Mathematical Modeling of Oncolytic Virotherapy

  • Johannes P. W. Heidbuechel
  • Daniel Abate-Daga
  • Christine E. Engeland
  • Heiko EnderlingEmail author
Part of the Methods in Molecular Biology book series (MIMB, volume 2058)


Mathematical modeling in biology has a long history as it allows the analysis and simulation of complex dynamic biological systems at little cost. A mathematical model trained on experimental or clinical data can be used to generate and evaluate hypotheses, to ask “what if” questions, and to perform in silico experiments to guide future experimentation and validation. Such models may help identify and provide insights into the mechanisms that drive changes in dynamic systems. While a mathematical model may never replace actual experiments, it can synergize with experiments to save time and resources by identifying experimental conditions that are unlikely to yield favorable outcomes, and by using optimization principles to identify experiments that are most likely to be successful. Over the past decade, numerous models have also been developed for oncolytic virotherapy, ranging from merely theoretic frameworks to fully integrated studies that utilize experimental data to generate actionable hypotheses. Here we describe how to develop such models for specific oncolytic virotherapy experimental setups, and which questions can and cannot be answered using integrated mathematical oncology.

Key words

Mathematical modeling Oncology Virus Oncolytic virotherapy Combination immunotherapy 



J.P.W.H. receives a PhD stipend by the Helmholtz International Graduate School for Cancer Research at the German Cancer Research Center (DKFZ). C.E.E. receives funding from the Wilhelm Sander-Stiftung (Grant 2018.058.1). H.E. and D.A.D. thank Dr. Alexander R. A. Anderson and the Moffitt Physical Sciences in Oncology Center for the organization and support of the fourth Moffitt IMO workshop on Viruses and Cancer, where parts of the idea of this project were conceived.


  1. 1.
    Kelly E, Russell SJ (2007) History of oncolytic viruses: genesis to genetic engineering. Mol Ther 15(4):651–659. Scholar
  2. 2.
    Dock G (1904) The influence of complicating diseases upon leukaemia. Am J Med Sci 127:563–592CrossRefGoogle Scholar
  3. 3.
    Hoster HA, Zanes RP Jr, Von Haam E (1949) Studies in Hodgkin’s syndrome; the association of viral hepatitis and Hodgkin’s disease; a preliminary report. Cancer Res 9(8):473–480PubMedGoogle Scholar
  4. 4.
    Pol J, Buque A, Aranda F, Bloy N, Cremer I, Eggermont A, Erbs P, Fucikova J, Galon J, Limacher JM, Preville X, Sautes-Fridman C, Spisek R, Zitvogel L, Kroemer G, Galluzzi L (2016) Trial watch-oncolytic viruses and cancer therapy. Oncoimmunology 5(2):e1117740. Scholar
  5. 5.
    Msaouel P, Opyrchal M, Dispenzieri A, Peng KW, Federspiel MJ, Russell SJ, Galanis E (2018) Clinical trials with oncolytic measles virus: current status and future prospects. Curr Cancer Drug Targets 18(2):177–187. Scholar
  6. 6.
    Pol J, Kroemer G, Galluzzi L (2016) First oncolytic virus approved for melanoma immunotherapy. Oncoimmunology 5(1):e1115641. Scholar
  7. 7.
    Russell SJ, Peng KW (2017) Oncolytic virotherapy: a contest between apples and oranges. Mol Ther 25(5):1107–1116. Scholar
  8. 8.
    Lichty BD, Breitbach CJ, Stojdl DF, Bell JC (2014) Going viral with cancer immunotherapy. Nat Rev Cancer 14(8):559–567. Scholar
  9. 9.
    Workenhe ST, Mossman KL (2014) Oncolytic virotherapy and immunogenic cancer cell death: sharpening the sword for improved cancer treatment strategies. Mol Ther 22(2):251–256. Scholar
  10. 10.
    Cassady KA, Haworth KB, Jackson J, Markert JM, Cripe TP (2016) To infection and beyond: the multi-pronged anti-cancer mechanisms of oncolytic viruses. Viruses 8(2). Scholar
  11. 11.
    Achard C, Surendran A, Wedge ME, Ungerechts G, Bell J, Ilkow CS (2018) Lighting a fire in the tumor microenvironment using oncolytic immunotherapy. EBioMedicine 31:17–24. Scholar
  12. 12.
