Intelligent solution predictive networks for non-linear tumor-immune delayed model

References

• Ahmad S, Ullah A, Akgül A, Baleanu D. 2022. Theoretical and numerical analysis of fractal fractional model of tumor-immune interaction with two different kernels. Alexandria Eng J. 61(7):5735–5752. doi:10.1016/j.aej.2021.10.065.
   Web of Science ®Google Scholar
• Altaf F, Chang C-L, Chaudhary NI, Raja MAZ, Cheema KM, Shu C-M, Milyani AH, et. al. 2022. Adaptive evolutionary computation for non-linear hammerstein control autoregressive systems with key term separation principle. Mathematics. 10(6):1001. doi:10.3390/math10061001.
   Web of Science ®Google Scholar
• Anwar N, Ahmad I, Raja MAZ, Naz S, Shoaib M, Kiani AK. 2022. Artificial intelligence knacks-based stochastic paradigm to study the dynamics of plant virus propagation model with impact of seasonality and delays. Eur Phys J Plus. 137(1):1–47. doi:10.1140/epjp/s13360-021-02248-4.
   PubMed Web of Science ®Google Scholar
• Banerjee S, Khajanchi S, Chaudhuri S. 2015. A mathematical model to elucidate brain tumor abrogation by immunotherapy with T11 target structure. PLoS One. 10(5):e0123611. doi:10.1371/journal.pone.0123611.
   PubMed Web of Science ®Google Scholar
• Barnaby JP, Sorribes IC, Jain HV. 2021. Relating prostate‐specific antigen leakage with vascular tumor growth in a mathematical model of prostate cancer response to androgen deprivation. Comp Sys Onco. 1(2):e1014. doi:10.1002/cso2.1014.
   Google Scholar
• Bukhari AH, Raja MAZ, Rafiq N, Shoaib M, Kiani AK, Shu C-M, at al. 2022. Design of intelligent computing networks for non-linear chaotic fractional Rossler system. Chaos Solitons Fractals. 157:111985. doi:10.1016/j.chaos.2022.111985.
   Web of Science ®Google Scholar
• Chaudhary NI, Raja MAZ, Khan ZA, Mehmood A, Shah SM. 2022. Design of fractional hierarchical gradient descent algorithm for parameter estimation of non-linear control autoregressive systems. Chaos Solitons Fractals. 157:111913. doi:10.1016/j.chaos.2022.111913.
   Web of Science ®Google Scholar
• Chen GM, Azzam A, Ding YY, Barrett DM, Grupp SA, Tan K. 2020. Dissecting the tumor–immune landscape in chimeric antigen receptor T-cell therapy: key challenges and opportunities for a systems immunology approach. Clin Cancer Res. 26(14):3505–3513. doi:10.1158/1078-0432.CCR-19-3888.
   PubMed Web of Science ®Google Scholar
• Chen SM, Krinsky AL, Woolaver RA, Wang X, Chen Z, Wang JH. 2020. Tumor immune microenvironment in head and neck cancers. Mol Carcinog. 59(7):766–774. doi:10.1002/mc.23162.
   PubMed Web of Science ®Google Scholar
• Cherraf A, Li M, Moulai-Khatir A. 2023. Interaction tumor-immune model with time-delay and immuno-chemotherapy protocol. Rend Circ Mat Palermo II Ser. 72(2):869–887. doi:10.1007/s12215-021-00615-9.
   Google Scholar
• d’Onofrio A. 2008. Metamodeling tumor–immune system interaction, tumor evasion and immunotherapy. Math Comput Modell. 47(5-6):614–637. doi:10.1016/j.mcm.2007.02.032.
   Google Scholar
• Das A, Dehingia K, Sarmah HK, Hosseini K, Sadri K, Salahshour S. 2022. Analysis of a delay-induced mathematical model of cancer. Adv Cont Discr Mod. 2022(1):15. doi:10.1186/s13662-022-03688-7.
   Google Scholar
• Das P, Das S, Das P, Rihan FA, Uzuntarla M, Ghosh D. 2021. Optimal control strategy for cancer remission using combinatorial therapy: a mathematical model-based approach. Chaos Solitons Fractals. 145:110789. doi:10.1016/j.chaos.2021.110789.
