\begin{algorithm}[h!]
	\caption{Incremental learning for infection rates prediction}
	\label{alg:nnmethod}
	\begin{algorithmic}[1]
            \Statex \textbf{Input:} ``Lookback'' window size $W$, Day ahead to predict $D$
            \State Wait $W$ days to fill window.
            \State Create model $f^W.init()$ \Comment $j = W$
            \State Observe instance $\grave{\beta}^W = \{\beta^W, \beta^{W-1}, ..., \beta^1\}$
            \State Predict $\hat{\beta}^{W+1} = f^W.predict(\grave{\beta}^W)$
    	\For{each day $j \in [W + 1, W + D -1)$} \Comment Only predictions these days
                \State Observe ground truth $\beta^j$
                \State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
                \State Predict $\hat{\beta}^{j + D} = f^W.predict(\grave{\beta}^j)$ \Comment $f^W$ hasn't been updated yet
		  \EndFor
    	\For{each day $j \in [W + D, \infty)$} \Comment Predictions and training
                \State Observe ground truth $\beta^j$
                \State Incremental training $f^j = f^{j-1}.train((\grave{\beta}^{j-D}, \beta^j))$ \Comment As in Eq (\ref{eq:training})
                \State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
                \State Predict $\hat{\beta}^{j + D} = f^j.predict(\grave{\beta}^j)$
		  \EndFor
	\end{algorithmic}
\end{algorithm}

\begin{algorithm}
[h!]
\caption{Incremental learning for infection rates prediction}
\begin{algorithmic}
[1]
\Statex \textbf{Input:} ``Lookback'' window size $W$, Day ahead to predict $D$
\State Wait $W$ days to fill window.
\State Create model $f^W.init()$ \Comment $j = W$
\State Observe instance $\grave{\beta}^W = \{\beta^W, \beta^{W-1}, ..., \beta^1\}$
\State Predict $\hat{\beta}^{W+1} = f^W.predict(\grave{\beta}^W)$
\For{each day $j \in [W + 1, W + D -1)$} \Comment Only predictions these days
\State Observe ground truth $\beta^j$
\State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
\State Predict $\hat{\beta}^{j + D} = f^W.predict(\grave{\beta}^j)$ \Comment $f^W$ hasn't been updated yet
\EndFor
\For{each day $j \in [W + D, \infty)$} \Comment Predictions and training
\State Observe ground truth $\beta^j$
\State Incremental training $f^j = f^{j-1}.train((\grave{\beta}^{j-D}, \beta^j))$ \Comment As in Eq (\ref{eq:training})
\State Create instance $\grave{\beta}^j = \{\beta^j, \beta^{j-1}, .., \beta^{j-W+1}\}$
\State Predict $\hat{\beta}^{j + D} = f^j.predict(\grave{\beta}^j)$
\EndFor
\end{algorithmic}
\end{algorithm}
{
    "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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