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Global dynamics of SARS-CoV-2/cancer model with immune responses. (English) Zbl 1510.92122

Summary: The world is going through a critical period due to a new respiratory disease called coronavirus disease 2019 (COVID-19). This disease is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Mathematical modeling is one of the most important tools that can speed up finding a drug or vaccine for COVID-19. COVID-19 can lead to death especially for patients having chronic diseases such as cancer, AIDS, etc. We construct a new within-host SARS-CoV-2/cancer model. The model describes the interactions between six compartments: nutrient, healthy epithelial cells, cancer cells, SARS-CoV-2 virus particles, cancer-specific CTLs, and SARS-CoV-2-specific antibodies. We verify the nonnegativity and boundedness of its solutions. We outline all possible equilibrium points of the proposed model. We prove the global stability of equilibria by constructing proper Lyapunov functions. We do some numerical simulations to visualize the obtained results. According to our model, lymphopenia in COVID-19 cancer patients may worsen the outcomes of the infection and lead to death. Understanding dysfunctions in immune responses during COVID-19 infection in cancer patients could have implications for the development of treatments for this high-risk group.

MSC:

92C60 Medical epidemiology
34C60 Qualitative investigation and simulation of ordinary differential equation models
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[1] Slimano, F.; Baudouin, A.; Zerbit, J.; Toulemonde-Deldicque, A., Cancer, immune suppression and coronavirus disease-19 (COVID-19): need to manage drug safety (French society for oncology pharmacy [SFPO] guidelines), Cancer Treat. Rev., 88, 102063 (2020)
[2] Coronavirus disease (COVID-19), Weekly Epidemiological Update (23 August 2020) (2020), World Health Organization (WHO)
[3] World health organization (WHO) coronavirus disease (COVID-19) advice for the public, https://www.who.int/emergencies/diseases/novel-coronavirus-2019/advice-for-public.
[4] Zhao, Q.; Meng, M.; Kumar, R.; Wu, Y., Lymphopenia is associated with severe coronavirus disease 2019 (COVID-19) infections: a systemic review and meta-analysis, Int. J. Infect. Dis., 96, 131-135 (2020)
[5] Akula, S. M.; Abrams, S. L.; Steelman, L. S.; Candido, S., Cancer therapy and treatments during COVID-19 era, Adv. Biol. Regul., 77, 100739 (2020)
[6] Wang, J., Mathematical models for COVID-19: applications, limitations, and potentials, J. Public Health Emerg., 4, 9, 1-4 (2020)
[7] Dariya, B.; Nagaraju, G. P., Understanding novel COVID-19: its impact on organ failure and risk assessment for diabetic and cancer patients, Cytokine Growth Factor Rev., 53, 43-52 (2020)
[8] Du, S. Q.; Yuan, W., Mathematical modeling of interaction between innate and adaptive immune responses in COVID-19 and implications for viral pathogenesis, J. Med. Virol., 92, 9, 1615-1628 (2020)
[9] Addeo, A.; Friedlaender, A., Cancer and COVID-19: unmasking their ties, Cancer Treat. Rev., 88, 102041 (2020)
[10] Indini, A.; Rijavec, E.; Ghidini, M.; Bareggi, C., Coronavirus infection and immune system: an insight of COVID-19 in cancer patients, Crit. Rev. Oncol. Hematol., 153, 103059 (2020)
[11] Guan, W.; Ni, Z.; Hu, Y.; Liang, W., Clinical characteristics of coronavirus disease 2019 in China, N. Engl. J. Med., 382, 18, 1708-1720 (2020)
[12] Gennaro, F.; Pizzol, D.; Marotta, C.; Antunes, M., Coronavirus diseases (COVID-19) current status and future perspectives: a narrative review, Int. J. Environ. Res. Public Health, 17, 8, 2690 (2020)
[13] Liu, W.; Tao, Z.; Wang, L.; Yuan, M., Analysis of factors associated with disease outcomes in hospitalized patients with 2019 novel coronavirus disease, Chin. Med. J., 133, 9, 1032-1038 (2020)
[14] Cohen, O.; Eisenberg, M.; Caveney, B.; Kirchgraber, P., Dynamics of SARS-CoV-2 and the adaptive immune response, LabCorp, 1-12 (2020)
[15] Assaad, S.; Avrillon, V.; Fournier, M.; Mastroianni, B., High mortality rate in cancer patients with symptoms of COVID-19 with or without detectable SARS-CoV-2 on RT-PCR, Eur. J. Cancer, 135, 251-259 (2020)
[16] Kuderer, N. M.; Choueiri, T. K.; Shah, D. P.; Shyr, Y., Clinical impact of COVID-19 on patients with cancer (CCC19): a cohort study, Lancet, 395, 10241, 1907-1918 (2020)
