## 4 Discussion
Current results (Table 1) reveal that quarantine plays an important role in the first stages of an epidemic. Our findings are in good agreement with those of other studies which have shown that stringent restrictions in the quarantine framework reduce the infected subpopulation [23; 24]. With regard to vaccination, the current study assumed that all vaccines available possess the same effectiveness and that they build immunity to the same extent in all individuals. It demonstrated, however, the pivotal role of a successful vaccination program in eliminating an epidemic wave (Table 3). Other studies have also shown that efficient vaccination programs with high compliance rates lead to disease restriction. [25]. Moreover, a recently published study [26; 27] based on a stochastic approach has confirmed that social distancing measures can be relaxed after the successful implementation of a vaccination program [28]. The above analysis suggests that the proposed straightforward approach can be easily implementedto examine in-silico different pandemic or epidemic situations and infer conclusions that may facilitate decision-making. Nevertheless, realistic rates based on real-world data have to be employed to carry out reliable simulations. Viral load seems to be a feature that can provide insights into the disease evolution and can largely facilitate inter-comparisons between models and/or between different scenarios within the same model. Viral load estimation for a certain period of time constitutes a useful tool for physicians and policymakers to decide on precautionary measures and for physicians to plan and develop therapeutic interventions. Policymakers can weigh the potential benefits of certain policies against the costs emanating from the employment of such policies. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Model Parameters of the Model** & **Cumulative Viral Load** \\ \hline \multirow{5}{*}{CSIRQV} & \(\alpha\) = 0.18, \(\beta\) = 0.06, \(\gamma\) = 0.006 & \multirow{5}{*}{0.23} \\  & \(\delta\) = 0.001, \(\epsilon\) = 0.008333, \(\zeta\) = 0.06, & \\  & \(\eta\) = 0.0001, \(\theta\) = 0.0006, \(\iota\) = 0.006, & \\  & \(\kappa\) = 0.0000333, \(\lambda\) = 0.00001, & \\  & \(\mu\) = 0.0001 & \\ \hline \multirow{5}{*}{CSIRQV\_1} & \(\alpha\) = 0.18, \(\beta\) = 0.06, \(\gamma\) = 0.006 & \multirow{5}{*}{0.09} \\  & \(\delta\) = 0.001, \(\epsilon\) = 0.008333, \(\zeta\) = 0.06, & \\  & \(\eta\) = 0.0001, \(\theta\) = 0.0006, \(\iota\) = 0.006, & \\  & \(\kappa\) = 0.0000333, \(\lambda\) = 0.00001, \(\mu\) = 0 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Viral Load estimations for different scenarios of the CSIRQV model (t = 365 days). This work suffers from certain limitations [29; 30]. In the CSIRQV model studied several assumptions have been made (e.g., constant inter-compartmental rates were assumed, although involved rates, such as the infection to recovery rate, \(\beta\), may be time-dependent; seasonal infection was not considered; no time-delays in vaccination were examined; immunity waning was not investigated; variable social contact was not considered). Additionally, validation of the described models with real-world data was not performed, in particular, with regard to rates \(\eta\), \(\lambda\) and \(\iota\). However, the main scope of the current study was to computationally approach the relevant models available and highlight their differences rather than validating specific models with data that may be subject to under-reporting. A vaccine-resistant mutation virus was not studied separately from a wild-type virus and, subsequently, different mutation rates were not considered.