Mathematical models for within-host competition of malaria parasites

Tianqi Song; Chuncheng Wang; Boping Tian

doi:10.3934/mbe.2019330

Mathematical Biosciences and Engineering, 2019, 16(6): 6623-6653. doi: 10.3934/mbe.2019330. Research article Special Issues

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Mathematical models for within-host competition of malaria parasites

Tianqi Song, Chuncheng Wang, Boping Tian

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

Received: , Accepted: , Published:

Special Issues: Mathematical Modeling of Mosquito-Borne Diseases

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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 re-sponse. 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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Keywords: 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. Mathematical Biosciences and Engineering, 2019, 16(6): 6623-6653. doi: 10.3934/mbe.2019330

References:

1. World malaria report, World Health Organization (2017).
2. L. C. Pollitt, S. Huijben, D. G. Sim, et al., Rapid response to selection, competitive release and increased transmission potential of artesunate-selected plasmodium chabaudi malaria parasites, PLoS Pathog., 10 (2014), e1004019.
3. E. Hansen, R. J. Woods and A. F. Read, How to use a chemotherapeutic agent when resistance to it threatens the patient, PloS Biol., 15 (2017), e2001110.
4. A. R. Wargo, S. Huijben, J. C. D. Roode, et al., Competitive release and facilitation of drug-resistant parasites after therapeutic chemotherapy in a rodent malaria model, Proc. Natl. Acad. Sci. USA, 104 (2007), 19914–19919.
5. D. I. Andersson and D. Hughes, Antibiotic resistance and its cost: is it possible to reverse resis-tance? Nat. Rev. Microbiol., 8 (2010), 260–271.
6. I. Hastings, A model for the origins and spread of drug-resistant malaria, Parasitology, 115 (1997), 133–141.
7. M. Bushman, L. Morton, N. Duah, et al., Within-host competition and drug resistance in the human malaria parasite plasmodium falciparum, Proc. R. Soc. B, 283 (2016), 20153038.
8. A. F. Read and H. Silvie, Evolutionary biology and the avoidance of antimicrobial resistance, Evol. Appl., 2 (2009), 40–51.
9. R. Ataide, E. A. Ashley, R. Powell, et al., Host immunity to plasmodium falciparum and the assessment of emerging artemisinin resistance in a multinational cohort, Proc. Natl. Acad. Sci. USA, 114 (2017), 3515–3520.
10. A. Handel and B. M. Elevin, Exploring the role of the immune response in preventing antibiotic resistance, J. Theor. Biol., 256 (2009), 655–662.
11. K. Drlica and X. Zhao, Mutant selection window hypothesis updated, Clin. Infect. Dis., 44 (2007), 681–688.
12. E. Gjini and P. H. Brito, Integrating antimicrobial therapy with host immunity to fight drug-resistant infections: classical vs. adaptive treatment, PLoS Comput. Biol., 12 (2016), e1004857.
13. M. J. Mackinnon, Drug resistance models for malaria, Acta Trop., 94 (2005), 207–217.
14. J. M. Tchuenche, C. Chiyaka, D. Chan, et al., A mathematical model for antimalarial drug resis-tance, Math. Med. Biol., 28 (2011), 335–355.
15. J. Hansen and T. Day, Coinfection and the evolution of drug resistance, J. Evol. Biol., 27 (2015), 2595–2604.
16. C. Chiyaka, W. Garira and S. Dube, Modelling immune response and drug therapy in human malaria infection, Comput. Math. Method Med., 9 (2008), 143–163.
17. Y. Li, S. Ruan and D. Xiao, The within-host dynamics of malaria infection with immune response., Math. Biosci. Eng., 8 (2011), 999–1018.
18. M. Bushman, R. Antia, V. Udhayakumar, et al., Within-host competition can delay evolution of drug resistance in malaria, PLoS Biol., 16 (2018), e2005712.
19. L. Mathieu and B. Sebastian, A combined within-host and between-hosts modelling framework for the evolution of resistance to antimalarial drugs, J. R. Soc. Interface, 13 (2016), 20160148.
20. C. Hetzel and R. M. Anderson, The within-host cellular dynamics of bloodstage malaria: theoret-ical and experimental studies, Parasitology, 113 (1996), 25–38.
21. R. M. Anderson, R. M. May and S. Gupta, Non-linear phenomena in host-parasite interactions, Parasitology, 99 (1989), S59–S79.
22. C. E. Cressler, W. A. Nelson, T. Day, et al., Disentangling the interaction among host resources, the immune system and pathogens, Ecol. Lett., 17 (2014), 284–293.
23. P. B. Greenspoon, S. Banton and N. Mideo, Immune system handling time may alter the outcome of competition between pathogens and the immune system, J. Theor. Biol., 447 (2018), 25–31.
24. P. Dreessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.
25. D. Xiao and W. H. Bossert, An intra-host mathematical model on interaction between hiv and malaria, Bull. Math. Biol., 72 (2010), 1892–1911.
26. S. Ruan and S. K. W. Gail, Bifurcation analysis of a chemostat model with a distribued delay, J. Math. Anal. Appl., 204 (1996), 786–812.
27. A. Saltelli, P. Annoni, I. Azzini, et al., Variance based sensitivity analysis of model output. design and estimator for the total sensitivity index, Comput. Phys. Commun., 181 (2010), 259–270.
28. I. M. Sobol, Sensitivity estimates for nonlinear mathematical models, in Mathematical Modeling and Computational Experiment, 2010.
29. N. Wale, D. G. Sim, M. J. Jones, et al., Resource limitation prevents the emergence of drug resis-tance by intensifying within-host competition, Proc. Natl. Acad. Sci. USA, 114 (2017), 13774.
30. A. F. Read, T. Day and S. Huijben, The evolution of drug resistance and the curious orthodoxy of aggressive chemotherapy, Proc. Natl. Acad. Sci. USA, 108 (2011), 10871–10877.
31. J. Stark, C. Chan and A. J. George, Oscillations in the immune system., Immunol. Rev., 216 (2007), 213–231.
32. B. Hellriegel, Modelling the immune response to malaria with ecological concepts: short-term behavior against long-term equilibrium, Proc. R. Soc. B-Biol. Sci., 250 (1992), 249–256.
33. P. Ankomah and B. R. Levin, Exploring the collaboration between antibiotics and the immune response in the treatment of acute, self-limiting infections, Proc. Natl. Acad. Sci. USA, 111 (2014), 8331–8.

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