	\begin{algorithmic}[1]
            \Statex \textbf{Inputs:} $s,i,d,a,r,e,v,h$, daily vaccinations
            \Statex \textbf{Output:} 
            {$\vec{\beta}_{uu}, \vec{\beta}_{vu}, \vec{\beta}_{vv}$, $\vec{\beta}_{uv}$} 
            \Statex \textbf{Initialization:} $n=7$ or $n= 14$
            \For{each time step $j$} 
                \State Select window $z_{j}=\{j-n+1,...,j\}$
                \State Initialize parameters $\beta_{uu}$, $\beta_{vu}$, $\beta_{vv}$, $\beta_{uv}$
                \State Calculate the initial cost $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$
                \State $flag=0$
                \While{$flag=0$}
                    \State Create the trial parameters set $P_{k}$
                    \State Calculate a cost using every parameter from $P_{k}$ set
                    \State Find the minimum of all costs $C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$ \If{$C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j}) < C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$}
                        \State $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j}) = C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$
                        \State Keep the modified infection rate and create new set of trial parameters $P_{k}'$
                        \Else
                        \State $flag=1$
                        \State {$\vec{\beta}_{uu}(j)=\beta_{uu}$}
                        \State{$\vec{\beta}_{vu}(j) =\beta_{vu}$}
                        \State{$\vec{\beta}_{vv}(j)=\beta_{vv}$}
                        \State{$\vec{\beta}_{uv}(j)=\beta_{uv}$}
                    \EndIf
                \EndWhile
            \EndFor
	\end{algorithmic}

\begin{algorithmic}
[1]
\Statex \textbf{Inputs:} $s,i,d,a,r,e,v,h$, daily vaccinations
\Statex \textbf{Output:}
{$\vec{\beta}_{uu}, \vec{\beta}_{vu}, \vec{\beta}_{vv}$, $\vec{\beta}_{uv}$}
\Statex \textbf{Initialization:} $n=7$ or $n= 14$
\For{each time step $j$}
\State Select window $z_{j}=\{j-n+1,...,j\}$
\State Initialize parameters $\beta_{uu}$, $\beta_{vu}$, $\beta_{vv}$, $\beta_{uv}$
\State Calculate the initial cost $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$
\State $flag=0$
\While{$flag=0$}
\State Create the trial parameters set $P_{k}$
\State Calculate a cost using every parameter from $P_{k}$ set
\State Find the minimum of all costs $C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$ \If{$C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j}) < C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j})$}
\State $C_{j}(n,i,d,\hat{i}_{j},\hat{d}_{j}) = C_{j}'(n,i,d,\hat{i}_{j},\hat{d}_{j})$
\State Keep the modified infection rate and create new set of trial parameters $P_{k}'$
\Else
\State $flag=1$
\State {$\vec{\beta}_{uu}(j)=\beta_{uu}$}
\State{$\vec{\beta}_{vu}(j) =\beta_{vu}$}
\State{$\vec{\beta}_{vv}(j)=\beta_{vv}$}
\State{$\vec{\beta}_{uv}(j)=\beta_{uv}$}
\EndIf
\EndWhile
\EndFor
\end{algorithmic}
{
    "title": "pandemic infection forecasting through compartmental model and   learning-based approaches",
    "id": "2401.06629",
    "abstract": "the emergence and spread of deadly pandemics has repeatedly occurred throughout history, causing widespread infections and loss of life. the rapid spread of pandemics have made governments across the world adopt a range of actions, including non-pharmaceutical measures to contain its impact. however, the dynamic nature of pandemics makes selecting intervention strategies challenging. hence, the development of suitable monitoring and forecasting tools for tracking infected cases is crucial for designing and implementing effective measures. motivated by this, we present a hybrid pandemic infection forecasting methodology that integrates compartmental model and learning-based approaches. in particular, we develop a compartmental model that includes time-varying infection rates, which are the key parameters that determine the pandemic's evolution. to identify the time-dependent infection rates, we establish a hybrid methodology that combines the developed compartmental model and tools from optimization and neural networks. specifically, the proposed methodology estimates the infection rates by fitting the model to available data, regarding the covid-19 pandemic in cyprus, and then predicting their future values through either a) extrapolation, or b) feeding them to neural networks. the developed approach exhibits strong accuracy in predicting infections seven days in advance, achieving low average percentage errors both using the extrapolation (9.90%) and neural network (5.04%) approaches.",
    "categories": "q-bio.pe math.oc q-bio.qm",
    "doi": "",
    "created": "2024-01-12",
    "updated": "",
    "authors": [
        "marianna karapitta",
        "andreas kasis",
        "charithea stylianides",
        "kleanthis malialis",
        "panayiotis kolios"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2401.06629"
}
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