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36. Mitchem, J.B.; Brennan, D.J.; Knolhoff, B.L.; Belt, B.A.; Zhu, Y.; Sanford, D.E.; Belaygorod, L.; Carpenter, D.;
Collins, L.; Piwnica-Worms, D.; et al. Targeting tumor-infiltrating macrophages decreases tumor-initiating
cells, relieves immunosuppression, and improves chemotherapeutic responses. Cancer Res. 2013, 73,
1128–1141. [CrossRef][PubMed]
37. Qian, B.; Deng, Y.; Im, J.H.; Muschel, R.J.; Zou, Y.; Li, J.; Lang, R.A.; Pollard, J.W. A distinct macrophage
population mediates metastatic breast cancer cell extravasation, establishment and growth. PLoS ONE 2009,
4, e6562. [CrossRef]
38. Lohela, M.; Casbon, A.-J.; Olow, A.; Bonham, L.; Branstetter, D.; Weng, N.; Smith, J.; Werb, Z. Intravital
imaging reveals distinct responses of depleting dynamic tumor-associated macrophage and dendritic cell
subpopulations. Proc. Natl. Acad. Sci. USA 2014, 111, E5086–E5095. [CrossRef]
39. Ngambenjawong, C.; Cieslewicz, M.; Schellinger, J.G.; Pun, S.H. Synthesis and evaluation of multivalent
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[CrossRef]
40. Mishalian, I.; Granot, Z.; Fridlender, Z.G. The diversity of circulating neutrophils in cancer. Immunobiology
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41. Davis, B.P.; Rothenberg, M.E. Eosinophils and cancer. Cancer Immunol. Res. 2014, 2, 1–8. [CrossRef][PubMed]
42. Hämmerling, G.J.; Carretero, R.; Beckhove, P.; Salgado, O.C.; Sektioglu, I.M.; Garbi, N. Eosinophils
orchestrate cancer rejection by normalizing tumor vessels and enhancing infiltration of CD8+ T cells.
Nat. Immunol. 2015, 16, 609–617.
43. Sakkal, S.; Miller, S.; Apostolopoulos, V.; Nurgali, K. Eosinophils in cancer: Favourable or unfavourable?
Curr. Med. Chem. 2016, 23, 650–666. [CrossRef][PubMed]
44. Shinde, S.B.; Kurhekar, M.P. Review of the systems biology of the immune system using agent-based models.
IET Syst. Biol. 2018, 12, 83–92. [CrossRef][PubMed]
45. Altrock, P.M.; Liu, L.L.; Michor, F. The mathematics of cancer: Integrating quantitative models. Nat. Rev. Cancer
2015, 15, 730–745. [CrossRef][PubMed]
46. Rejniak, K.A.; McCawley, L.J. Current trends in mathematical modeling of tumor-microenvironment
interactions: A survey of tools and applications. Exp. Biol. Med. 2010, 235, 411–423. [CrossRef][PubMed]
47. Eftimie, R.; Bramson, J.L.; Earn, D.J.D. Interactions between the immune system and cancer: A brief review
of non-spatial mathematical models. Bull. Math. Biol. 2011, 73, 2–32. [CrossRef]
48. Alemani, D.; Pappalardo, F.; Pennisi, M.; Motta, S.; Brusic, V. Combining cellular automata and lattice
Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and
immune competition. J. Immunol. Methods 2012, 376, 55–68. [CrossRef]
49. Bellomo, N.; Delitala, M. From the mathematical kinetic, and stochastic game theory to modelling mutations,
onset, progression and immune competition of cancer cells. Phys. Life Rev. 2008, 5, 183–206. [CrossRef]
50. Eladdadi, A.; de Pillis, L.; Kim, P. Modelling tumour-immune dynamics, disease progression and treatment.
Lett. Biomath. 2018, 5, S1–S5. [CrossRef]
51. Dritschel, H.; Waters, S.L.; Roller, A.; Byrne, H.M. A mathematical model of cytotoxic and helper T cell
interactions in a tumour microenvironment. Lett. Biomath. 2018, 5, S36–S68. [CrossRef]
52. Nikolopoulou, E.; Johnson, L.R.; Harris, D.; Nagy, J.D.; Stites, E.C.; Kuang, Y. Tumour-immune dynamics
with an immune checkpoint inhibitor. Lett. Biomath. 2018, 5, S137–S159. [CrossRef]
53. Salgia, R.; Mambetsariev, I.; Hewelt, B.; Achuthan, S.; Li, H.; Poroyko, V.; Wang, Y.; Sattler, M. Modeling
small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models. Oncotarget
2018, 9, 26226–26242. [CrossRef][PubMed]
54. Konstorum, A.; Vella, A.T.; Adler, A.J.; Laubenbacher, R.C. Addressing current challenges in cancer
immunotherapy with mathematical and computational modelling. J. R. Soc. Interface 2017, 14, 20170150.
