Real-Time Estimation of <i>R</i>₀ for COVID-19 Spread

• Main Authors: Theodore E. Simos, Charalampos Tsitouras, Vladislav N. Kovalnogov, Ruslan V. Fedorov, Dmitry A. Generalov
• Format: Article
• Language: English
• Published: MDPI AG 2021-03-01
• Series: Mathematics
• Subjects: SIR epidemic model; COVID-19; ordinary differential equations; splines; least squares
• Online Access: https://www.mdpi.com/2227-7390/9/6/664
• ISSN: 2227-7390

We propose a real-time approximation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> in an SIR-type model that applies to the COVID-19 epidemic outbreak. A very useful direct formula expressing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula> is found. Then, various type of models are considered, namely, finite differences, cubic splines, Piecewise Cubic Hermite interpolation and linear least squares approximation. Preserving the monotonicity of the formula under consideration proves to be of crucial importance. This latter property is preferred over accuracy, since it maintains positive <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>. Only the Linear Least Squares technique guarantees this, and is finally proposed here. Tests on real COVID-19 data confirm the usefulness of our approach.