    Arulanandam R, Batenchuk C, Angarita FA, Ottolino-Perry K, Cousineau S, Mottashed A, Burgess E, Falls TJ, De Silva N, Tsang J, Howe GA, Bourgeois-Daigneault MC, Conrad DP, Daneshmand M, Breitbach CJ, Kirn DH, Raptis L, Sad S, Atkins H, Huh MS, Diallo JS, Lichty BD, Ilkow CS, Le Boeuf F, Addison CL, McCart JA, Bell JC (2015) VEGF-mediated induction of PRD1-BF1/Blimp1 expression sensitizes tumor vasculature to oncolytic virus infection. Cancer Cell 28(2):210–224. Scholar
  13. 13.
    Miest TS, Cattaneo R (2014) New viruses for cancer therapy: meeting clinical needs. Nat Rev Microbiol 12(1):23–34. Scholar
  14. 14.
    Ungerechts G, Bossow S, Leuchs B, Holm PS, Rommelaere J, Coffey M, Coffin R, Bell J, Nettelbeck DM (2016) Moving oncolytic viruses into the clinic: clinical-grade production, purification, and characterization of diverse oncolytic viruses. Mol Ther 3:16018. Scholar
  15. 15.
    Twumasi-Boateng K, Pettigrew JL, Kwok YYE, Bell JC, Nelson BH (2018) Oncolytic viruses as engineering platforms for combination immunotherapy. Nat Rev Cancer 18(7):419–432. Scholar
  16. 16.
    Russell SJ, Peng KW, Bell JC (2012) Oncolytic virotherapy. Nat Biotechnol 30(7):658–670. Scholar
  17. 17.
    Heidbuechel JPW, Engeland CE (2019) Paramyxoviruses for tumor-targeted immunomodulation: design and evaluation ex vivo. J Vis Exp (143):e58651.
  18. 18.
    Martin NT, Bell JC (2018) Oncolytic virus combination therapy: killing one bird with two stones. Mol Ther 26(6):1414–1422. Scholar
  19. 19.
    Zamarin D, Holmgaard RB, Subudhi SK, Park JS, Mansour M, Palese P, Merghoub T, Wolchok JD, Allison JP (2014) Localized oncolytic virotherapy overcomes systemic tumor resistance to immune checkpoint blockade immunotherapy. Sci Transl Med 6(226):226ra232. Scholar
  20. 20.
    Engeland CE, Grossardt C, Veinaide R, Bossow S, Lutz D, Kaufmann JK, Shevchenko I, Umansky V, Nettelbeck DM, Weichert W, Jager D, von Katie C, Ungerechts G (2014) CTLA-4 and PD-L1 checkpoint blockade enhances oncolytic measles virus therapy. Mol Ther 22(11):1949–1959. Scholar
  21. 21.
    Ribas A, Dummer R, Puzanov I, VanderWalde A, Andtbacka RHI, Michielin O, Olszanski AJ, Malvehy J, Cebon J, Fernandez E, Kirkwood JM, Gajewski TF, Chen L, Gorski KS, Anderson AA, Diede SJ, Lassman ME, Gansert J, Hodi FS, Long GV (2017) Oncolytic virotherapy promotes intratumoral T cell infiltration and improves anti-PD-1 immunotherapy. Cell 170(6):1109–1119.e1110. Scholar
  22. 22.
    Ajina A, Maher J (2017) Prospects for combined use of oncolytic viruses and CAR T-cells. J Immunother Cancer 5(1):90. Scholar
  23. 23.
    Wing A, Fajardo CA, Posey AD Jr, Shaw C, Da T, Young RM, Alemany R, June CH, Guedan S (2018) Improving CART-cell therapy of solid tumors with oncolytic virus-driven production of a bispecific T-cell engager. Cancer Immunol Res 6(5):605–616. Scholar
  24. 24.
    Nishio N, Diaconu I, Liu H, Cerullo V, Caruana I, Hoyos V, Bouchier-Hayes L, Savoldo B, Dotti G (2014) Armed oncolytic virus enhances immune functions of chimeric antigen receptor-modified T cells in solid tumors. Cancer Res 74(18):5195–5205. Scholar
  25. 25.
