American Institute of Mathematical Sciences

Advanced
June  2013, 18(4): 1017-1030. doi: 10.3934/dcdsb.2013.18.1017

A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma

Yuri Kogan 1, , Zvia Agur 1, and  Moran Elishmereni 1,

1. 

10 Hate'ena St., P.O.B. 282, Bene Ataroth 60991, Israel, Israel, Israel

Received  May 2012 Revised  August 2012 Published  February 2013

Aggressive cancers develop immune suppression mechanisms, allowing them to evade specific immune responses. Patients with active melanoma are polarized towards a T helper (Th) 2-type immune phenotype, which subverts effective anticancer Th1-type cellular immunity. The pro-inflammatory factor, interleukin (IL)-12, can potentially restore Th1 responses in such patients, but still shows limited clinical efficacy and substantial side effects. We developed a model for the Th1/Th2 imbalance in melanoma patients and its regulation via IL-12 treatment. The model focuses on the interactions between the two Th cell types as mediated by their respective key cytokines, interferon (IFN)-$\gamma$ and IL-10. Theoretical and numerical analysis showed a landscape consisting of a single, globally attracting steady state, which is stable under large ranges of relevant parameter values. Our results suggest that in melanoma, the cellular arm of the immune system cannot reverse tumor immunotolerance naturally, and that immunotherapy may be the only way to overturn tumor dominance. We have shown that given a toxicity threshold for IFN$\gamma$, the maximal allowable IL-12 concentration to yield a Th1-polarized state can be estimated. Moreover, our analysis pinpoints the IL-10 secretion rate as a significant factor influencing the Th1:Th2 balance, suggesting its use as a personal immunomarker for prognosis.
Keywords: cancer, interferon-$\gamma$, Interleukin-12, phase plane analysis, interleukin-10, ODE, immune system..
Mathematics Subject Classification: 92B05, 37N2.
Citation: Yuri Kogan, Zvia Agur, Moran Elishmereni. A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 1017-1030. doi: 10.3934/dcdsb.2013.18.1017
References:
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J. M. Kirkwood, A. A. Tarhini, M. C. Panelli, S. J. Moschos, H. M. Zarour, L. H. Butterfield and H. J. Gogas, Next generation of immunotherapy for melanoma, J. Clin. Oncol., 26 (2008), 3445-3455. Google Scholar

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W. H. Fridman, F. Pages, C. Sautes-Fridman and J. Galon, The immune contexture in human tumours: impact on clinical outcome, Nat. Rev. Cancer, 12 (2012), 298-306. Google Scholar

[4]

A. J. Cochran, R. R. Huang, J. Lee, E. Itakura, S. P. L. Leong and R. Essner, Tumour-induced immune modulation of sentinel lymph nodes, Nat. Rev. Immunol., 6(9) (2006), 659-670. Google Scholar

[5]

L. Lauerova, L. Dusek, M. Simickova, I. Kocak, M. Vagundova, J. Zaloudik and J. Kovarik, Malignant melanoma associates with Th1/Th2 imbalance that coincides with disease progression and immunotherapy response, Neoplasma, 49 (2002), 159-166. Google Scholar

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R. Botella-Estrada, M. Escudero, J. E. O'Connor, E. Nagore, B. Fenollosa, O. Sanmartin, C. Requena and C. Guillen, Cytokine production by peripheral lymphocytes in melanoma, Eur. Cytokine Netw., 16 (2005), 47-55. Google Scholar

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W. K. Nevala, C. M. Vachon, A. A. Leontovich, C. G. Scott, M. A. Thompson and S. N. Markovic, Evidence of systemic Th2-driven chronic inflammation in patients with metastatic melanoma, Clin. Cancer Res., 15 (2009), 1931-1939. Google Scholar

[8]

W. Dummer, J. C. Becker, A. Schwaaf, M. Leverkus, T. Moll and E. B. Brocker, Elevated serum levels of interleukin-10 in patients with metastatic malignant melanoma, Melanoma Res., 5 (1995), 67-68. Google Scholar

[9]

A. M. Lana, D. R. Wen and A. J.Cochran, The morphology, immunophenotype and distribution of paracortical dendritic leucocytes in lymph nodes regional to cutaneous melanoma, Melanoma Res., 11 (2001), 401-410. Google Scholar

[10]

R. Botella-Estrada, F. Dasi, D. Ramos, E. Nagore, M. J. Herrero, J. Gimenez, C. Fuster, O. Sanmartin, C. Guillen and S. Alino, Cytokine expression and dendritic cell density in melanoma sentinel nodes, Melanoma Res., 15 (2005), 99-106. Google Scholar

