The Within-Host dynamics of malaria infection with immune response
Malaria infection is one of the most serious global healthproblems of our time. In this article the blood-stage dynamics ofmalaria in an infected host are studied by incorporating red bloodcells, malaria parasitemia and immune effectors into a mathematicalmodel with nonlinear bounded Michaelis-Mente...
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| Format: | Article |
| Language: | English |
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AIMS Press
2011-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.999 |
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| author | Yilong Li Shigui Ruan Dongmei Xiao |
| author_facet | Yilong Li Shigui Ruan Dongmei Xiao |
| author_sort | Yilong Li |
| collection | DOAJ |
| description | Malaria infection is one of the most serious global healthproblems of our time. In this article the blood-stage dynamics ofmalaria in an infected host are studied by incorporating red bloodcells, malaria parasitemia and immune effectors into a mathematicalmodel with nonlinear bounded Michaelis-Menten-Monod functionsdescribing how immune cells interact with infected red blood cellsand merozoites. By a theoretical analysis of this model, we show thatthere exists a threshold value $R_0$, namely the basic reproduction number,for the malaria infection. The malaria-free equilibrium is global asymptoticallystable if $R_01$, there exist two kinds ofinfection equilibria: malaria infection equilibrium (withoutspecific immune response) and positive equilibrium (with specificimmune response). Conditions on the existence and stability of bothinfection equilibria are given. Moreover, it has been showedthat the model can undergo Hopf bifurcation at thepositive equilibrium and exhibit periodic oscillations. Numericalsimulations are also provided to demonstrate these theoreticalresults. |
| format | Article |
| id | doaj-art-08bf9d856c99438a9e40830c57d0849c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-08bf9d856c99438a9e40830c57d0849c2025-01-24T02:02:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-07-0184999101810.3934/mbe.2011.8.999The Within-Host dynamics of malaria infection with immune responseYilong Li0Shigui Ruan1Dongmei Xiao2Department of Mathematics, East China University of Science and Technology, Shanghai 200237Department of Mathematics, East China University of Science and Technology, Shanghai 200237Department of Mathematics, East China University of Science and Technology, Shanghai 200237Malaria infection is one of the most serious global healthproblems of our time. In this article the blood-stage dynamics ofmalaria in an infected host are studied by incorporating red bloodcells, malaria parasitemia and immune effectors into a mathematicalmodel with nonlinear bounded Michaelis-Menten-Monod functionsdescribing how immune cells interact with infected red blood cellsand merozoites. By a theoretical analysis of this model, we show thatthere exists a threshold value $R_0$, namely the basic reproduction number,for the malaria infection. The malaria-free equilibrium is global asymptoticallystable if $R_01$, there exist two kinds ofinfection equilibria: malaria infection equilibrium (withoutspecific immune response) and positive equilibrium (with specificimmune response). Conditions on the existence and stability of bothinfection equilibria are given. Moreover, it has been showedthat the model can undergo Hopf bifurcation at thepositive equilibrium and exhibit periodic oscillations. Numericalsimulations are also provided to demonstrate these theoreticalresults.https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.999periodic oscillations.malaria infectionwithin-host dynamicsthresh- oldmathematical model |
| spellingShingle | Yilong Li Shigui Ruan Dongmei Xiao The Within-Host dynamics of malaria infection with immune response Mathematical Biosciences and Engineering periodic oscillations. malaria infection within-host dynamics thresh- old mathematical model |
| title | The Within-Host dynamics of malaria infection with immune response |
| title_full | The Within-Host dynamics of malaria infection with immune response |
| title_fullStr | The Within-Host dynamics of malaria infection with immune response |
| title_full_unstemmed | The Within-Host dynamics of malaria infection with immune response |
| title_short | The Within-Host dynamics of malaria infection with immune response |
| title_sort | within host dynamics of malaria infection with immune response |
| topic | periodic oscillations. malaria infection within-host dynamics thresh- old mathematical model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.999 |
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