A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response
The spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous m...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022597?viewType=HTML |
| _version_ | 1818049770078339072 |
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| author | Somayeh Fouladi Mohammad Kohandel Brydon Eastman |
| author_facet | Somayeh Fouladi Mohammad Kohandel Brydon Eastman |
| author_sort | Somayeh Fouladi |
| collection | DOAJ |
| description | The spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous model of the spread of SARS-CoV-2 in Ontario, "Modeling the impact of a public response on the COVID-19 pandemic in Ontario, " to include the discretized, Caputo fractional derivative in the susceptible compartment. We perform identifiability and sensitivity analysis on both the integer-order and fractional-order SEIRD model and contrast the quality of the fits. We note that both methods produce fits of similar qualitative strength, though the inclusion of the fractional derivative operator quantitatively improves the fits by almost 27% corroborating the appropriateness of fractional operators for the purposes of phenomenological disease forecasting. In contrasting the fit procedures, we note potential simplifications for future study. Finally, we use all four models to provide an estimate of the time-dependent basic reproduction number for the spread of SARS-CoV-2 in Ontario between January 2020 and February 2021. |
| first_indexed | 2024-12-10T10:42:51Z |
| format | Article |
| id | doaj.art-60874c3bf4454adbb8962cd924ff501f |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-10T10:42:51Z |
| publishDate | 2022-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-60874c3bf4454adbb8962cd924ff501f2022-12-22T01:52:15ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-09-011912127921281310.3934/mbe.2022597A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public responseSomayeh Fouladi0Mohammad Kohandel 1Brydon Eastman21. Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada 2. Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, P.O. Box 115, Shahrekord, Iran1. Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, Canada1. Department of Applied Mathematics, University of Waterloo, 200 University Ave W, Waterloo, ON N2L 3G1, CanadaThe spread of SARS-CoV-2 in the Canadian province of Ontario has resulted in millions of infections and tens of thousands of deaths to date. Correspondingly, the implementation of modeling to inform public health policies has proven to be exceptionally important. In this work, we expand a previous model of the spread of SARS-CoV-2 in Ontario, "Modeling the impact of a public response on the COVID-19 pandemic in Ontario, " to include the discretized, Caputo fractional derivative in the susceptible compartment. We perform identifiability and sensitivity analysis on both the integer-order and fractional-order SEIRD model and contrast the quality of the fits. We note that both methods produce fits of similar qualitative strength, though the inclusion of the fractional derivative operator quantitatively improves the fits by almost 27% corroborating the appropriateness of fractional operators for the purposes of phenomenological disease forecasting. In contrasting the fit procedures, we note potential simplifications for future study. Finally, we use all four models to provide an estimate of the time-dependent basic reproduction number for the spread of SARS-CoV-2 in Ontario between January 2020 and February 2021.https://www.aimspress.com/article/doi/10.3934/mbe.2022597?viewType=HTMLidentifiability analysisnumerical simulationcaputo fractional derivativel1-2 discretizationparameter estimationeffective reproduction numbercovid-19 |
| spellingShingle | Somayeh Fouladi Mohammad Kohandel Brydon Eastman A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response Mathematical Biosciences and Engineering identifiability analysis numerical simulation caputo fractional derivative l1-2 discretization parameter estimation effective reproduction number covid-19 |
| title | A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response |
| title_full | A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response |
| title_fullStr | A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response |
| title_full_unstemmed | A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response |
| title_short | A comparison and calibration of integer and fractional-order models of COVID-19 with stratified public response |
| title_sort | comparison and calibration of integer and fractional order models of covid 19 with stratified public response |
| topic | identifiability analysis numerical simulation caputo fractional derivative l1-2 discretization parameter estimation effective reproduction number covid-19 |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022597?viewType=HTML |
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