# COVID-19 Pandemic Prediction for Hungary; A Hybrid Machine Learning Approach
###### Abstract
\[\frac{dI}{dt}=\alpha SI-\beta I \tag{2}\]  
where \(\beta\) represents the parameter of the daily rate of spread. Furthermore, the susceptible individuals excluded from the SIR-based models are calculated. Furthermore, the class \(R\), representing individuals excluded from the spread of infection, is computed as follows:  
\[\frac{dR}{dt}=\beta I \tag{3}\]  
Considering the above-mentioned assumptions, and under the unconstrained conditions of the excluded group, Equation (3), the outbreak modeling with SIR is finally stated as:  
\[I\left(t\right)\approx I_{0}\;exp\left\{\left(\alpha-\beta\right)\right\}. \tag{4}\]  
Furthermore, to evaluate the accuracy of the SIR-based models, the outbreak model's median success function is used, which is represented as:  
\[f=\frac{Prediction}{True\;value}. \tag{5}\]Several analytical solutions to the SIR models have been provided in the literature [15; 16]. As the different nations take different actions toward slowing down the outbreak, the SIR-based model must be adapted according to the local assumptions [17]. The inaccuracy of many SIR-based models in predicting the outbreak and mortality rate has been evidenced during the COVID-19 in many nations. The critical success of a SIR-based model relies on choosing the right model according to the context and the relevant assumptions. SIS (susceptible-infectious-susceptible), SIRD (susceptible-infected-recovered-deceased-model), MSIR (Maternally-derived-immunity-susceptible-infected-recovered), SEIR (Susceptible-exposed-infected-recovered), SEIS (Susceptible-exposed-infected-susceptible), MSEIR (Maternally-derived-immunity-susceptible-exposed-infected-recovered-susceptible) models are among the popular derived-immunity-susceptible-exposed-infected-recovered-susceptible) models are among the popular models used for predicting COVID-19 outbreaks worldwide. The more advanced variation of SIR-d models carefully considers the vital dynamics and constant population [16]. For instance, at the presence of the long-lasting immunity assumption when the immunity is not realized upon recovery from infection, the susceptible-infectious-susceptible (SIS) model was suggested [18]. In contrast, the susceptible-infected-recovered-deceased-model (SIRD) is used when immunity is assumed [19]. In the case of COVID-19, different nations took different approaches in this regard. SEIR models have been reported among the most popular tools to predict the notable outbreaks. To advance an SEIR model, often, the incubation period of an infected person is carefully estimated to achieve more accurate predictions. In the case of Varicella and Zika outbreaks, the SEIR models showed increased model accuracy [20; 21]. To do so, SEIR models might assign the incubation period to a random variable. Furthermore, similar to the standard SIR-based models, SEIR models work on the ideology of the disease-free-equilibrium [22; 23]. However, it should be noted that SEIR models can not fit well where the contact network is non-stationary through time [24]. Social mixing as a critical factor of non-stationarity determines the reproductive number \(R_{0}\), which is the number of susceptible individuals for infection. The value of \(R_{0}\) for COVID-19 was estimated to be 4, which greatly trigged the pandemic [1]. The lockdown measures aimed at reducing the \(R_{0}\) value down to 1. Nevertheless, the SEIR models are reported to be difficult to fit in the case of COVID-19 due to the non-stationarity of mixing caused by nudging intervention measures. Therefore, to develop more accurate SIR-based models, in-depth information about the social movement and the quality of lockdown measures would be essential. Another drawback of SIR-based models is the short lead-time. For long-term prediction, the accuracy of the most SIR-based models declines. For the COVID-19 outbreak case of Italy, for instance, the accuracy of the model drops significantly. The performance of \(f=1\) for the lead-time of 120 h reduces to \(f=0.86\) for 144 h lead time [17].