Model parameters, descriptions, and values are chosen for simulations
Notation
Value
Description
C
7 × 10–1
Cancer cells
I
2.1 × 10–2
Immune system
E
3.8 × 10–1
Elimination of cancer cells
IC
5.7 × 10–2
Complex formed between the immune system and cancer cells
c
1 × 10–7
Concentration of chemokines
n
3.42 × 10–10
Concentration of immune cells
k
1.8 × 10–8
Degradation rate of chemokines
Dn
1.3 × 10–4
Diffusion coefficient of immune cells
t
Est
Time
χ
Est
Sensitivity of immune cells to chemokines
D
4.13 × 10–2
Diffusion coefficient of chemokines
cn
5 × 10–3
Sensitivity of concentration of chemokines
Note. Adapted from “Modeling cancer immunoediting in tumor microenvironment with system characterizationthrough the ising-model Hamiltonian” by Rojas-Domínguez A, Arroyo-Duarte R, Rincón-Vieyra F, Alvarado-Mentado M. BMC Bioinformatics. 2022;30:200. (https://bmcbioinformatics.biomedcentral.com/articles/10.1186/s12859-022-04731-w#citeas). CC BY.
Declarations
Acknowledgments
This work is supported under a research project entitled “Mathematical modeling of tumor growth and its treatments” granted by the U.P. State Government under the supervision of Prof. Sanjeev Kumar.
Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies.Philos Trans R Soc Lond. 1825;115:513–83. [DOI]
Winsor CP. The Gompertz Curve as a Growth Curve.Proc Natl Acad Sci U S A. 1932;18:1–8. [DOI] [PubMed] [PMC]
Laird AK, Tyler SA, Barton AD. Dynamics of normal growth.Growth. 1965;29:233–48. [PubMed]
Burton AC. Rate of growth of solid tumours as a problem of diffusion.Growth. 1966;30:157–76. [PubMed]
Orme ME, Chaplain MAJ. A mathematical model of vascular tumour growth and invasion.Math Comput Modell. 1996;23:43–60. [DOI]
Anderson AR, Chaplain MA. Continuous and discrete mathematical models of tumor-induced angiogenesis.Bull Math Biol. 1998;60:857–99. [DOI] [PubMed]
Bellomo N, Preziosi L. Modelling and mathematical problems related to tumor evolution and its interaction with the immune system.Math Comput Modell. 2000;32:413–52. [DOI]
Sherratt JA, Chaplain MA. A new mathematical model for avascular tumour growth.J Math Biol. 2001;43:291–312. [DOI] [PubMed]
Tsoularis A, Wallace J. Analysis of logistic growth models.Math Biosci. 2002;179:21–55. [DOI] [PubMed]
Villasana M, Radunskaya A. A delay differential equation model for tumor growth.J Math Biol. 2003;47:270–94. [DOI] [PubMed]
Misra JC, Dravid B. A mathematical model in the study of genes for identifying transcription factor binding sites.Comput Math Appl. 2006;51:621–30. [DOI]
Murray JD. Mathematical Biology: I. An Introduction. 3rd ed. Springer-Verlag Berlin Heidelberg; 2002.
Yang HM. Mathematical modeling of solid cancer growth with angiogenesis.Theor Biol Med Model. 2012;9:2. [DOI] [PubMed] [PMC]
Dixit DS, Kumar D, Kumar S, Johri R. Mathematical Modelling For Chemotherapy Of Tumor Growth With Aspect Of Biological Stoichiometry.Global J Pure Appl Math. 2015;11:2581–7.
Li Y, Cheng H, Wang J, Wang Y. Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy.Adv Differ Equ. 2018:32. [DOI]
Wei HC. A mathematical model of tumour growth with Beddington-DeAngelis functional response: a case of cancer without disease.J Biol Dyn. 2018;12:194–210. [DOI] [PubMed]
Yin A, Moes DJAR, van Hasselt JGC, Swen JJ, Guchelaar HJ. A Review of Mathematical Models for Tumor Dynamics and Treatment Resistance Evolution of Solid Tumors.CPT Pharmacometrics Syst Pharmacol. 2019;8:720–37. [DOI] [PubMed] [PMC]
Ira JI, Islam MS, Misra JC, Kamrujjaman M. Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control.Int J Ground Sediment Water. 2020;11:659–79. [DOI]
Pourhasanzade F, Sabzpoushan SH. A New Mathematical Model for Controlling Tumor Growth Based on Microenvironment Acidity and Oxygen Concentration.Biomed Res Int. 2021;2021:8886050. [DOI] [PubMed] [PMC]
Rojas-Domínguez A, Arroyo-Duarte R, Rincón-Vieyra F, Alvarado-Mentado M. Modeling cancer immunoediting in tumor microenvironment with system characterization through the ising-model Hamiltonian.BMC Bioinformatics. 2022;23:200. [DOI] [PubMed] [PMC]
Ullah MA, Mallick UK. Mathematical Modeling and Analysis on the Effects of Surgery and Chemotherapy on Lung Cancer.J Appl Math. 2023;2023:1–16. [DOI]
Wei K, Du Z, Deng J, Yang J, Chen H. A Novel Pyroptosis-Based Prognostic Model Correlated with the Parainflammatory Immune Microenvironment of Pancreatic Cancer.J Appl Math. 2023;2023:1–26. [DOI]