A Mathematical Model for Tumor–Immune Dynamics in Multiple Myeloma

  • Jill Gallaher
  • Kamila Larripa
  • Urszula Ledzewicz
  • Marissa Renardy
  • Blerta Shtylla
  • Nessy Tania
  • Diana White
  • Karen Wood
  • Li Zhu
  • Chaitali Passey
  • Michael Robbins
  • Natalie Bezman
  • Suresh Shelat
  • Hearn Jay Cho
  • Helen Moore
Part of the Association for Women in Mathematics Series book series (AWMS, volume 14)


We propose a mathematical model that describes the dynamics of multiple myeloma and three distinct populations of the innate and adaptive immune system: cytotoxic T cells, natural killer cells, and regulatory T cells. The model includes significant biologically- and therapeutically-relevant pathways for inhibitory and stimulatory interactions between these populations. Due to the model complexity, we propose a reduced version that captures the principal biological aspects for advanced disease, while still including potential targets for therapeutic interventions. Analysis of the reduced two-dimensional model revealed details about long-term model behavior. In particular, theoretical results describing equilibria and their associated stability are described in detail. Consistent with the theoretical analysis, numerical results reveal parameter regions for which bistability exits. The two stable states in these cases may correspond to long-term disease control or a higher level of disease burden. This initial analysis of the dynamical system provides a foundation for later work, which will consider combination therapies, their expected outcomes, and optimization of regimens.



This work was initiated during the Association for Women in Mathematics collaborative workshop Women Advancing Mathematical Biology hosted by the Mathematical Biosciences Institute (MBI) at Ohio State University in April 2017. Funding for the workshop was provided by MBI, NSF ADVANCE “Career Advancement for Women Through Research-Focused Networks” (NSF-HRD 1500481), Society for Mathematical Biology, and Microsoft Research. The authors thank the anonymous reviewers for helpful comments that led to improvements in this manuscript.


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Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  • Jill Gallaher
    • 1
  • Kamila Larripa
    • 2
  • Urszula Ledzewicz
    • 3
    • 4
  • Marissa Renardy
    • 5
    • 6
  • Blerta Shtylla
    • 7
  • Nessy Tania
    • 8
  • Diana White
    • 9
  • Karen Wood
    • 10
    • 11
  • Li Zhu
    • 12
  • Chaitali Passey
    • 13
  • Michael Robbins
    • 14
  • Natalie Bezman
    • 15
  • Suresh Shelat
    • 16
  • Hearn Jay Cho
    • 17
  • Helen Moore
    • 18
    • 19
  1. 1.H. Lee Moffitt Cancer CenterTampaUSA
  2. 2.Department of MathematicsHumboldt State UniversityArcataUSA
  3. 3.Department of Mathematics and StatisticsSouthern Illinois University EdwardsvilleEdwardsvilleUSA
  4. 4.Institute of MathematicsLodz University of TechnologyLodzPoland
  5. 5.Department of MathematicsThe Ohio State UniversityColumbusUSA
  6. 6.Current Address: Department of Microbiology and ImmunologyUniversity of MichiganAnn ArborUSA
  7. 7.Mathematics DepartmentPomona CollegeClaremontUSA
  8. 8.Department of Mathematics and StatisticsSmith CollegeNorthamptonUSA
  9. 9.Department of MathematicsClarkson UniversityPotsdamUSA
  10. 10.Department of MathematicsUniversity of California at IrvineIrvineUSA
  11. 11.Current Address: The Aerospace CorporationEl SegundoUSA
  12. 12.Clinical Pharmacology and PharmacometricsBristol-Myers SquibbPrincetonUSA
  13. 13.GenmabPrincetonUSA
  14. 14.Hematology Medical StrategyBristol-Myers SquibbLawrence TownshipUSA
  15. 15.Immuno-Oncology DiscoveryBristol-Myers SquibbRedwood CityUSA
  16. 16.Oncology Clinical DevelopmentBristol-Myers SquibbLawrence TownshipUSA
  17. 17.Tisch Cancer InstituteMt. Sinai School of MedicineNew YorkUSA
  18. 18.Quantitative Clinical PharmacologyBristol-Myers SquibbPrincetonUSA
  19. 19.Current Address: Drug Metabolism and PharmacokineticsAstraZenecaWalthamUSA

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