    Bressy C, Benihoud K (2014) Association of oncolytic adenoviruses with chemotherapies: an overview and future directions. Biochem Pharmacol 90(2):97–106. Scholar
  26. 26.
    Wennier ST, Liu J, McFadden G (2012) Bugs and drugs: oncolytic virotherapy in combination with chemotherapy. Curr Pharm Biotechnol 13(9):1817–1833CrossRefGoogle Scholar
  27. 27.
    Fillat C, Maliandi MV, Mato-Berciano A, Alemany R (2014) Combining oncolytic virotherapy and cytotoxic therapies to fight cancer. Curr Pharm Des 20(42):6513–6521CrossRefGoogle Scholar
  28. 28.
    Li H, Peng KW, Russell SJ (2012) Oncolytic measles virus encoding thyroidal sodium iodide symporter for squamous cell cancer of the head and neck radiovirotherapy. Hum Gene Ther 23(3):295–301. Scholar
  29. 29.
    Opyrchal M, Allen C, Iankov I, Aderca I, Schroeder M, Sarkaria J, Galanis E (2012) Effective radiovirotherapy for malignant gliomas by using oncolytic measles virus strains encoding the sodium iodide symporter (MV-NIS). Hum Gene Ther 23(4):419–427. Scholar
  30. 30.
    Mansfield D, Pencavel T, Kyula JN, Zaidi S, Roulstone V, Thway K, Karapanagiotou L, Khan AA, McLaughlin M, Touchefeu Y, Seth R, Melcher AA, Vile RG, Pandha HS, Harrington KJ (2013) Oncolytic vaccinia virus and radiotherapy in head and neck cancer. Oral Oncol 49(2):108–118. Scholar
  31. 31.
    Santiago DN, Heidbuechel JPW, Kandell WM, Walker R, Djeu J, Engeland CE, Abate-Daga D, Enderling H (2017) Fighting cancer with mathematics and viruses. Viruses 9(9):239. Scholar
  32. 32.
    Michor F, Beal K (2015) Improving cancer treatment via mathematical modeling: surmounting the challenges is worth the effort. Cell 163(5):1059–1063. Scholar
  33. 33.
    Araujo RP, McElwain DL (2004) A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull Math Biol 66(5):1039–1091. Scholar
  34. 34.
    Dingli D, Cascino MD, Josic K, Russell SJ, Bajzer Z (2006) Mathematical modeling of cancer radiovirotherapy. Math Biosci 199(1):55–78. Scholar
  35. 35.
    Friedman A, Tian JP, Fulci G, Chiocca EA, Wang J (2006) Glioma virotherapy: effects of innate immune suppression and increased viral replication capacity. Cancer Res 66(4):2314–2319. Scholar
  36. 36.
    Tian JP (2011) The replicability of oncolytic virus: defining conditions in tumor virotherapy. Math Biosci Eng 8(3):841–860. Scholar
  37. 37.
    Rommelfanger DM, Offord CP, Dev J, Bajzer Z, Vile RG, Dingli D (2012) Dynamics of melanoma tumor therapy with vesicular stomatitis virus: explaining the variability in outcomes using mathematical modeling. Gene Ther 19(5):543–549. Scholar
  38. 38.
    Crivelli JJ, Foldes J, Kim PS, Wares JR (2012) A mathematical model for cell cycle-specific cancer virotherapy. J Biol Dyn 6 Suppl 1:104–120. Scholar
  39. 39.
    Jacobsen K, Pilyugin SS (2015) Analysis of a mathematical model for tumor therapy with a fusogenic oncolytic virus. Math Biosci 270(Pt B):169–182. Scholar
  40. 40.
    Paiva LR, Binny C, Ferreira SC Jr, Martins ML (2009) A multiscale mathematical model for oncolytic virotherapy. Cancer Res 69(3):1205–1211. Scholar
  41. 41.
    Paiva LR, Silva HS, Ferreira SC, Martins ML (2013) Multiscale model for the effects of adaptive immunity suppression on the viral therapy of cancer. Phys Biol 10(2):025005. Scholar
  42. 42.
    Camara BI, Mokrani H, Afenya EK (2013) Mathematical modeling of glioma therapy using oncolytic viruses. Math Biosci Eng 10(3):565–578. Scholar
  43. 43.
