Fuzzy optimal treatment of AIDS-related non-Hodgkin’s cancer

Authors

1 Assis. Prof., Mech. Eng., Shahrood Univ. of Tech., Shahrood, Iran.

2 MSc student., Mech. Eng., Shahrood Univ. of Tech., Shahrood, Iran.

3 PhD., Math. Sci., Shahrood Univ. of Tech., Shahrood, Iran.

Abstract

The Aids-related non-Hodgkin’s lymphomas are the second most frequent cancer. A proposed treatment strategy should be implemented as short as possible. A long time treatment protocol not only devitalizes the immune system but also cause to drug resistance. It is observed in many cases that the immune system is able to diminish the tumor cells without any external treatment. Based on these, an extended model for cancer during the treatment has been proposed. A mixed chemo-immunotherapy proposed which the chemotherapy limits the tumor cell growth and the immunotherapy modifies the dynamics of the system. Hence, the equilibrium points of the system, their stabilities and the bifurcation of the system investigated. In order to obtain an optimal dose and considering the conditions of a patient the SDRE method combined with a fuzzy system. The simulation results show an efficient treatment should not only reduce the population of cancer cells but also must modify the dynamics of the system.

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References

[1] Culshaw RV, Ruan S (2000) A delay-differential equation model of HIV infection of CD4+T-Cells. Math Biosci 165 (1): 27-39.
[2] Boshoff C, Weiss R (2002) AIDS-related malignancies. Nat Rev Cancer 2 (5):373-382.
[3] Hashmi MU, Suleman M, Zaidi SMJ, Habib M (2014) Modeling the tumor-immune interaction cultured with chemotherapy and cytokine interleukin il-2 under the influence of immunodeficiency viruses. Am-Eurasian J Toxicol Sci 6(4): 74-82.
[4] Rihan A, Abdel Rahman DH (2013) Delay differential model for tumor-immune dynamics with HIV infection of CD4+ T-cells. International Journal of Computer Mathematics 90 (3): 594-614.
[5] Aogo R, Nyabadza F (2017) Modelling the dynamics of HIV-related non-Hodgkin lymphomas in the presence of HIV treatment and chemotherapy. Math Method Appl Sci        1-22.
[6] Nazari M, Ghaffari A, Arab F (2015) Finite duration treatment of cancer by using vaccine therapy and optimal chemotherapy: State-dependent riccati equation control and extended kalman filteR. J Biol Syst 23(1).
[7] Ghaffari A, Nazari M, Arab F (2015) Suboptimal mixed vaccine and chemotherapy in finite duration cancer treatment: state-dependent Riccati equation control. J Braz Soc Mech Sci 37(1): 45-56.
[8] Ruff R, Puetter A, Levy LS (2007) Growth regulation of simian and human AIDS-related non-hodgkin's lymphoma cell lines by TGF-beta1and IL-6. BMC Cancer 7(1): 7-35.
[9] Nazari M, Ghaffari A (2015) The effect of finite duration inputs on the dynamics of a system: Proposing a new approach for cancer treatment. Int J Biomath 8(3): 1-19.
[10]  Ghaffari A, Nazari M, Khazaee M, Bahmaei B (2014) Changing the dynamics of a system by using finite duration inputs: Application to cancer modeling and treatment. Journal of Solid and Fluid Mechanics 4(1): 79-91.
[11] De Pillis LG, Gu W, Radunskaya AE (2006) Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J Theor Biol 238: 841-862.
[12] De Pillis LG, Gu W, Radunskaya AE (2006) Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J Theor Biol 238(4): 841-862.
[13] Ghaffari A, Khazaee M (2012) Cancer dynamics for identical twin brothers. Theor Biol Med Model 9(1):4.
[14] Pinho STR, Freedman HI, Nani F (2002) Chemotherapy model for the treatment of cancer with metastasis. Math Comput Model 36: 773-803.
[15] Cimen T (2010) Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method. Annu Rev Control 34: 32-51.
[16] Wu X, Liu Q, Zhang K, Cheng M, Xin X (2018) Optimal switching control for drug therapy process in cancer chemotherapy. Eur J Control 42: 49-58
[17] Chen T, Kirkby NF, Jena R (2012) Optimal dosing of cancer chemotherapy using model predictive control and moving horizon state/parameter estimation. Comput Meth Prog Bio 108(3): 337-1340.
[18] Babaei N, Salamci M (2017) Controller design for personalized drug administration in cancer therapy: Successive approximation approach. Optim Contr Appl Met 1-38.
[19] Rihan FA, Lakshmanan S, Maurer H (2019) Optimal control of tumour-immune model with time-delay and immuno-chemotherapy. Appl Math Comput 353: 147-165.
[20] Ghaffari A, Bahmaei B, Nazari M (2016) Amixed radiotherapy and chemotherapy model for treatment of cancer withmetastasis. Math Method Appl Sci 39(15): 4603-4617.
[21] Batmani Y, Khaloozadeh H (2012) Optimal chemotherapy in cancer treatment: State dependent Riccati equation control and extended Kalman filter. Optim Contr Appl Met 34: 562-577.
[22] Babaei N, Salamci MU (2019) Mixed therapy in cancer treatment for personalized drug administration using model reference adaptive control. Eur J Control. In press.
Journal of Solid and Fluid Mechanics
Volume 9, Issue 2
June 2019
Pages 211-225

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