[11]

J. H. Lee, H. Torisu-Itakara, A. J. Cochran, A. Kadison, Y. Huynh, D. L. Morton and R. Essner, Quantitative analysis of melanoma-induced cytokine-mediated immunosuppression in melanoma sentinel nodes, Clin. Cancer Res., 11 (2005), 107-112. Google Scholar

[12]

T. Tatsumi, L. S. Kierstead, E. Ranieri, L. Gesualdo, F. P. Schena, J. H. Finke, R. M. Bukowski, J. Mueller-Berghaus, J. M. Kirkwood, W. W. Kwok and W. J. Storkus, Disease-associated bias in T helper type 1 (Th1)/Th2 CD4+ T cell responses against MAGE-6 in HLA-DRB10401+ patients with renal cell carcinoma or melanoma, J. Experimental Medicine, 196 (2002), 619-628. Google Scholar

[13]

D. D. Kharkevitch, D. Seito, G. C. Balch, T. Maeda, C. M. Balch and K. Itoh, Characterization of autologous tumor-specific T-helper 2 cells in tumor-infiltrating lymphocytes from a patient with metastatic melanoma, Int. J. Cancer, 58 (1994), 317-323. Google Scholar

[14]

G. Trinchieri, Interleukin-12: A proinflammatory cytokine with immunoregulatory functions that bridge innate resistance and antigen-specific adaptive immunity, Annu. Rev. Immunol., 13 (1995), 251-276. Google Scholar

[15]

M. P. Colombo and G. Trinchieri, Interleukin-12 in anti-tumor immunity and immunotherapy, Cytokine Growth Factor Rev., 13 (2002), 155-168. Google Scholar

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G. Trinchieri, Interleukin-12 and the regulation of innate resistance and adaptive immunity, Nat. Rev. Immunol., 3 (2003), 133-146. Google Scholar

[17]

M. Del Vecchio, E. Bajetta, S. Canova, M. T. Lotze, A. Wesa, G. Parmiani and A. Anichini, Interleukin-12: biological properties and clinical application, Clin. Cancer Res., 13 (2007), 4677-4685. Google Scholar

[18]

M. A. Cheever, Twelve immunotherapy drugs that could cure cancers, Immunol. Rev., 222 (2008), 357-368. Google Scholar

[19]

Z. Agur, From the evolution of toxin resistance to virtual clinical trials: The role of mathematical models in oncology, Future Oncol., 6 (2010), 917-927. Google Scholar

[20]

R. Eftimie, J. L. Bramson and D. J. Earn, Interactions between the immune system and cancer: A brief review of non-spatial mathematical models, Bull. Math. Biol., 73 (2011), 2-32. doi: 10.1007/s11538-010-9526-3.  Google Scholar

[21]

D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol., 37 (1998), 235-252. Google Scholar

[22]

F. Nani and H. I. Freedman, A mathematical model of cancer treatment by immunotherapy, Math. Biosci., 163 (2000), 159-199. doi: 10.1016/S0025-5564(99)00058-9.  Google Scholar

[23]

L. G. de Pillis, W. Gu and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations, J. Theor. Biol., 238 (2006), 841-862. doi: 10.1016/j.jtbi.2005.06.037.  Google Scholar

[24]

A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by interleukin-21: Potential treatment strategies evaluated in a mathematical model, Cancer Res, 66 (2006), 7293-7300. Google Scholar

[25]

A. Cappuccio, M. Elishmereni and Z. Agur, Optimization of interleukin-21 immunotherapeutic strategies, J. Theor. Biol., 248 (2007), 259-266. doi: 10.1016/j.jtbi.2007.05.015.  Google Scholar

[26]

M. Elishmereni, Y. Kheifetz, H. Sondergaard, R. V. Overgaard and Z. Agur, An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers, PLoS Comput. Biol., 7 (2011), e1002206. Google Scholar

[27]

N. Kronik, Y. Kogan, V. Vainstein and Z. Agur, Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics, Cancer Immunol. Immunother., 57 (2008), 425-439. Google Scholar

[28]

N. Kronik, Y. Kogan, M. Elishmereni, K. Halevi-Tobias, S. Vuk-Pavlovic and Z. Agur, Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models, PLoS One, 5 (2010), e15482. Google Scholar

[29]

Y. Kogan, K. Halevi-Tobias, M. Elishmereni, S. Vuk-Pavlovic and Z. Agur, Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization, Cancer Res., 72 (2012), 2218-2227. Google Scholar

[30]