   Web of Science ®Google Scholar
• Das P, Das S, Upadhyay RK, Das P. 2020. Optimal treatment strategies for delayed cancer-immune system with multiple therapeutic approach. Chaos, Solitons Fractals. 136:109806. doi:10.1016/j.chaos.2020.109806.
   Web of Science ®Google Scholar
• Das P, Mondal P, Das P, Roy TK. 2022. Stochastic persistence and extinction in tumor-immune system perturbed by white noise. Int J Dynam Control. 10(2):620–629. doi:10.1007/s40435-021-00829-w.
   Google Scholar
• Das P, Mukherjee S, Das P, Banerjee S. 2020. Characterizing chaos and multifractality in noise-assisted tumor-immune interplay. Nonlinear Dyn. 101(1):675–685. doi:10.1007/s11071-020-05781-6.
   Web of Science ®Google Scholar
• Das P, Upadhyay RK, Das P, Ghosh D. 2020. Exploring dynamical complexity in a time-delayed tumor-immune model. Chaos. 30(12):123118. doi:10.1063/5.0025510.
   PubMed Web of Science ®Google Scholar
• 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. doi:10.1016/j.jtbi.2005.06.037.
   PubMed Web of Science ®Google Scholar
• Dehingia K, Das P, Upadhyay RK, Misra AK, Rihan FA, Hosseini K. 2023. Modelling and analysis of delayed tumour–immune system with hunting T-cells. Math Comput Simul. 203:669–684. doi:10.1016/j.matcom.2022.07.009.
   Web of Science ®Google Scholar
• Dehingia K, Hosseini K, Salahshour S, Baleanu D. 2022. A detailed study on a tumor model with delayed growth of pro-tumor macrophages. Int J Appl Comput Math. 8(5):245. doi:10.1007/s40819-022-01433-y.
   Google Scholar
• Dehingia K, Sarmah HK, Alharbi Y, Hosseini K. 2021. Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes. Adv Differ Equ. 2021(1):27. doi:10.1186/s13662-021-03621-4.
   Web of Science ®Google Scholar
• Dehingia K, Sarmah HK, Jeelani MB. 2021. A brief review on cancer research and its treatment through mathematical modelling. Ann Cancer Res Ther. 29(1):34–40.
   Google Scholar
• Eskandari Z, Avazzadeh Z, Khoshsiar Ghaziani R, Li B. 2022. Dynamics and bifurcations of a discrete‐time Lotka–Volterra model using nonstandard finite difference discretization method. Math Methods App Sci. doi:10.1002/mma.8859.
   Web of Science ®Google Scholar
• Foryś U, Marciniak-Czochra A. 2003. Logistic equations in tumour growth modelling. Int J Appl Math Comput Sci. 13(3):317–325.
   Google Scholar
• Ghosh D, Khajanchi S, Mangiarotti S, Denis F, Dana SK, Letellier C. 2017. How tumor growth can be influenced by delayed interactions between cancer cells and the microenvironment? Biosystems. 158:17–30. doi:10.1016/j.biosystems.2017.05.001.
   PubMed Web of Science ®Google Scholar
• Ghosh S, Banerjee S. 2022. Delay induced interaction of humoral-and cell-mediated immune responses with cancer. Theory Biosci. 141(1):27–40. doi:10.1007/s12064-022-00364-y.
   PubMed Web of Science ®Google Scholar
• Khajanchi S, Banerjee S. 2014. Stability and bifurcation analysis of delay induced tumor immune interaction model. Appl Math Comput. 248:652–671. doi:10.1016/j.amc.2014.10.009.
   Web of Science ®Google Scholar
• Khajanchi S, Banerjee S. 2017. Quantifying the role of immunotherapeutic drug T11 target structure in progression of malignant gliomas: mathematical modeling and dynamical perspective. Math Biosci. 289:69–77. doi:10.1016/j.mbs.2017.04.006.
   PubMed Web of Science ®Google Scholar
• Khajanchi S, Banerjee S. 2018. Influence of multiple delays in brain tumor and immune system interaction with T11 target structure as a potent stimulator. Math Biosci. 302:116–130. doi:10.1016/j.mbs.2018.06.001.
