Mathematical models for within-host competition of malaria parasites

Tianqi Song; Chuncheng Wang; Boping Tian; Tianqi Song; Chuncheng Wang; Boping Tian

doi:10.3934/mbe.2019330

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 6623-6653. doi: 10.3934/mbe.2019330

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Mathematical models for within-host competition of malaria parasites

School of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, 150001, China

Received: 02 May 2019 Accepted: 15 July 2019 Published: 19 July 2019

In this paper, we formulate two within-host infection models to simulate dynamics of the drug sensitive and drug resistant malaria parasites, where the first model solely considers the within-host competition between these two strains, and the second model further considers the immune response. Detailed theoretical analysis of the second model are made, including the existence, stability and bifurcation of the equilibrium, which have also been verified by numerical simulations. Both theoretical and numerical results show that competition or chronic control of drug sensitive parasites could inhibit the evolution of drug resistant ones to some extent. However, if the immune response is considered, periodic solution could be observed, and they will persist for all relatively small treatment rate. This may lead to the recurrence of resistance for the chronic control strategy, even though it could delay the resistance emergence. In addition, global sensitivity analysis is implemented to provide the information on the significance of model parameters on the state variables.
- within-host model,
- drug resistance,
- competition,
- immune response,
- sensitivity analysis
Citation: Tianqi Song, Chuncheng Wang, Boping Tian. Mathematical models for within-host competition of malaria parasites[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6623-6653. doi: 10.3934/mbe.2019330

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Abstract

In this paper, we formulate two within-host infection models to simulate dynamics of the drug sensitive and drug resistant malaria parasites, where the first model solely considers the within-host competition between these two strains, and the second model further considers the immune response. Detailed theoretical analysis of the second model are made, including the existence, stability and bifurcation of the equilibrium, which have also been verified by numerical simulations. Both theoretical and numerical results show that competition or chronic control of drug sensitive parasites could inhibit the evolution of drug resistant ones to some extent. However, if the immune response is considered, periodic solution could be observed, and they will persist for all relatively small treatment rate. This may lead to the recurrence of resistance for the chronic control strategy, even though it could delay the resistance emergence. In addition, global sensitivity analysis is implemented to provide the information on the significance of model parameters on the state variables.

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