E. Jager, V. H. van der Velden, J. G. te Marvelde, R. B. Walter, Z. Agur and V. Vainstein, Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization, PLoS One, 6 (2011), e24265. Google Scholar

[31]

Z. Agur and S. Vuk-Pavlovic, Mathematical modeling in immunotherapy of cancer: Personalizing clinical trials, Mol. Ther., 20 (2012), 1-2. Google Scholar

[32]

F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control, J. Theor. Biol., 247 (2007), 723-732. doi: 10.1016/j.jtbi.2007.04.003.  Google Scholar

[33]

L. G. de Pillis, A. E. Radunskaya and C. L. Wiseman, A validated mathematical model of cell-mediated immune response to tumor growth, Cancer Res., 65 (2005), 7950-7958. Google Scholar

[34]

M. A. Fishman and A. S. Perelson, Th1/Th2 cross regulation, J. Theor. Biol., 170 (1994), 25-56. Google Scholar

[35]

M. A. Fishman and L. A. Segel, Modeling immunotherapy for allergy, Bull. Math. Biol., 58 (1996), 1099-1121. Google Scholar

[36]

M. A. Fishman and A. S. Perelson, Th1/Th2 differentiation and cross-regulation, Bull. Math. Biol., 61 (1999), 403-436. Google Scholar

[37]

A. Yates, C. Bergmann, J. L. Van Hemmen, J. Stark and R. Callard, Cytokine-modulated regulation of helper T cell populations, J. Theor. Biol., 206 (2000), 539-560. Google Scholar

[38]

C. Bergmann, J. L. Van Hemmen and L. A.Segel, Th1 or Th2: How an appropriate T helper response can be made, Bull. Math. Biol., 63 (2001), 405-430. Google Scholar

[39]

A. Yates, R. Callard and J. Stark, Combining cytokine signalling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: a model for cellular decision-making, J. Theor. Biol., 231 (2004), 181-196. doi: 10.1016/j.jtbi.2004.06.013.  Google Scholar

[40]

R. E. Callard, Decision-making by the immune response, Immunol. Cell Biol., 85 (2007), 300-305. Google Scholar

[41]

F. Gross, G. Metzner and U. Behn, Mathematical modeling of allergy and specific immunotherapy: Th1-Th2-Treg interactions, J. Theor. Biol., 269 (2011), 70-78. Google Scholar

[42]

M. L. Disis, Immunologic biomarkers as correlates of clinical response to cancer immunotherapy, Cancer Immunol. Immunother., 60 (2011), 433-442. Google Scholar

[43]

J. P. Leonard, M. L. Sherman, G. L. Fisher, L. J. Buchanan, G. Larsen, M. B. Atkins, J. A. Sosman, J. P. Dutcher, N. J. Vogelzang and J. L. Ryan, Effects of single-dose interleukin-12 exposure on interleukin-12-associated toxicity and interferon-gamma production, Blood, 90 (1997), 2541-2548. Google Scholar

[44]

J. M. Weiss, J. J. Subleski, J. M. Wigginton, R. H. Wiltrout, Immunotherapy of cancer by IL-12-based cytokine combinations, Expert Opin. Biol. Ther., 7 (2007), 1705-1721. Google Scholar

show all references

References:
[1]

J. M. Kirkwood, A. A. Tarhini, M. C. Panelli, S. J. Moschos, H. M. Zarour, L. H. Butterfield and H. J. Gogas, Next generation of immunotherapy for melanoma, J. Clin. Oncol., 26 (2008), 3445-3455. Google Scholar

[2]

G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape, Nat. Immunol., 3 (2002), 991-998. Google Scholar

[3]

W. H. Fridman, F. Pages, C. Sautes-Fridman and J. Galon, The immune contexture in human tumours: impact on clinical outcome, Nat. Rev. Cancer, 12 (2012), 298-306. Google Scholar

[4]

A. J. Cochran, R. R. Huang, J. Lee, E. Itakura, S. P. L. Leong and R. Essner, Tumour-induced immune modulation of sentinel lymph nodes, Nat. Rev. Immunol., 6(9) (2006), 659-670. Google Scholar

[5]

L. Lauerova, L. Dusek, M. Simickova, I. Kocak, M. Vagundova, J. Zaloudik and J. Kovarik, Malignant melanoma associates with Th1/Th2 imbalance that coincides with disease progression and immunotherapy response, Neoplasma, 49 (2002), 159-166. Google Scholar

[6]