   PubMed Web of Science ®Google Scholar
• Khajanchi S, Banerjee S. 2019. A strategy of optimal efficacy of T11 target structure in the treatment of brain tumor. J Biol Syst. 27(02):225–255. doi:10.1142/S0218339019500104.
   Google Scholar
• Khajanchi S, Ghosh D. 2015. The combined effects of optimal control in cancer remission. Appl Math Comput. 271:375–388. doi:10.1016/j.amc.2015.09.012.
   Web of Science ®Google Scholar
• Khajanchi S, Nieto JJ. 2019. Mathematical modeling of tumor-immune competitive system, considering the role of time delay. Appl Math Comput. 340:180–205. doi:10.1016/j.amc.2018.08.018.
   Web of Science ®Google Scholar
• Khajanchi S, Perc M, Ghosh D. 2018. The influence of time delay in a chaotic cancer model. Chaos. 28(10):103101. doi:10.1063/1.5052496.
   PubMed Web of Science ®Google Scholar
• Khajanchi S. 2015. Bifurcation analysis of a delayed mathematical model for tumor growth. Chaos Solitons Fractals. 77:264–276. doi:10.1016/j.chaos.2015.06.001.
   Web of Science ®Google Scholar
• Khajanchi S. 2019. Stability analysis of a mathematical model for glioma-immune interaction under optimal therapy. Int J Nonlinear Sci Numer Simul. 20(3-4):269–285. doi:10.1515/ijnsns-2017-0206.
   Web of Science ®Google Scholar
• Khajanchi S. 2020. Chaotic dynamics of a delayed tumor–immune interaction model. Int J Biomath. 13(02):2050009. doi:10.1142/S1793524520500096.
   Google Scholar
• Khajanchi S. 2021. The impact of immunotherapy on a glioma immune interaction model. Chaos Solitons Fractals. 152:111346. doi:10.1016/j.chaos.2021.111346.
   Web of Science ®Google Scholar
• Khan I, Raja MAZ, Khan MAR, Shoaib M, Islam S, Shah Z. 2022. Design of backpropagated intelligent networks for non-linear second-order Lane–Emden pantograph delay differential systems. Arab J Sci Eng. 47(2):1197–1210. doi:10.1007/s13369-021-05814-1.
   Web of Science ®Google Scholar
• Khan ZA, Raja MAZ, Chaudhary NI, Mehmood K, He Y. 2022. MISGD: moving-information-based stochastic gradient descent paradigm for personalized fuzzy recommender systems. Int J Fuzzy Syst. 24(1):686–712. doi:10.1007/s40815-021-01177-9.
   Web of Science ®Google Scholar
• Li B, Liang H, He Q. 2021. Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model. Chaos Solitons Fractals. 146:110856. doi:10.1016/j.chaos.2021.110856.
   Web of Science ®Google Scholar
• Li B, Liang H, Shi L, He Q. 2022. Complex dynamics of Kopel model with nonsymmetric response between oligopolists. Chaos Solitons Fractals. 156:111860. doi:10.1016/j.chaos.2022.111860.
   Web of Science ®Google Scholar
• Li HZ, Liu XD, Yan R, Liu C. 2020. Hopf bifurcation analysis of a tumor virotherapy model with two time delays. Physica A. 553:124266. doi:10.1016/j.physa.2020.124266.
   Web of Science ®Google Scholar
• Li J, Ma X, Chen Y, Zhang D. 2022. Complex dynamic behaviors of a tumor-immune system with two delays in tumor actions. Discrete Continuous Dynam Syst-B. 27(12):7065–7087.
   Google Scholar
• Makaryan SZ, Cess CG, Finley SD. 2020. Modeling immune cell behavior across scales in cancer. Wiley Interdiscip Rev Syst Biol Med. 12(4):e1484.
   PubMed Web of Science ®Google Scholar
• Marušić M, Bajzer Ž, Freyer JP, Vuk‐Pavlović S. 1994. Analysis of growth of multicellular tumour spheroids by mathematical models. Cell Prolif. 27(2):73–94. doi:10.1111/j.1365-2184.1994.tb01407.x.
   PubMed Web of Science ®Google Scholar
• Mehmood A, Raja MAZ, Shi P, Chaudhary NI. 2022. Weighted differential evolution-based heuristic computing for identification of Hammerstein systems in electrically stimulated muscle modeling. Soft Comput. 26(17):8929–8945. doi:10.1007/s00500-021-06701-5.
