Mathematical Biosciences and Engineering, 2011, 8(4): 999-1018. doi: 10.3934/mbe.2011.8.999.

Primary: 34C23, 34D23; Secondary: 92C60.

Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

The Within-Host dynamics of malaria infection with immune response

1. Department of Mathematics, East China University of Science and Technology, Shanghai 200237
2. Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250
3. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

Malaria infection is one of the most serious global health problems of our time. In this article the blood-stage dynamics of malaria in an infected host are studied by incorporating red blood cells, malaria parasitemia and immune effectors into a mathematical model with nonlinear bounded Michaelis-Menten-Monod functions describing how immune cells interact with infected red blood cells and merozoites. By a theoretical analysis of this model, we show that there exists a threshold value $R_0$, namely the basic reproduction number, for the malaria infection. The malaria-free equilibrium is global asymptotically stable if $R_0<1$. If $R_0>1$, there exist two kinds of infection equilibria: malaria infection equilibrium (without specific immune response) and positive equilibrium (with specific immune response). Conditions on the existence and stability of both infection equilibria are given. Moreover, it has been showed that the model can undergo Hopf bifurcation at the positive equilibrium and exhibit periodic oscillations. Numerical simulations are also provided to demonstrate these theoretical results.
  Figure/Table
  Supplementary
  Article Metrics

Keywords periodic oscillations.; Malaria infection; within-host dynamics; thresh- old; mathematical model

Citation: Yilong Li, Shigui Ruan, Dongmei Xiao. The Within-Host dynamics of malaria infection with immune response. Mathematical Biosciences and Engineering, 2011, 8(4): 999-1018. doi: 10.3934/mbe.2011.8.999

 

This article has been cited by

  • 1. Hongyan Chen, Wendi Wang, Rui Fu, Jianfeng Luo, Global analysis of a mathematical model on malaria with competitive strains and immune responses, Applied Mathematics and Computation, 2015, 259, 132, 10.1016/j.amc.2015.02.073
  • 2. Neha Thakre, Priyanka Fernandes, Ann-Kristin Mueller, Frederik Graw, Examining the Reticulocyte Preference of Two Plasmodium berghei Strains during Blood-Stage Malaria Infection, Frontiers in Microbiology, 2018, 9, 10.3389/fmicb.2018.00166
  • 3. Caroline O. Buckee, Amy Wesolowski, Nathan N. Eagle, Elsa Hansen, Robert W. Snow, Mobile phones and malaria: Modeling human and parasite travel, Travel Medicine and Infectious Disease, 2013, 11, 1, 15, 10.1016/j.tmaid.2012.12.003
  • 4. Woldegebriel A. Woldegerima, Miranda I. Teboh-Ewungkem, Gideon A. Ngwa, The Impact of Recruitment on the Dynamics of an Immune-Suppressed Within-Human–Host Model of the Plasmodium falciparum Parasite, Bulletin of Mathematical Biology, 2018, 10.1007/s11538-018-0436-0
  • 5. Liming Cai, Necibe Tuncer, Maia Martcheva, How does within-host dynamics affect population-level dynamics? Insights from an immuno-epidemiological model of malaria, Mathematical Methods in the Applied Sciences, 2017, 40, 18, 6424, 10.1002/mma.4466
  • 6. Ramses Djidjou Demasse, Arnaud Ducrot, An Age-Structured Within-Host Model for Multistrain Malaria Infections, SIAM Journal on Applied Mathematics, 2013, 73, 1, 572, 10.1137/120890351
  • 7. Steffen E. Eikenberry, Abba B. Gumel, Mathematical modeling of climate change and malaria transmission dynamics: a historical review, Journal of Mathematical Biology, 2018, 10.1007/s00285-018-1229-7
  • 8. Maia Martcheva, Xue-Zhi Li, Linking immunological and epidemiological dynamics of HIV: the case of super-infection, Journal of Biological Dynamics, 2013, 7, 1, 161, 10.1080/17513758.2013.820358
  • 9. Titus Okello Orwa, Rachel Waema Mbogo, Livingstone Serwadda Luboobi, Mathematical Model for Hepatocytic-Erythrocytic Dynamics of Malaria, International Journal of Mathematics and Mathematical Sciences, 2018, 2018, 1, 10.1155/2018/7019868
  • 10. Titus Okello Orwa, Rachel Waema Mbogo, Livingstone Serwadda Luboobi, Mathematical model for the in-host malaria dynamics subject to malaria vaccines, Letters in Biomathematics, 2018, 5, 1, 222, 10.1080/23737867.2018.1526132
  • 11. F.B. Agusto, M.C.A. Leite, M.E. Orive, The transmission dynamics of a within-and between-hosts malaria model, Ecological Complexity, 2019, 38, 31, 10.1016/j.ecocom.2019.02.002
  • 12. Titus Okello Orwa, Rachel Waema Mbogo, Livingstone Serwadda Luboobi, Uncertainty and Sensitivity Analysis Applied to an In-Host Malaria Model with Multiple Vaccine Antigens, International Journal of Applied and Computational Mathematics, 2019, 5, 3, 10.1007/s40819-019-0658-3
  • 13. Titus Okello Orwa, Rachel Waema Mbogo, Livingstone Serwadda Luboobi, Multiple-Strain Malaria Infection and Its Impacts on Plasmodium falciparum Resistance to Antimalarial Therapy: A Mathematical Modelling Perspective, Computational and Mathematical Methods in Medicine, 2019, 2019, 1, 10.1155/2019/9783986

Reader Comments

your name: *   your email: *  

Copyright Info: 2011, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved