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Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response

Author

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  • Ahmed Elaiw

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Afnan Al Agha

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

Malaria is one of the most dangerous global diseases. This paper studies a reaction-diffusion model for the within-host dynamics of malaria infection with both antibody and cell-mediated immune responses. The model explores the interactions between uninfected red blood cells (erythrocytes), three types of infected red blood cells, free merozoites, CTLs and antibodies. It contains some parameters to measure the effect of antimalarial drugs and isoleucine starvation on the blood cycle of malaria infection. The basic properties of the model are discussed. All possible equilibrium points and the threshold conditions required for their existence are addressed. The global stability of all equilibria are proved by selecting suitable Lyapunov functionals and using LaSalle’s invariance principle. The characteristic equations are used to study the local instability conditions of the equilibria. Some numerical simulations are conducted to support the theoretical results. The results indicate that antimalarial drugs with high efficacy can clear the infection and take the system towards the disease-free state. Increasing the efficacy of isoleucine starvation has a similar effect as antimalarial drugs and can eliminate the disease. The presence of immune responses with low efficacy of treatments does not provide a complete protection against the disease. However, the immune responses reduce the concentrations of all types of infected cells and limit the production of malaria parasites.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:563-:d:344268
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    References listed on IDEAS

    as
    1. Elaiw, A.M. & Hobiny, A.D. & Al Agha, A.D., 2020. "Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.
    3. A. M. Elaiw & E. Kh. Elnahary, 2019. "Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays," Mathematics, MDPI, vol. 7(2), pages 1-35, February.
    4. Ashrafi Niger & Abba Gumel, 2011. "Immune Response and Imperfect Vaccine in Malaria Dynamics," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(2), pages 55-86.
    5. 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.
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    Cited by:

    1. Ahmed M. Elaiw & Afnan D. Al Agha, 2022. "Global Stability of a Reaction–Diffusion Malaria/COVID-19 Coinfection Dynamics Model," Mathematics, MDPI, vol. 10(22), pages 1-31, November.

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