A new perspective on infection forces with demonstration by a DDE infectious disease model
In this paper, we revisit the notion of infection force from a new angle which can offer a new perspective to motivate and justify some infection force functions. Our approach can not only explain many existing infection force functions in the literature, it can also motivate new forms of infection...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-03-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022227?viewType=HTML |
| _version_ | 1828311120596697088 |
|---|---|
| author | Tianyu Cheng Xingfu Zou |
| author_facet | Tianyu Cheng Xingfu Zou |
| author_sort | Tianyu Cheng |
| collection | DOAJ |
| description | In this paper, we revisit the notion of infection force from a new angle which can offer a new perspective to motivate and justify some infection force functions. Our approach can not only explain many existing infection force functions in the literature, it can also motivate new forms of infection force functions, particularly infection forces depending on disease surveillance of the past. As a demonstration, we propose an SIRS model with delay. We comprehensively investigate the disease dynamics represented by this model, particularly focusing on the local bifurcation caused by the delay and another parameter that reflects the weight of the past epidemics in the infection force. We confirm Hopf bifurcations both theoretically and numerically. The results show that, depending on how recent the disease surveillance data are, their assigned weight may have a different impact on disease control measures. |
| first_indexed | 2024-04-13T15:55:26Z |
| format | Article |
| id | doaj.art-8d047919286e4d2da575eed8bf57057a |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-13T15:55:26Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-8d047919286e4d2da575eed8bf57057a2022-12-22T02:40:44ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-03-011954856488010.3934/mbe.2022227A new perspective on infection forces with demonstration by a DDE infectious disease modelTianyu Cheng0Xingfu Zou1Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7, CanadaDepartment of Mathematics, University of Western Ontario, London, ON, N6A 5B7, CanadaIn this paper, we revisit the notion of infection force from a new angle which can offer a new perspective to motivate and justify some infection force functions. Our approach can not only explain many existing infection force functions in the literature, it can also motivate new forms of infection force functions, particularly infection forces depending on disease surveillance of the past. As a demonstration, we propose an SIRS model with delay. We comprehensively investigate the disease dynamics represented by this model, particularly focusing on the local bifurcation caused by the delay and another parameter that reflects the weight of the past epidemics in the infection force. We confirm Hopf bifurcations both theoretically and numerically. The results show that, depending on how recent the disease surveillance data are, their assigned weight may have a different impact on disease control measures.https://www.aimspress.com/article/doi/10.3934/mbe.2022227?viewType=HTMLinfection forcespractically susceptiblesirs modeldelay differential equationhopf bifurcation |
| spellingShingle | Tianyu Cheng Xingfu Zou A new perspective on infection forces with demonstration by a DDE infectious disease model Mathematical Biosciences and Engineering infection forces practically susceptible sirs model delay differential equation hopf bifurcation |
| title | A new perspective on infection forces with demonstration by a DDE infectious disease model |
| title_full | A new perspective on infection forces with demonstration by a DDE infectious disease model |
| title_fullStr | A new perspective on infection forces with demonstration by a DDE infectious disease model |
| title_full_unstemmed | A new perspective on infection forces with demonstration by a DDE infectious disease model |
| title_short | A new perspective on infection forces with demonstration by a DDE infectious disease model |
| title_sort | new perspective on infection forces with demonstration by a dde infectious disease model |
| topic | infection forces practically susceptible sirs model delay differential equation hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022227?viewType=HTML |
| work_keys_str_mv | AT tianyucheng anewperspectiveoninfectionforceswithdemonstrationbyaddeinfectiousdiseasemodel AT xingfuzou anewperspectiveoninfectionforceswithdemonstrationbyaddeinfectiousdiseasemodel AT tianyucheng newperspectiveoninfectionforceswithdemonstrationbyaddeinfectiousdiseasemodel AT xingfuzou newperspectiveoninfectionforceswithdemonstrationbyaddeinfectiousdiseasemodel |