R. Botella-Estrada, M. Escudero, J. E. O'Connor, E. Nagore, B. Fenollosa, O. Sanmartin, C. Requena and C. Guillen, Cytokine production by peripheral lymphocytes in melanoma, Eur. Cytokine Netw., 16 (2005), 47-55. Google Scholar

[7]

W. K. Nevala, C. M. Vachon, A. A. Leontovich, C. G. Scott, M. A. Thompson and S. N. Markovic, Evidence of systemic Th2-driven chronic inflammation in patients with metastatic melanoma, Clin. Cancer Res., 15 (2009), 1931-1939. Google Scholar

[8]

W. Dummer, J. C. Becker, A. Schwaaf, M. Leverkus, T. Moll and E. B. Brocker, Elevated serum levels of interleukin-10 in patients with metastatic malignant melanoma, Melanoma Res., 5 (1995), 67-68. Google Scholar

[9]

A. M. Lana, D. R. Wen and A. J.Cochran, The morphology, immunophenotype and distribution of paracortical dendritic leucocytes in lymph nodes regional to cutaneous melanoma, Melanoma Res., 11 (2001), 401-410. Google Scholar

[10]

R. Botella-Estrada, F. Dasi, D. Ramos, E. Nagore, M. J. Herrero, J. Gimenez, C. Fuster, O. Sanmartin, C. Guillen and S. Alino, Cytokine expression and dendritic cell density in melanoma sentinel nodes, Melanoma Res., 15 (2005), 99-106. Google Scholar

[11]

J. H. Lee, H. Torisu-Itakara, A. J. Cochran, A. Kadison, Y. Huynh, D. L. Morton and R. Essner, Quantitative analysis of melanoma-induced cytokine-mediated immunosuppression in melanoma sentinel nodes, Clin. Cancer Res., 11 (2005), 107-112. Google Scholar

[12]

T. Tatsumi, L. S. Kierstead, E. Ranieri, L. Gesualdo, F. P. Schena, J. H. Finke, R. M. Bukowski, J. Mueller-Berghaus, J. M. Kirkwood, W. W. Kwok and W. J. Storkus, Disease-associated bias in T helper type 1 (Th1)/Th2 CD4+ T cell responses against MAGE-6 in HLA-DRB10401+ patients with renal cell carcinoma or melanoma, J. Experimental Medicine, 196 (2002), 619-628. Google Scholar

[13]

D. D. Kharkevitch, D. Seito, G. C. Balch, T. Maeda, C. M. Balch and K. Itoh, Characterization of autologous tumor-specific T-helper 2 cells in tumor-infiltrating lymphocytes from a patient with metastatic melanoma, Int. J. Cancer, 58 (1994), 317-323. Google Scholar

[14]

G. Trinchieri, Interleukin-12: A proinflammatory cytokine with immunoregulatory functions that bridge innate resistance and antigen-specific adaptive immunity, Annu. Rev. Immunol., 13 (1995), 251-276. Google Scholar

[15]

M. P. Colombo and G. Trinchieri, Interleukin-12 in anti-tumor immunity and immunotherapy, Cytokine Growth Factor Rev., 13 (2002), 155-168. Google Scholar

[16]

G. Trinchieri, Interleukin-12 and the regulation of innate resistance and adaptive immunity, Nat. Rev. Immunol., 3 (2003), 133-146. Google Scholar

[17]

M. Del Vecchio, E. Bajetta, S. Canova, M. T. Lotze, A. Wesa, G. Parmiani and A. Anichini, Interleukin-12: biological properties and clinical application, Clin. Cancer Res., 13 (2007), 4677-4685. Google Scholar

[18]

M. A. Cheever, Twelve immunotherapy drugs that could cure cancers, Immunol. Rev., 222 (2008), 357-368. Google Scholar

[19]

Z. Agur, From the evolution of toxin resistance to virtual clinical trials: The role of mathematical models in oncology, Future Oncol., 6 (2010), 917-927. Google Scholar

[20]

R. Eftimie, J. L. Bramson and D. J. Earn, Interactions between the immune system and cancer: A brief review of non-spatial mathematical models, Bull. Math. Biol., 73 (2011), 2-32. doi: 10.1007/s11538-010-9526-3.  Google Scholar

[21]

D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol., 37 (1998), 235-252. Google Scholar

[22]

F. Nani and H. I. Freedman, A mathematical model of cancer treatment by immunotherapy, Math. Biosci., 163 (2000), 159-199. doi: 10.1016/S0025-5564(99)00058-9.  Google Scholar

[23]

L. G. de Pillis, W. Gu and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations, J. Theor. Biol., 238 (2006), 841-862. doi: 10.1016/j.jtbi.2005.06.037.  Google Scholar

