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Direct estimation of SIR model parameters through second‐order finite differences
Author(s) -
Medvedeva Marina,
Simos Theodore E.,
Tsitouras Charalampos,
Katsikis Vasilios
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6985
Subject(s) - ode , mathematics , ordinary differential equation , simple (philosophy) , simplicity , epidemic model , differential equation , least squares function approximation , mathematical optimization , mathematical analysis , statistics , population , philosophy , demography , epistemology , estimator , sociology
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.