   Web of Science ®Google Scholar
• Nyarko PR, Anokye M. 2020. Mathematical modeling and numerical simulation of a multiscale cancer invasion of host tissue. AIMS Mathematics. 5(4):3111–3124. doi:10.3934/math.2020200
   Google Scholar
• Pereira CA, Vermeire BC. 2020. Fully-discrete analysis of high-order spatial discretizations with optimal explicit runge–kutta methods. J Sci Comput. 83(3):1–35. doi:10.1007/s10915-020-01243-8.
   Web of Science ®Google Scholar
• Pourhasanzade F, Sabzpoushan SH. 2021. A new mathematical model for controlling tumor growth based on microenvironment acidity and oxygen concentration. Biomed Res Int. 2021:1–18. doi:10.1155/2021/8886050.
   PubMed Web of Science ®Google Scholar
• Raja MAZ, Awan SE, Shoaib M, Awais M. 2022. Backpropagated intelligent networks for the entropy generation and joule heating in hydromagnetic nanomaterial rheology over surface with variable thickness. Arab J Sci Eng. 47(6):7753–7777. doi:10.1007/s13369-022-06667-y.
   Web of Science ®Google Scholar
• Raja MAZ, Mehmood A, Ashraf S, Awan KM, Shi P. 2022. Design of evolutionary finite difference solver for numerical treatment of computer virus propagation with countermeasures model. Math Comput Simul. 193:409–430. doi:10.1016/j.matcom.2021.10.004.
   Web of Science ®Google Scholar
• Raja MAZ, Naz H, Shoaib M, Mehmood A. 2022. Design of backpropagated neurocomputing paradigm for Stuxnet virus dynamics in control infrastructure. Neural Comput Applic. 34(7):5771–5790. doi:10.1007/s00521-021-06721-0.
   Web of Science ®Google Scholar
• Raja MAZ, Shoaib M, Khan Z, Zuhra S, Saleel CA, Nisar KS, Islam S, Khan I. 2022. Supervised neural networks learning algorithm for three dimensional hybrid nanofluid flow with radiative heat and mass fluxes. Ain Shams Eng J. 13(2):101573. doi:10.1016/j.asej.2021.08.015.
   Web of Science ®Google Scholar
• Raja MAZ, Tabassum R, El-Zahar ER, Shoaib M, Khan MI, Malik MY, Khan SU, Qayyum S. 2022a. Intelligent computing through neural networks for entropy generation in MHD third-grade nanofluid under chemical reaction and viscous dissipation. Waves Random Complex Medium. :1–25. doi:10.1080/17455030.2022.2044095.
   Web of Science ®Google Scholar
• Raja MAZ, Tabassum R, El-Zahar ER, Shoaib M, Khan MI, Malik MY, Khan SU, Qayyum S. 2022b. Heat transport in entropy-optimized flow of viscoelastic fluid due to Riga plate: analysis of artificial neural network. Waves Random Complex Medium. :1–25. doi:10.1080/17455030.2022.2028933.
   Web of Science ®Google Scholar
• Rihan FA, Alsakaji HJ, Kundu S, Mohamed O. 2022. Dynamics of a time-delay differential model for tumour-immune interactions with random noise. Alexandria Eng J. 61(12):11913–11923. doi:10.1016/j.aej.2022.05.027.
   Web of Science ®Google Scholar
• 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. doi:10.1016/j.amc.2019.02.002.
   Web of Science ®Google Scholar
• Rihan FA, Velmurugan G. 2020. Dynamics of fractional-order delay differential model for tumor-immune system. Chaos Solitons Fractals. 132:109592. doi:10.1016/j.chaos.2019.109592.
   Web of Science ®Google Scholar
• Rihan FA. 2021. Delay differential equations of tumor-immune system with treatment and control. Delay differential equations and applications to biology. Singapore: Springer; p. 167–189.
   Google Scholar
• Ruan S. 2021. Nonlinear dynamics in tumor-immune system interaction models with delays. Discrete Continuous Dynam Syst-B. 26(1):541–602. doi:10.3934/dcdsb.2020282.