[24]

A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by interleukin-21: Potential treatment strategies evaluated in a mathematical model, Cancer Res, 66 (2006), 7293-7300. Google Scholar

[25]

A. Cappuccio, M. Elishmereni and Z. Agur, Optimization of interleukin-21 immunotherapeutic strategies, J. Theor. Biol., 248 (2007), 259-266. doi: 10.1016/j.jtbi.2007.05.015.  Google Scholar

[26]

M. Elishmereni, Y. Kheifetz, H. Sondergaard, R. V. Overgaard and Z. Agur, An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers, PLoS Comput. Biol., 7 (2011), e1002206. Google Scholar

[27]

N. Kronik, Y. Kogan, V. Vainstein and Z. Agur, Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics, Cancer Immunol. Immunother., 57 (2008), 425-439. Google Scholar

[28]

N. Kronik, Y. Kogan, M. Elishmereni, K. Halevi-Tobias, S. Vuk-Pavlovic and Z. Agur, Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models, PLoS One, 5 (2010), e15482. Google Scholar

[29]

Y. Kogan, K. Halevi-Tobias, M. Elishmereni, S. Vuk-Pavlovic and Z. Agur, Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization, Cancer Res., 72 (2012), 2218-2227. Google Scholar

[30]

E. Jager, V. H. van der Velden, J. G. te Marvelde, R. B. Walter, Z. Agur and V. Vainstein, Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization, PLoS One, 6 (2011), e24265. Google Scholar

[31]

Z. Agur and S. Vuk-Pavlovic, Mathematical modeling in immunotherapy of cancer: Personalizing clinical trials, Mol. Ther., 20 (2012), 1-2. Google Scholar

[32]

F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control, J. Theor. Biol., 247 (2007), 723-732. doi: 10.1016/j.jtbi.2007.04.003.  Google Scholar

[33]

L. G. de Pillis, A. E. Radunskaya and C. L. Wiseman, A validated mathematical model of cell-mediated immune response to tumor growth, Cancer Res., 65 (2005), 7950-7958. Google Scholar

[34]

M. A. Fishman and A. S. Perelson, Th1/Th2 cross regulation, J. Theor. Biol., 170 (1994), 25-56. Google Scholar

[35]

M. A. Fishman and L. A. Segel, Modeling immunotherapy for allergy, Bull. Math. Biol., 58 (1996), 1099-1121. Google Scholar

[36]

M. A. Fishman and A. S. Perelson, Th1/Th2 differentiation and cross-regulation, Bull. Math. Biol., 61 (1999), 403-436. Google Scholar

[37]

A. Yates, C. Bergmann, J. L. Van Hemmen, J. Stark and R. Callard, Cytokine-modulated regulation of helper T cell populations, J. Theor. Biol., 206 (2000), 539-560. Google Scholar

[38]

C. Bergmann, J. L. Van Hemmen and L. A.Segel, Th1 or Th2: How an appropriate T helper response can be made, Bull. Math. Biol., 63 (2001), 405-430. Google Scholar

[39]

A. Yates, R. Callard and J. Stark, Combining cytokine signalling with T-bet and GATA-3 regulation in Th1 and Th2 differentiation: a model for cellular decision-making, J. Theor. Biol., 231 (2004), 181-196. doi: 10.1016/j.jtbi.2004.06.013.  Google Scholar

[40]

R. E. Callard, Decision-making by the immune response, Immunol. Cell Biol., 85 (2007), 300-305. Google Scholar

[41]

F. Gross, G. Metzner and U. Behn, Mathematical modeling of allergy and specific immunotherapy: Th1-Th2-Treg interactions, J. Theor. Biol., 269 (2011), 70-78. Google Scholar

[42]

M. L. Disis, Immunologic biomarkers as correlates of clinical response to cancer immunotherapy, Cancer Immunol. Immunother., 60 (2011), 433-442. Google Scholar

[43]

J. P. Leonard, M. L. Sherman, G. L. Fisher, L. J. Buchanan, G. Larsen, M. B. Atkins, J. A. Sosman, J. P. Dutcher, N. J. Vogelzang and J. L. Ryan, Effects of single-dose interleukin-12 exposure on interleukin-12-associated toxicity and interferon-gamma production, Blood, 90 (1997), 2541-2548. Google Scholar

[44]

J. M. Weiss, J. J. Subleski, J. M. Wigginton, R. H. Wiltrout, Immunotherapy of cancer by IL-12-based cytokine combinations, Expert Opin. Biol. Ther., 7 (2007), 1705-1721. Google Scholar

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