[17] Landman, A.; Feetham, L.; Stuckey, D., Cancer patients in SARS-CoV-2 infection: a nationwide analysis in China, Lancet Oncol., 21, 3, 335-337 (2020)
[18] Jyotsana, N.; King, M., The impact of COVID-19 on cancer risk and treatment, Cell. Mol. Bioeng. (2020)
[19] Currie, C.; Fowler, J.; Kotiadis, K.; Monks, T., How simulation modelling can help reduce the impact of COVID-19, J. Simul., 14, 2, 83-97 (2020)
[20] Krishna, M. V.; Prakash, J., Mathematical modelling on phase based transmissibility of coronavirus, Infect. Dis. Model., 5, 375-385 (2020)
[21] Rajagopal, K.; Hasanzadeh, N.; Parastesh, F.; Hamarash, I., A fractional-order model for the novel coronavirus (COVID-19) outbreak, Nonlinear Dyn., 101, 711-718 (2020)
[22] Chen, T.; Rui, J.; Wang, Q.; Zhao, Z., A mathematical model for simulating the phase-based transmissibility of a novel coronavirus, Infect. Dis. Poverty, 9, 24, 1-8 (2020)
[23] Yang, C.; Wang, J., A mathematical model for the novel coronavirus epidemic in Wuhan, China, Math. Biosci. Eng., 17, 3, 2708-2724 (2020) · Zbl 1470.92367
[24] Liu, Z.; Magal, P.; Seydi, O.; Webb, G., Understanding unreported cases in the COVID-19 epidemic outbreak in Wuhan, China, and the importance of major public health interventions, Biology, 9, 3, 1-12 (2020)
[25] Nowak, M. A.; Bangham, C. R.M., Population dynamics of immune responses to persistent viruses, Science, 272, 74-79 (1996)
[26] AlAgha, A. D.; Elaiw, A. M., Stability of a general reaction-diffusion HIV-1 dynamics model with humoral immunity, Eur. Phys. J. Plus, 134, 8, 1-18 (2019)
[27] Elaiw, A. M.; Almuallem, N. A., Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells, Appl. Math. Comput., 265, 1067-1089 (2015) · Zbl 1410.34160
[28] Perelson, A.; Kirschner, D.; De Boer, R., Dynamics of HIV infection of CD4+ T cells, Math. Biosci., 114, 1, 81-125 (1993) · Zbl 0796.92016
[29] Elaiw, A. M.; Al Agha, A. D., Global dynamics of a general diffusive HBV infection model with capsids and adaptive immune response, Adv. Differ. Equ., 2019, 519, 1-31 (2019) · Zbl 1487.92039
[30] Wang, K.; Wang, W., Propagation of HBV with spatial dependence, Math. Biosci., 210, 78-95 (2007) · Zbl 1129.92052
[31] Hattaf, K.; Yousfi, N., A generalized HBV model with diffusion and two delays, Comput. Math. Appl., 69, 31-40 (2015) · Zbl 1362.92075
[32] Elaiw, A. M.; Almalki, S. E.; Hobiny, A. D., Global properties of saturated chikungunya virus dynamics models with cellular infection and delays, Adv. Differ. Equ., 2019, 476, 1-33 (2019) · Zbl 1487.92040
[33] Li, C.; Xu, J.; Liu, J.; Zhou, Y., The within-host viral kinetics of SARS-CoV-2, Math. Biosci. Eng., 17, 4, 2853-2861 (2020) · Zbl 1467.92062
[34] I. Ghosh, Within host dynamics of SARS-CoV-2 in humans: modeling immune responses and antiviral treatments (2020) arXiv:2006.02936.
[35] Hattaf, K.; Yousfi, N., Dynamics of SARS-Cov-2 infection model with two modes of transmission and immune response, Math. Biosci. Eng., 17, 5, 5326-5340 (2020) · Zbl 1470.92303
[36] Pinky, L.; Dobrovolny, H. M., SARS-CoV-2 coinfections: could influenza and the common cold be beneficial?, J. Med. Virol., 1-8 (2020)
[37] Wang, Z.; Guo, Z.; Peng, H., A mathematical model verifying potent oncolytic efficacy of m1 virus, Math. Biosci., 276, 19-27 (2016) · Zbl 1341.92035
[38] Elaiw, A. M.; Hobiny, A. D.; Al Agha, A. D., Global dynamics of reaction-diffusion oncolytic m1 virotherapy with immune response, Appl. Math. Comput., 367, 1-21 (2020) · Zbl 1433.35164
[39] Korobeinikov, A., Global properties of basic virus dynamics models, Bull. Math. Biol., 66, 4, 879-883 (2004) · Zbl 1334.92409
[40] Elaiw, A. M., Global properties of a class of HIV models, Nonlinear Anal., 11, 4, 2253-2263 (2010) · Zbl 1197.34073
[41] Elaiw, A. M., Global properties of a class of virus infection models with multitarget cells, Nonlinear Dyn., 69, 1-2, 423-435 (2012) · Zbl 1254.92064
[42] Khalil, H. K., Nonlinear Systems (1996), Prentice-Hall: Prentice-Hall New Jersey
[43] Derosa, L.; Melenotte, C.; Griscelli, F.; Gachot, B., The immuno-oncological challenge of COVID-19, Nat. Cancer, 1, 10, 946-964 (2020)
[44] Bakouny, Z.; Hawley, J. E.; Choueiri, T. K.; Peters, S., COVID-19 and cancer: current challenges and perspectives, Cancer Cell, 38, 629-646 (2020)
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