in [7]. \[Y(t)=\rho I(t)N \tag{5}\]  
where \(\rho\) (\(\rho\leq 1\)) is the fraction of infective persons who can be identified by diagnosis and \(N\) is the population figure of the region. \(R_{0}\) is considered an important parameter since it enables us to know the secondary cases produced by one infected person in an area [20]. Hence, the outbreak of an infectious disease can be determined by using this value. The \(R_{0}\) value of an infectious disease at greater than one means there could be a chance of outbreak or epidemic while a value at less than one determines that there is no risk of an outbreak [21]. In the case of COVID-19, if the \(R_{0}\) value is considered at 3, a person with this disease can infect three persons and then they can infect nine persons, then they can infect 81 persons, then they can infect 243 persons, and so on. The reason for this is that the infection rate grows exponentially. Therefore, a single confirmed case in a locality is enough to infect all its population if strict measures are not followed.