<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Medvedeva, Marina</style></author><author><style face="normal" font="default" size="100%">Theodore E. Simos</style></author><author><style face="normal" font="default" size="100%">Tsitouras, Charalampos</style></author><author><style face="normal" font="default" size="100%">Vasilios Katsikis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Direct estimation of SIR model parameters through second-order finite differences</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematical Methods in the Applied Sciences</style></secondary-title><short-title><style face="normal" font="default" size="100%">Mathematical Methods in the Applied Sciences</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Covid-19</style></keyword><keyword><style  face="normal" font="default" size="100%">finite differences</style></keyword><keyword><style  face="normal" font="default" size="100%">least squares</style></keyword><keyword><style  face="normal" font="default" size="100%">SIR epidemic model</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2020</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2020</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1002/mma.6985</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">John Wiley &amp; Sons, Ltd</style></publisher><volume><style face="normal" font="default" size="100%">n/a</style></volume><isbn><style face="normal" font="default" size="100%">0170-4214</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">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.</style></abstract><issue><style face="normal" font="default" size="100%">n/a</style></issue><notes><style face="normal" font="default" size="100%">https://doi.org/10.1002/mma.6985</style></notes></record></records></xml>