   Google Scholar
• Sabir Z, Botmart T, Asif Zahoor Raja M, Weera W, Sadat R, Ali MR, Alsulami AA, Alghamdi A. 2022. Artificial neural network scheme to solve the non-linear influenza disease model. Biomed Signal Process Control. 75:103594. doi:10.1016/j.bspc.2022.103594.
   Web of Science ®Google Scholar
• Sabir Z, Raja MAZ, Alnahdi AS, Jeelani MB, Abdelkawy MA. 2022. Numerical investigations of the nonlinear smoke model using the Gudermannian neural networks. Math Biosci Eng. 19(1):351–370. doi:10.3934/mbe.2022018.
   PubMed Web of Science ®Google Scholar
• Sabir Z, Raja MAZ, Mahmoud SR, Balubaid M, Algarni A, Alghtani AH, Aly AA, Le D-N. 2022. A novel design of Morlet wavelet to solve the dynamics of nervous stomach non-linear model. Int J Comput Intell Syst. 15(1):1–15. doi:10.1007/s44196-021-00057-2.
   Web of Science ®Google Scholar
• Saifullah S, Ahmad S, Jarad F. 2022. Study on the dynamics of a piecewise tumor–immune interaction model. Fractals. 30(08):2240233. doi:10.1142/S0218348X22402332.
   Web of Science ®Google Scholar
• Sardar M, Biswas S, Khajanchi S. 2021. The impact of distributed time delay in a tumor-immune interaction system. Chaos Solitons Fractals. 142:110483. doi:10.1016/j.chaos.2020.110483.
   Web of Science ®Google Scholar
• Sardar M, Khajanchi S, Biswas S, Abdelwahab SF, Nisar KS. 2021. Exploring the dynamics of a tumor-immune interplay with time delay. Alexandria Eng J. 60(5):4875–4888. doi:10.1016/j.aej.2021.03.041.
   Web of Science ®Google Scholar
• Sarkar RR, Banerjee S. 2005. Cancer self remission and tumor stability–a stochastic approach. Math Biosci. 196(1):65–81. doi:10.1016/j.mbs.2005.04.001.
   PubMed Web of Science ®Google Scholar
• Shoaib M, Kausar M, Nisar KS, Raja MAZ, Zeb M, Morsy A. 2022. The design of intelligent networks for entropy generation in Ree-Eyring dissipative fluid flow system along quartic autocatalysis chemical reactions. Int Commun Heat Mass Transfer. 133:105971. doi:10.1016/j.icheatmasstransfer.2022.105971.
   Web of Science ®Google Scholar
• Singh PP, Roy BK. 2022. Chaos and multistability behaviors in 4D dissipative cancer growth/decay model with unstable line of equilibria. Chaos Solitons Fractals. 161:112312. doi:10.1016/j.chaos.2022.112312.
   Web of Science ®Google Scholar
• Ullah Khan W, Asif Zahoor Raja M, He Y, Ishtiaq Chaudhary N. 2022. A novel application of integrated grasshopper optimization heuristics for attenuation of noise interferences. Ain Shams Eng J. 13(2):101536. doi:10.1016/j.asej.2021.06.022.
   Web of Science ®Google Scholar
• Wan X, Xu Y, Wu X, Xie C. 2022. Observer-based quantized control for discrete-time switched systems with infinitely distributed delay. J Franklin Inst. 359(8):3597–3613. doi:10.1016/j.jfranklin.2022.03.012.
   Web of Science ®Google Scholar
• Welsh M. 2022. Perspectives on vascular regulation of mechanisms controlling selective immune cell function in the tumor immune response. IJMS. 23(4):2313. doi:10.3390/ijms23042313.
   Google Scholar
• World Health Organization (WHO) report. https://www.who.int/health-topics/cancer#tab=tab_1.
   Google Scholar
• Zhang L, Rahman MU, Ahmad S, Riaz MB, Jarad F. 2022. Dynamics of fractional order delay model of coronavirus disease. MATH. 7(3):4211–4232. doi:10.3934/math.2022234.
   Google Scholar
• Zhao XE, Hu B. 2020. The impact of time delay in a tumor model. Nonlinear Anal Real World Appl. 51:103015. doi:10.1016/j.nonrwa.2019.103015.
   Web of Science ®Google Scholar