    Kim PS, Crivelli JJ, Choi IK, Yun CO, Wares JR (2015) Quantitative impact of immunomodulation versus oncolysis with cytokine-expressing virus therapeutics. Math Biosci Eng 12(4):841–858. Scholar
  44. 44.
    Macnamara C, Eftimie R (2015) Memory versus effector immune responses in oncolytic virotherapies. J Theor Biol 377:1–9. Scholar
  45. 45.
    Wang Z, Guo Z, Peng H (2016) A mathematical model verifying potent oncolytic efficacy of M1 virus. Math Biosci 276:19–27. Scholar
  46. 46.
    Barish S, Ochs MF, Sontag ED, Gevertz JL (2017) Evaluating optimal therapy robustness by virtual expansion of a sample population, with a case study in cancer immunotherapy. Proc Natl Acad Sci U S A 114(31):E6277–E6286. Scholar
  47. 47.
    Malinzi J, Ouifki R, Eladdadi A, Torres DFM, White JKA (2018) Enhancement of chemotherapy using oncolytic virotherapy: mathematical and optimal control analysis. Math Biosci Eng 15(6):1435–1463. Scholar
  48. 48.
    Jenner AL, Yun CO, Kim PS, Coster ACF (2018) Mathematical modelling of the interaction between cancer cells and an oncolytic virus: insights into the effects of treatment protocols. Bull Math Biol 80(6):1615–1629. Scholar
  49. 49.
    Boemo MA, Byrne HM (2019) Mathematical modelling of a hypoxia-regulated oncolytic virus delivered by tumour-associated macrophages. J Theor Biol 461:102–116. Scholar
  50. 50.
    Ratajczyk E, Ledzewicz U, Leszczynski M, Friedman A (2017) The role of TNF-alpha inhibitor in glioma virotherapy: a mathematical model. Math Biosci Eng 14(1):305–319. Scholar
  51. 51.
    Timalsina A, Tian JP, Wang J (2017) Mathematical and computational modeling for tumor virotherapy with mediated immunity. Bull Math Biol 79(8):1736–1758. Scholar
  52. 52.
    Ashyani A, RabieiMotlagh O, Mohammadinejad HM (2018) A mathematical approach to effects of CTLs on cancer virotherapy in the second injection of virus. J Theor Biol 453:78–87. Scholar
  53. 53.
    Malinzi J, Eladdadi A, Sibanda P (2017) Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment. J Biol Dyn 11(1):244–274. Scholar
  54. 54.
    Friedman A, Lai X (2018) Combination therapy for cancer with oncolytic virus and checkpoint inhibitor: a mathematical model. PLoS One 13(2):e0192449. Scholar
  55. 55.
    Mahasa KJ, Eladdadi A, de Pillis L, Ouifki R (2017) Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach. PLoS One 12(9):e0184347. Scholar
  56. 56.
    Rodriguez-Brenes IA, Hofacre A, Fan H, Wodarz D (2017) Complex dynamics of virus spread from low infection multiplicities: implications for the spread of oncolytic viruses. PLoS Comput Biol 13(1):e1005241. Scholar
  57. 57.
    Wodarz D, Hofacre A, Lau JW, Sun Z, Fan H, Komarova NL (2012) Complex spatial dynamics of oncolytic viruses in vitro: mathematical and experimental approaches. PLoS Comput Biol 8(6):e1002547. Scholar
  58. 58.
    Murray JD (2013) Mathematical biology II. Springer, New York, NYGoogle Scholar
  59. 59.
    Edelstein-Keshet L (1988) Mathematical models in biology. SIAM, Philadelphia, PAGoogle Scholar
  60. 60.
    Ciarletta PH, Hillen T, Othmer H, Trucu D (2016) Mathematical models and methods for living systems. Springer, ChamCrossRefGoogle Scholar
  61. 61.
    Otto SPD, Day T (2011) A biologist’s guide to mathematical modeling in ecology and evolution. Princeton University Press, PrincetonCrossRefGoogle Scholar
  62. 62.
    Kuang YN, Nagy JD, Eikenberry SE (2016) Introduction to mathematical oncology. CRC Press, Boca Raton, FLGoogle Scholar
  63. 63.
