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Bulletin of Mathematical Biology

, Volume 81, Issue 11, pp 4564–4619 | Cite as

The Impact of Recruitment on the Dynamics of an Immune-Suppressed Within-Human–Host Model of the Plasmodium falciparum Parasite

  • Woldegebriel A. Woldegerima
  • Miranda I. Teboh-EwungkemEmail author
  • Gideon A. Ngwa
Special Issue: Mathematical Epidemiology

Abstract

A model is developed and used to study within-human malaria parasite dynamics. The model integrates actors involved in the development–progression of parasitemia, gametocytogenesis and mechanisms for immune response activation. Model analyses under immune suppression reveal different dynamical behaviours for different healthy red blood cell (HRBC) generation functions. Existence of a threshold parameter determines conditions for HRBCs depletion. Oscillatory dynamics reminiscent of malaria parasitemia are obtained. A dependence exists on the type of recruitment function used to generate HRBCs, with complexities observed for a more nonlinear function. An upper bound that delimits the size of feasible parasitized steady-state solution exists for a logistic function but not a constant function. The upper bound is completely characterized and is affected by parameters associated with HRBCs recruitment, parasitized red blood cells generation and the release and time-to-release of free merozoites. A stable density size for mature gametocytes, the bridge to invertebrate hosts, is derived.

Keywords

Within-human–host dynamics Innate and adaptive immune response Parasitemia Gametocytogenesis Global stability Red blood cells Malaria Recruitment 

Notes

Acknowledgements

The first author, WA, acknowledges support from the Department of Mathematics at Lehigh University, MIT-E’s Lehigh University Development fund, and Lehigh University as a whole, for supporting him and making available to him Lehigh’s resources, and for sponsoring as well as hosting him for more than two months as a visiting pre-doctoral scholar, enabling him to make significant progress on the work related to this manuscript and his thesis under the mentorship of MIT-E in conjunction with GAN via SKYPE. WA also acknowledges support from the African Institute for the Mathematical Sciences (AIMS) Cameroon that paid his flight for him to visit Lehigh University as a visiting pre-doctoral scholar, paving the path towards a successful completion of this manuscript and his doctoral dissertation. GAN acknowledges the grants and support of the Cameroon Ministry of Higher Education through the initiative for the modernization of research in Cameroon’s Higher Education. All three authors, WA, MIT-E and GAN acknowledge the support of the NSF -Directorate for Mathematical and Physical Science grant DMS-1544434 that created the opportunity for all three authors, who were present at the grant related activities (on School on Stochastic Analysis, Financial and Actuarial Mathematics with Applications) to meet as a unit for the first time and commence discussions on the manuscript and related project.

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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BueaBueaCameroon
  2. 2.African Institute for the Mathematical Sciences (AIMS) CameroonLimbeCameroon
  3. 3.Department of MathematicsLehigh UniversityBethlehemUSA

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