# COVID-19 Outbreak Prediction with Machine Learning
## 1 Introduction  
Access to accurate outbreak prediction models is essential to obtain insights into the likely spread and consequences of infectious diseases. Governments and other legislative bodies rely on insights from prediction models to suggest new policies and to assess the effectiveness of the enforced policies [1]. The novel coronavirus disease (COVID-19) has been reported to have infected more than 2 million people, with more than 132,000 confirmed deaths worldwide. The recent global COVID-19 pandemic has exhibited a nonlinear and complex nature [2]. In addition, the outbreak has differences with other recent outbreaks, which brings into question the ability of standard models to deliver accurate results [3]. In addition to the numerous known and unknown variables involved in the spread, the complexity of population-wide behavior in various geopolitical areas and differences in containment strategies dramatically increased model uncertainty [4]. Consequently, standard epidemiological models face new challenges to deliver more reliable results. To overcome this challenge, many novel models have emerged which introduce several assumptions to modeling (e.g., adding social distancing in the form of curfews, quarantines, etc.) [5; 6; 7]. To elaborate on the effectiveness of enforcing such assumptions, understanding standard dynamic epidemiological (e.g., susceptible-infected-recovered, SIR) models is essential [8]. The modeling strategy is formed around the assumption of transmitting the infectious disease through contacts, considering three different classes of well-mixed populations; susceptible to infection (class \(S\)), infected (class \(I\)), and the removed population (class \(R\) is devoted to those who have recovered, developed immunity, been isolated, or passed away). It is further assumed that the class \(I\) transmits the infection to class \(S\) where the number of probable transmissions is proportional to the total number of contacts [9; 10; 11]. The number of individuals in the class \(S\) progresses as a time series, often computed using a basic differential equation as follows (Equation (1)):  
\[\frac{dS}{dt}=-\alpha SI \tag{1}\]  
where \(I\) is the infected population, and \(S\) is the susceptible population, both as fractions. \(\alpha\) represents the daily reproduction rate of the differential equation, regulating the number of susceptible infectious contacts. The value of \(S\) in the time series produced by the differential equation gradually declines. Initially, it is assumed that at the early stage of the outbreak \(S\approx 1\) while the number of individuals in class \(I\) is negligible. Thus, the increment \(\frac{dI}{dt}\) becomes linear and the class \(I\) eventually can be computed as follows (Equation (2)):  
\[\frac{dI}{dt}=\alpha SI-\beta I \tag{2}\]  
where \(\beta\) regulates the daily rate of new infections by quantifying the number of infected individuals competent in the transmission. Furthermore, the class \(R\), representing individuals excluded from the spread of infection, is computed as follows:  
\[\frac{dR}{dt}=\beta I \tag{3}\]  
Under the unconstrained conditions of the excluded group, Equation (3), the outbreak exponential growth can be computed as follows (Equation (4)):  
\[I\ (t)\approx\ I_{0}\ \exp[(\alpha-\beta)] \tag{4}\]  
The outbreaks of a wide range of infectious diseases have been modeled using Equation (4). However, for the COVID-19 outbreak prediction, due to the strict measures enforced by authorities, the susceptibility to infection has been manipulated dramatically. For example, in China, Italy, France, Hungary, and Spain the SIR model cannot present promising results, as individuals committed voluntarily to quarantine and limited their social interaction. However, for countries where containmentmeasures were delayed (e.g., United States) the model has shown relative accuracy [12].