[CrossRef][PubMed]
55. Chiacchio, F.; Pennisi, M.; Russo, G.; Motta, S.; Pappalardo, F. Agent-based modeling of the immune system:
NetLogo, a promising framework. BioMed Res. Int. 2014, 907171. [CrossRef][PubMed]
56. An, G.; Mi, Q.; Dutta-Moscato, J.; Vodovotz, Y. Agent-based models in translational systems biology.
Wiley Interdiscip. Rev. Syst. Biol. Med. 2009, 1, 159–171. [CrossRef]
57
35. Burger, G.A.; Danen, E.H.J.; Beltman, J.B. Deciphering epithelial—Mesenchymal transition regulatory
networks in cancer through computational approaches. Front. Oncol. 2017, 7, 162. [CrossRef][PubMed]
36. Mitchem, J.B.; Brennan, D.J.; Knolhoff, B.L.; Belt, B.A.; Zhu, Y.; Sanford, D.E.; Belaygorod, L.; Carpenter, D.;
Collins, L.; Piwnica-Worms, D.; et al. Targeting tumor-infiltrating macrophages decreases tumor-initiating
cells, relieves immunosuppression, and improves chemotherapeutic responses. Cancer Res. 2013, 73,
1128–1141. [CrossRef][PubMed]
37. Qian, B.; Deng, Y.; Im, J.H.; Muschel, R.J.; Zou, Y.; Li, J.; Lang, R.A.; Pollard, J.W. A distinct macrophage
population mediates metastatic breast cancer cell extravasation, establishment and growth. PLoS ONE 2009,
4, e6562. [CrossRef]
38. Lohela, M.; Casbon, A.-J.; Olow, A.; Bonham, L.; Branstetter, D.; Weng, N.; Smith, J.; Werb, Z. Intravital
imaging reveals distinct responses of depleting dynamic tumor-associated macrophage and dendritic cell
subpopulations. Proc. Natl. Acad. Sci. USA 2014, 111, E5086–E5095. [CrossRef]
39. Ngambenjawong, C.; Cieslewicz, M.; Schellinger, J.G.; Pun, S.H. Synthesis and evaluation of multivalent
M2pep peptides for targeting alternatively activated M2 macrophages. J. Control. Release 2016, 224, 103–111.
[CrossRef]
40. Mishalian, I.; Granot, Z.; Fridlender, Z.G. The diversity of circulating neutrophils in cancer. Immunobiology
2017, 222, 82–88. [CrossRef]
41. Davis, B.P.; Rothenberg, M.E. Eosinophils and cancer. Cancer Immunol. Res. 2014, 2, 1–8. [CrossRef][PubMed]
42. Hämmerling, G.J.; Carretero, R.; Beckhove, P.; Salgado, O.C.; Sektioglu, I.M.; Garbi, N. Eosinophils
orchestrate cancer rejection by normalizing tumor vessels and enhancing infiltration of CD8+ T cells.
Nat. Immunol. 2015, 16, 609–617.
43. Sakkal, S.; Miller, S.; Apostolopoulos, V.; Nurgali, K. Eosinophils in cancer: Favourable or unfavourable?
Curr. Med. Chem. 2016, 23, 650–666. [CrossRef][PubMed]
44. Shinde, S.B.; Kurhekar, M.P. Review of the systems biology of the immune system using agent-based models.
IET Syst. Biol. 2018, 12, 83–92. [CrossRef][PubMed]
45. Altrock, P.M.; Liu, L.L.; Michor, F. The mathematics of cancer: Integrating quantitative models. Nat. Rev. Cancer
2015, 15, 730–745. [CrossRef][PubMed]
46. Rejniak, K.A.; McCawley, L.J. Current trends in mathematical modeling of tumor-microenvironment
interactions: A survey of tools and applications. Exp. Biol. Med. 2010, 235, 411–423. [CrossRef][PubMed]
47. Eftimie, R.; Bramson, J.L.; Earn, D.J.D. Interactions between the immune system and cancer: A brief review
of non-spatial mathematical models. Bull. Math. Biol. 2011, 73, 2–32. [CrossRef]
48. Alemani, D.; Pappalardo, F.; Pennisi, M.; Motta, S.; Brusic, V. Combining cellular automata and lattice
Boltzmann method to model multiscale avascular tumor growth coupled with nutrient diffusion and
immune competition. J. Immunol. Methods 2012, 376, 55–68. [CrossRef]
49. Bellomo, N.; Delitala, M. From the mathematical kinetic, and stochastic game theory to modelling mutations,
onset, progression and immune competition of cancer cells. Phys. Life Rev. 2008, 5, 183–206. [CrossRef]
50. Eladdadi, A.; de Pillis, L.; Kim, P. Modelling tumour-immune dynamics, disease progression and treatment.
Lett. Biomath. 2018, 5, S1–S5. [CrossRef]
51. Dritschel, H.; Waters, S.L.; Roller, A.; Byrne, H.M. A mathematical model of cytotoxic and helper T cell
interactions in a tumour microenvironment. Lett. Biomath. 2018, 5, S36–S68. [CrossRef]
52. Nikolopoulou, E.; Johnson, L.R.; Harris, D.; Nagy, J.D.; Stites, E.C.; Kuang, Y. Tumour-immune dynamics
with an immune checkpoint inhibitor. Lett. Biomath. 2018, 5, S137–S159. [CrossRef]
53. Salgia, R.; Mambetsariev, I.; Hewelt, B.; Achuthan, S.; Li, H.; Poroyko, V.; Wang, Y.; Sattler, M. Modeling
small cell lung cancer (SCLC) biology through deterministic and stochastic mathematical models. Oncotarget
2018, 9, 26226–26242. [CrossRef][PubMed]
54. Konstorum, A.; Vella, A.T.; Adler, A.J.; Laubenbacher, R.C. Addressing current challenges in cancer
immunotherapy with mathematical and computational modelling. J. R. Soc. Interface 2017, 14, 20170150.
[CrossRef][PubMed]
55. Chiacchio, F.; Pennisi, M.; Russo, G.; Motta, S.; Pappalardo, F. Agent-based modeling of the immune system:
NetLogo, a promising framework. BioMed Res. Int. 2014, 907171. [CrossRef][PubMed]
56. An, G.; Mi, Q.; Dutta-Moscato, J.; Vodovotz, Y. Agent-based models in translational systems biology.
Wiley Interdiscip. Rev. Syst. Biol. Med. 2009, 1, 159–171. [CrossRef]
57