An age-structured epidemic model with boosting and waning of immune status
In this paper, we developed an age-structured epidemic model that takes into account boosting and waning of immune status of host individuals. For many infectious diseases, the immunity of recovered individuals may be waning as time evolves, so reinfection could occur, but also their immune status c...
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2021
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oai:doaj.org-article:0fbceec54932413b9662411dd238d4c02021-11-09T02:42:44ZAn age-structured epidemic model with boosting and waning of immune status10.3934/mbe.20212891551-0018https://doaj.org/article/0fbceec54932413b9662411dd238d4c02021-06-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021289?viewType=HTMLhttps://doaj.org/toc/1551-0018In this paper, we developed an age-structured epidemic model that takes into account boosting and waning of immune status of host individuals. For many infectious diseases, the immunity of recovered individuals may be waning as time evolves, so reinfection could occur, but also their immune status could be boosted if they have contact with infective agent. According to the idea of the Aron's malaria model, we incorporate a boosting mechanism expressed by reset of recovery-age (immunity clock) into the SIRS epidemic model. We established the mathematical well-posedness of our formulation and showed that the initial invasion condition and the endemicity can be characterized by the basic reproduction number $ R_0 $. Our focus is to investigate the condition to determine the direction of bifurcation of endemic steady states bifurcated from the disease-free steady state, because it is a crucial point for disease prevention strategy whether there exist subcritical endemic steady states. Based on a recent result by Martcheva and Inaba <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, we have determined the direction of bifurcation that endemic steady states bifurcate from the disease-free steady state when the basic reproduction number passes through the unity. Finally, we have given a necessary and sufficient condition for backward bifurcation to occur. Kento OkuwaHisashi InabaToshikazu KuniyaAIMS Pressarticleboosting and waningimmunity clockepidemic modelaron modelage-structurebasic reproduction numberBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 5707-5736 (2021) |
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boosting and waning immunity clock epidemic model aron model age-structure basic reproduction number Biotechnology TP248.13-248.65 Mathematics QA1-939 |
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boosting and waning immunity clock epidemic model aron model age-structure basic reproduction number Biotechnology TP248.13-248.65 Mathematics QA1-939 Kento Okuwa Hisashi Inaba Toshikazu Kuniya An age-structured epidemic model with boosting and waning of immune status |
| description |
In this paper, we developed an age-structured epidemic model that takes into account boosting and waning of immune status of host individuals. For many infectious diseases, the immunity of recovered individuals may be waning as time evolves, so reinfection could occur, but also their immune status could be boosted if they have contact with infective agent. According to the idea of the Aron's malaria model, we incorporate a boosting mechanism expressed by reset of recovery-age (immunity clock) into the SIRS epidemic model. We established the mathematical well-posedness of our formulation and showed that the initial invasion condition and the endemicity can be characterized by the basic reproduction number $ R_0 $. Our focus is to investigate the condition to determine the direction of bifurcation of endemic steady states bifurcated from the disease-free steady state, because it is a crucial point for disease prevention strategy whether there exist subcritical endemic steady states. Based on a recent result by Martcheva and Inaba <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, we have determined the direction of bifurcation that endemic steady states bifurcate from the disease-free steady state when the basic reproduction number passes through the unity. Finally, we have given a necessary and sufficient condition for backward bifurcation to occur.
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| format |
article |
| author |
Kento Okuwa Hisashi Inaba Toshikazu Kuniya |
| author_facet |
Kento Okuwa Hisashi Inaba Toshikazu Kuniya |
| author_sort |
Kento Okuwa |
| title |
An age-structured epidemic model with boosting and waning of immune status |
| title_short |
An age-structured epidemic model with boosting and waning of immune status |
| title_full |
An age-structured epidemic model with boosting and waning of immune status |
| title_fullStr |
An age-structured epidemic model with boosting and waning of immune status |
| title_full_unstemmed |
An age-structured epidemic model with boosting and waning of immune status |
| title_sort |
age-structured epidemic model with boosting and waning of immune status |
| publisher |
AIMS Press |
| publishDate |
2021 |
| url |
https://doaj.org/article/0fbceec54932413b9662411dd238d4c0 |
| work_keys_str_mv |
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