Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 44, Issue 5, Pages 3819-3826Publisher
WILEY
DOI: 10.1002/mma.6985
Keywords
COVID-19; finite differences; least squares; SIR epidemic model
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The SIR model is used for infectious disease modeling, and parameter estimation through least squares approach shows the simplicity and accuracy of the method.
SIR model is widely used for modeling the infectious diseases. This is a system of ordinary differential equations (ODEs). The numbers of susceptible, infectious, or immunized individuals are the compartments in these equations and change in time. Two parameters are the factor of differentiating these models. Here, we are not interested in solving the ODEs describing a certain SIR model. Given the observed data, we try to estimate the parameters that determine the model. For this, we propose a least squares approach using second-order centered differences for replacing the derivatives appeared in the ODEs. Then we arrive at a simple linear system that can be solved explicitly and furnish the approximations of the parameters. Numerical results over various artificial data verify the simplicity and accuracy of the new method.
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