A generalized distributed delay model of COVID-19: An endemic model with immunity waning
The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been spreading worldwide for over two years, with millions of reported cases and deaths. The deployment of mathematical modeling in the fight against COVID-19 has recorded tremendous success. However, most of these models target th...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023249?viewType=HTML |
| _version_ | 1811165008043704320 |
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| author | Sarafa A. Iyaniwura Rabiu Musa Jude D. Kong |
| author_facet | Sarafa A. Iyaniwura Rabiu Musa Jude D. Kong |
| author_sort | Sarafa A. Iyaniwura |
| collection | DOAJ |
| description | The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been spreading worldwide for over two years, with millions of reported cases and deaths. The deployment of mathematical modeling in the fight against COVID-19 has recorded tremendous success. However, most of these models target the epidemic phase of the disease. The development of safe and effective vaccines against SARS-CoV-2 brought hope of safe reopening of schools and businesses and return to pre-COVID normalcy, until mutant strains like the Delta and Omicron variants, which are more infectious, emerged. A few months into the pandemic, reports of the possibility of both vaccine- and infection-induced immunity waning emerged, thereby indicating that COVID-19 may be with us for longer than earlier thought. As a result, to better understand the dynamics of COVID-19, it is essential to study the disease with an endemic model. In this regard, we developed and analyzed an endemic model of COVID-19 that incorporates the waning of both vaccine- and infection-induced immunities using distributed delay equations. Our modeling framework assumes that the waning of both immunities occurs gradually over time at the population level. We derived a nonlinear ODE system from the distributed delay model and showed that the model could exhibit either a forward or backward bifurcation depending on the immunity waning rates. Having a backward bifurcation implies that $ R_c < 1 $ is not sufficient to guarantee disease eradication, and that the immunity waning rates are critical factors in eradicating COVID-19. Our numerical simulations show that vaccinating a high percentage of the population with a safe and moderately effective vaccine could help in eradicating COVID-19. |
| first_indexed | 2024-04-10T15:30:39Z |
| format | Article |
| id | doaj.art-ce4e4d3ab70d4493b47c2eddd0569fbe |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-10T15:30:39Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-ce4e4d3ab70d4493b47c2eddd0569fbe2023-02-14T01:17:30ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-01-012035379541210.3934/mbe.2023249A generalized distributed delay model of COVID-19: An endemic model with immunity waningSarafa A. Iyaniwura0Rabiu Musa1Jude D. Kong21. Department of Mathematics and Institute of Applied Mathematics (IAM), University of British Columbia, Vancouver, British Columbia, Canada2. Faculty of Mathematics, Technion Israel Institute of Technology, Haifa 32000, Israel3. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada 4. Africa-Canada Artificial Intelligence and Data Innovation Consortium (ACADIC), York University, Toronto, Ontario, CanadaThe severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been spreading worldwide for over two years, with millions of reported cases and deaths. The deployment of mathematical modeling in the fight against COVID-19 has recorded tremendous success. However, most of these models target the epidemic phase of the disease. The development of safe and effective vaccines against SARS-CoV-2 brought hope of safe reopening of schools and businesses and return to pre-COVID normalcy, until mutant strains like the Delta and Omicron variants, which are more infectious, emerged. A few months into the pandemic, reports of the possibility of both vaccine- and infection-induced immunity waning emerged, thereby indicating that COVID-19 may be with us for longer than earlier thought. As a result, to better understand the dynamics of COVID-19, it is essential to study the disease with an endemic model. In this regard, we developed and analyzed an endemic model of COVID-19 that incorporates the waning of both vaccine- and infection-induced immunities using distributed delay equations. Our modeling framework assumes that the waning of both immunities occurs gradually over time at the population level. We derived a nonlinear ODE system from the distributed delay model and showed that the model could exhibit either a forward or backward bifurcation depending on the immunity waning rates. Having a backward bifurcation implies that $ R_c < 1 $ is not sufficient to guarantee disease eradication, and that the immunity waning rates are critical factors in eradicating COVID-19. Our numerical simulations show that vaccinating a high percentage of the population with a safe and moderately effective vaccine could help in eradicating COVID-19. https://www.aimspress.com/article/doi/10.3934/mbe.2023249?viewType=HTMLsars-cov-2covid-19endemic modeldistributed delay equationsvaccinationimmunity waninglinear chain trickglobal stability |
| spellingShingle | Sarafa A. Iyaniwura Rabiu Musa Jude D. Kong A generalized distributed delay model of COVID-19: An endemic model with immunity waning Mathematical Biosciences and Engineering sars-cov-2 covid-19 endemic model distributed delay equations vaccination immunity waning linear chain trick global stability |
| title | A generalized distributed delay model of COVID-19: An endemic model with immunity waning |
| title_full | A generalized distributed delay model of COVID-19: An endemic model with immunity waning |
| title_fullStr | A generalized distributed delay model of COVID-19: An endemic model with immunity waning |
| title_full_unstemmed | A generalized distributed delay model of COVID-19: An endemic model with immunity waning |
| title_short | A generalized distributed delay model of COVID-19: An endemic model with immunity waning |
| title_sort | generalized distributed delay model of covid 19 an endemic model with immunity waning |
| topic | sars-cov-2 covid-19 endemic model distributed delay equations vaccination immunity waning linear chain trick global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023249?viewType=HTML |
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