    Aho K, Derryberry D, Peterson T (2014) Model selection for ecologists: the worldviews of AIC and BIC. Ecology 95(3):631–636CrossRefGoogle Scholar
  64. 64.
    Eisenberg MC, Jain HV (2017) A confidence building exercise in data and identifiability: modeling cancer chemotherapy as a case study. J Theor Biol 431:63–78. Scholar
  65. 65.
    Anderson RM, May RM (1992) Infectious diseases of humans: dynamics and control. Oxford university press, OxfordGoogle Scholar
  66. 66.
    Kim Y, Lee HG, Dmitrieva N, Kim J, Kaur B, Friedman A (2014) Choindroitinase ABC I-mediated enhancement of oncolytic virus spread and anti tumor efficacy: a mathematical model. PLoS One 9(7):e102499CrossRefGoogle Scholar
  67. 67.
    Yu F, Wang X, Guo ZS, Bartlett DL, Gottschalk SM, Song XT (2014) T-cell engager-armed oncolytic vaccinia virus significantly enhances antitumor therapy. Mol Ther 22(1):102–111. Scholar
  68. 68.
    Fajardo CA, Guedan S, Rojas LA, Moreno R, Arias-Badia M, de Sostoa J, June CH, Alemany R (2017) Oncolytic adenoviral delivery of an EGFR-targeting T-cell engager improves antitumor efficacy. Cancer Res 77(8):2052–2063. Scholar
  69. 69.
    Freedman JD, Hagel J, Scott EM, Psallidas I, Gupta A, Spiers L, Miller P, Kanellakis N (2017) Oncolytic adenovirus expressing bispecific antibody targets T-cell cytotoxicity in cancer biopsies. EMBO Mol Med 9(8):1067–1087. Scholar
  70. 70.
    Speck T, Heidbuechel JPW, Veinalde R, Jaeger D, von Kalle C, Ball CR, Ungerechts G, Engeland CE (2018) Targeted BiTE expression by an oncolytic vector augments therapeutic efficacy against solid tumors. Clin Cancer Res 24(9):2128–2137. Scholar
  71. 71.
    Freedman JD, Duffy MR, Lei-Rossmann J, Muntzer A, Scott EM, Hagel J, Campo L, Bryant RJ, Verrill C, Lambert A, Miller P, Champion BR, Seymour LW, Fisher KD (2018) An oncolytic virus expressing a T-cell engager simultaneously targets cancer and immunosuppressive stromal cells. Cancer Res 78:6852. Scholar
  72. 72.
    Gatenby RA, Maini PK (2003) Mathematical oncology: cancer summed up. Nature 421(6921):321. Scholar
  73. 73.
    Anderson AR, Quaranta V (2008) Integrative mathematical oncology. Nat Rev Cancer 8(3):227–234. Scholar
  74. 74.
    Altrock PM, Liu LL, Michor F (2015) The mathematics of cancer: integrating quantitative models. Nat Rev Cancer 15(12):730–745. Scholar
  75. 75.
    McGuire MF, Enderling H, Wallace DI, Batra J, Jordan M, Kumar S, Panetta JC, Pasquier E (2013) Formalizing an integrative, multidisciplinary cancer therapy discovery workflow. Cancer Res 73(20):6111–6117. Scholar
  76. 76.
    Box GEP (1976) Science and statistics. J Am Stat Assoc 71(356):791–799. Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  • Johannes P. W. Heidbuechel
    • 1
    • 2
  • Daniel Abate-Daga
    • 3
  • Christine E. Engeland
    • 1
  • Heiko Enderling
    • 4
    Email author
  1. 1.Research Group Mechanisms of Oncolytic Immunotherapy, Clinical Cooperation Unit VirotherapyNational Center for Tumor Diseases (NCT), German Cancer Research Center (DKFZ), University Hospital HeidelbergHeidelbergGermany
  2. 2.Faculty of BiosciencesHeidelberg UniversityHeidelbergGermany
  3. 3.Department of ImmunologyH. Lee Moffitt Cancer Center & Research InstituteTampaUSA
  4. 4.Department of Integrated Mathematical OncologyH. Lee Moffitt Cancer Center & Research InstituteTampaUSA

Personalised recommendations