Basic reinfection number and backward bifurcation
Some epidemiological models exhibit bi-stable dynamics even when the basic reproduction number $ {{{\cal R}_{0}}} $ is below $ 1 $, through a phenomenon known as a backward bifurcation. Causes for this phenomenon include exogenous reinfection, super-infection, relapse, vaccination exercises, heterog...
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2021
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oai:doaj.org-article:9c09ab7947d448e1b20a12eaf0baad162021-11-23T03:06:23ZBasic reinfection number and backward bifurcation10.3934/mbe.20214001551-0018https://doaj.org/article/9c09ab7947d448e1b20a12eaf0baad162021-09-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021400?viewType=HTMLhttps://doaj.org/toc/1551-0018Some epidemiological models exhibit bi-stable dynamics even when the basic reproduction number $ {{{\cal R}_{0}}} $ is below $ 1 $, through a phenomenon known as a backward bifurcation. Causes for this phenomenon include exogenous reinfection, super-infection, relapse, vaccination exercises, heterogeneity among subpopulations, etc. To measure the reinfection forces, this paper defines a second threshold: the basic reinfection number. This number characterizes the type of bifurcation when the basic reproduction number is equal to one. If the basic reinfection number is greater than one, the bifurcation is backward. Otherwise it is forward. The basic reinfection number with the basic reproduction number together gives a complete measure for disease control whenever reinfections (or relapses) matter. We formulate the basic reinfection number for a variety of epidemiological models. Baojun Song AIMS Pressarticledisease dynamicsdifferential equationsbifurcationbasic reinfection numberBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 8064-8083 (2021) |
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DOAJ |
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DOAJ |
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EN |
| topic |
disease dynamics differential equations bifurcation basic reinfection number Biotechnology TP248.13-248.65 Mathematics QA1-939 |
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disease dynamics differential equations bifurcation basic reinfection number Biotechnology TP248.13-248.65 Mathematics QA1-939 Baojun Song Basic reinfection number and backward bifurcation |
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Some epidemiological models exhibit bi-stable dynamics even when the basic reproduction number $ {{{\cal R}_{0}}} $ is below $ 1 $, through a phenomenon known as a backward bifurcation. Causes for this phenomenon include exogenous reinfection, super-infection, relapse, vaccination exercises, heterogeneity among subpopulations, etc. To measure the reinfection forces, this paper defines a second threshold: the basic reinfection number. This number characterizes the type of bifurcation when the basic reproduction number is equal to one. If the basic reinfection number is greater than one, the bifurcation is backward. Otherwise it is forward. The basic reinfection number with the basic reproduction number together gives a complete measure for disease control whenever reinfections (or relapses) matter. We formulate the basic reinfection number for a variety of epidemiological models. |
| format |
article |
| author |
Baojun Song |
| author_facet |
Baojun Song |
| author_sort |
Baojun Song |
| title |
Basic reinfection number and backward bifurcation |
| title_short |
Basic reinfection number and backward bifurcation |
| title_full |
Basic reinfection number and backward bifurcation |
| title_fullStr |
Basic reinfection number and backward bifurcation |
| title_full_unstemmed |
Basic reinfection number and backward bifurcation |
| title_sort |
basic reinfection number and backward bifurcation |
| publisher |
AIMS Press |
| publishDate |
2021 |
| url |
https://doaj.org/article/9c09ab7947d448e1b20a12eaf0baad16 |
| work_keys_str_mv |
AT baojunsong basicreinfectionnumberandbackwardbifurcation |
| _version_ |
1718417335709073408 |