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Global analysis of a mathematical model on malaria with competitive strains and immune responses

Author

Listed:
  • Chen, Hongyan
  • Wang, Wendi
  • Fu, Rui
  • Luo, Jianfeng

Abstract

Saturated infection incidences and immune responses are incorporated into a mathematical model of malaria with two competitive strains of Plasmodium falciparum. The basic reproductive numbers of pathogens and the response numbers of host immunity are formulated. The complete classifications of global stability of the model are established in terms of these numbers by using the persistence theory and Lyapunov methods. It is found that two strains of parasites coexist within a host when the reproductive numbers and responsive numbers satisfy the explicit conditions defined by two inequalities, and undergo the competitive exclusion otherwise.

Suggested Citation

  • Chen, Hongyan & Wang, Wendi & Fu, Rui & Luo, Jianfeng, 2015. "Global analysis of a mathematical model on malaria with competitive strains and immune responses," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 132-152.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:132-152
    DOI: 10.1016/j.amc.2015.02.073
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    References listed on IDEAS

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    1. Rob J De Boer, 2012. "Which of Our Modeling Predictions Are Robust?," PLOS Computational Biology, Public Library of Science, vol. 8(7), pages 1-5, July.
    2. Louis H. Miller & Dror I. Baruch & Kevin Marsh & Ogobara K. Doumbo, 2002. "The pathogenic basis of malaria," Nature, Nature, vol. 415(6872), pages 673-679, February.
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    Cited by:

    1. Ahmed Elaiw & Afnan Al Agha, 2020. "Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response," Mathematics, MDPI, vol. 8(4), pages 1-32, April.
    2. Mittal, R.C. & Goel, Rohit & Ahlawat, Neha, 2021. "An Efficient Numerical Simulation of a Reaction-Diffusion Malaria Infection Model using B-splines Collocation," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Tianqi Song & Yishi Wang & Yang Li & Guoliang Fan, 2024. "A Mathematical Analysis of Competitive Dynamics and Aggressive Treatment in the Evolution of Drug Resistance in Malaria Parasites," Mathematics, MDPI, vol. 12(10), pages 1-16, May.
    4. Luo, Jianfeng & Zhao, Yi, 2023. "Bifurcation analysis of a non-smooth prey–predator model by a differential linear complementarity system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 581-599.

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