Wang, Wei; Ren, Xinzhi; Ma, Wanbiao; Lai, Xiulan New insights into pharmacologic inhibition of pyroptotic cell death by necrosulfonamide: a PDE model. (English) Zbl 1453.92084 Nonlinear Anal., Real World Appl. 56, Article ID 103173, 21 p. (2020). Summary: Pyroptosis is a highly inflammatory form of cell death, which uses intracellularly generated pores to destroy electrolyte homeostasis and perform cell death. Gasdermin D, the pore-forming effector protein of pyroptosis, plays a critical role in coordinating membrane lysis and the release of highly inflammatory molecules. Recently, necrosulfonamide as a direct chemical inhibitor of gasdermin D has been confirmed to bind gasdermin D to inhibit pyroptotic cell death. To provide a more effective theoretical guidance for the influence of gasdermin D inhibitors on pyroptosis, we derive a novel PDE model from the genetic level, and study its threshold dynamics in terms of the basic reproduction number \(R_0\). It turns out that threshold dynamics is determined by the sign of \(R_0 - 1\). Under some suitable parameters, our numerical simulations show that environmental heterogeneity may increase transmission risk \(R_0\) in time periodic environments. We may underestimate \(R_0\) if the time average system is used. Based on some published experimental data, the administration of necrosulfonamide maybe strengthen the health condition of patients rapidly, which may become a new strategy to maintain CD4+ T cell counts at a safe level. Cited in 2 Documents MSC: 92C32 Pathology, pathophysiology 92C37 Cell biology 35K57 Reaction-diffusion equations 35B09 Positive solutions to PDEs Keywords:pyroptosis; pharmacologic inhibition; reaction-diffusion equation model; basic reproduction number; threshold dynamics; periodic solution PDFBibTeX XMLCite \textit{W. Wang} et al., Nonlinear Anal., Real World Appl. 56, Article ID 103173, 21 p. (2020; Zbl 1453.92084) Full Text: DOI References: [1] Muro-Cacho, C.; Pantaleo, G.; Fauci, A., Analysis of apoptosis in lymph nodes of HIV-infected persons. intensity of apoptosis correlates with the general state of activation of the lymphoid tissue and not with stage of disease or viral burden, J. Immunol., 154, 5555-5566 (1995) [2] Doitsh, G., Abortive HIV infection mediates CD4 T cell depletion and inflammation in human lymphoid tissue, Cell, 143, 789-801 (2010) [3] Doitsh, G., Pyroptosis drives CD4 T-cell depletion in HIV-1 infection, Nature, 505, 509-514 (2014) [4] Rathkey, J., Chemical disruption of the pyroptotic pore-forming protein gasdermin D inhibits inflammatory cell death and sepsis, Sci. Immunol., 3, eaat2738 (2018) [5] Huang, Y.; Rosenkranz, S.; Wu, H., Modeling HIV dynamics and antiviral response with consideration of time-varying drug exposures, adherence and phenotypic sensitivity, Math. Biosci., 184, 156-186 (2003) · Zbl 1030.92016 [6] Perelson, A.; Kirschner, D.; Boer, R., Dynamics of HIV infection of CD4 + T cells, Math. Biosci., 114, 81-125 (1993) · Zbl 0796.92016 [7] Rong, L.; Perelson, A., Modeling latently infected cell activation: viral and latent reservoir persistence, and viral blips in hiv-infected patients on potent therapy, PLoS Comput. Biol., 5 (2009), e1000533 [8] Rong, L.; Feng, Z.; Perelson, A., Mathematical analysis of age-structured HIV-1 dynamics with combination antiretroviral therapy, SIAM J. Appl. Math., 67, 731-756 (2007) · Zbl 1121.92043 [9] Shen, M.; Xiao, Y.; Rong, L.; Ancel Meyers, L., Conflict and accord of optimal treatment strategies for HIV infection within and between hosts, Math. Biosci., 309, 107-117 (2019) · Zbl 1409.92152 [10] Tang, B.; Xiao, Y.; Sivaloganathan, S.; Wu, J., A piecewise model of virus-immune system with effector cell-guided therapy, Appl. Math. Model., 47, 227-248 (2017) · Zbl 1446.92024 [11] Wang, S.; Zhang, J.; Xu, F.; Song, X., Dynamics of virus infection models with density-dependent diffusion, Comput. Math. Appl., 74, 2403-2422 (2017) · Zbl 1396.92087 [12] Wang, S.; Hottz, P.; Schechter, M.; Rong, L., Modeling the slow CD4+ T cell decline in HIV-infected individuals, PLoS Comput. Biol., 11, 1-25 (2015) [13] Wang, W.; Zhang, T., Caspase-1-mediated pyroptosis of the predominance for driving CD4+ T cells death: a nonlocal spatial mathematical model, Bull. Math. Biol., 80, 540-582 (2018) · Zbl 1391.92024 [14] Ruddle, N., Lymphatic vessels and tertiary lymphoid organs, J. Clin. Invest., 124, 953-959 (2014) [15] Strain, M.; Richman, D.; Wong, J.; Levine, H., Spatiotemporal dynamics of HIV propagation, J. Theoret. Biol., 218, 85-96 (2002) [16] Fackler, O.; Murooka, T.; Imle, A.; Mempel, T., Adding new dimensions: towards an integrative understanding of HIV-1 spread, Nat. Rev. Microbiol., 12, 563-574 (2014) [17] Kodera, M.; Grailer, J.; Karalewitz, A.; Subramanian, H.; Steeber, D., T lymphocyte migration to lymph nodes is maintained during homeostatic proliferation, Microsc. Microanal., 14, 211-224 (2008) [18] Miller, M.; Wei, S.; Parker, I.; Cahalan, M., Two-photon imaging of lymphocyte motility and antigen response in intact lymph node, Science, 296, 1869-1873 (2002) [19] Beltman, J.; Maree, A.; Lynch, J.; Miller, J.; de Boer, R., Lymph node topology dictates T cell migration behavior, J. Exp. Med., 204, 771-780 (2007) [20] Fung, H.; Stone, E.; Piacenti, F., Tenofovir disoproxil fumarate: a nucleotide reverse transcriptase inhibitor for the treatment of HIV infection, Clin. Ther., 24, 1515-1548 (2002) [21] Garoff, H.; Hewson, R.; Opstelten, D., Virus maturation by budding, Microbiol. Mol. Biol. Rev., 62, 1171-1190 (1998) [22] Wang, X.; Liu, S.; Song, X., A within-host virus model with multiple infected stages under time-varying environments, Appl. Math. Comput., 266, 119-134 (2015) · Zbl 1410.92141 [23] Wang, W.; Ma, W.; Feng, Z., Complex dynamics of a time periodic nonlocal and time-delayed model of reaction-diffusion equations for modeling CD4+ T cells decline, J. Comput. Appl. Math., 367, Article 112430 pp. (2020) · Zbl 1426.92020 [24] Stancevic, O.; Angstmann, C.; Murray, J.; Henry, B., Turing patterns from dynamics of early HIV infection, Bull. Math. Biol., 75, 774-795 (2013) · Zbl 1273.92035 [25] Lai, X.; Zou, X., Repulsion effect on superinfecting virions by infected cells, Bull. Math. Biol., 76, 2806-2833 (2014) · Zbl 1329.92074 [26] Nakaoka, S.; Iwami, S.; Sato, K., Dynamics of HIV infection in lymphoid tissue network, J. Math. Biol., 72, 909-938 (2016) · Zbl 1337.92131 [27] Pankavich, S.; Parkinson, C., Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity, Discrete Contin. Dyn. Syst. Ser. B, 21, 1237-1257 (2016) · Zbl 1346.35094 [28] Ren, X.; Tian, Y.; Liu, L.; Liu, X., A reaction-diffusion within-host HIV model with cell-to-cell transmission, J. Math. Biol., 76, 1831-1872 (2018) · Zbl 1391.92055 [29] Zhao, G.; Ruan, S., Spatial and temporal dynamics of a nonlocal viral infection model, SIAM J. Appl. Math., 78, 1954-1980 (2018) · Zbl 1410.35261 [30] Lin, H.; Wang, F., Global dynamics of a nonlocal reaction-diffusion system modeling the West Nile virus transmission, Nonlinear Anal. RWA, 46, 352-373 (2019) · Zbl 1412.35346 [31] Vaidya, N.; Wang, F.; Zou, X., Avian influenza dynamics in wild birds with bird mobility and spatial heterogeneous environment, Discrete Contin. Dyn. Syst. Ser. B, 17, 2829-2848 (2012) · Zbl 1258.35033 [32] Morgan, J.; Hollis, S., The existence of periodic solutions to reaction-diffusion systems with periodic data, SIAM J. Math. Anal., 26, 1225-1232 (1995) · Zbl 0849.35052 [33] Bacaër, N.; Guernaoui, S., The epidemic threshold of vector-borne diseases with seasonality, J. Math. Biol., 53, 421-436 (2006) · Zbl 1098.92056 [34] Pinto, C.; Carvalho, A.; Tavares, J., Time-varying pharmacodynamics in a simple non-integer HIV infection model, Math. Biosci., 307, 1-12 (2019) · Zbl 1409.92150 [35] Peng, R.; Zhao, X., A reaction-diffusion SIS epidemic model in a time-periodic environment, Nonlinearity, 25, 1451-1471 (2012) · Zbl 1250.35172 [36] Wang, X.; Zhao, X., A periodic vector-bias malaria model with incubation period, SIAM J. Appl. Math., 77, 181-201 (2017) · Zbl 1401.35188 [37] Cui, R.; Lou, Y., A spatial SIS model in advective heterogeneous environments, J. Differential Equations, 261, 3305-3343 (2016) · Zbl 1342.92231 [38] Cui, R.; Lam, K.; Lou, Y., Dynamics and asymptotic profiles of steady states of an epidemic model in advective environments, J. Differential Equations, 263, 2343-2373 (2017) · Zbl 1388.35086 [39] Lou, Y.; Zhao, X., A reaction-diffusion malaria model with incubation period in the vector population, J. Math. Biol., 62, 543-568 (2011) · Zbl 1232.92057 [40] Wang, W.; Ma, W.; Lai, X., Repulsion effect on superinfecting virions by infected cells for virus infection dynamic model with absorption effect and chemotaxis, Nonlinear Anal. RWA, 33, 253-283 (2017) · Zbl 1352.92094 [41] Wang, J.; Yang, J.; Kuniya, T., Dynamics of a PDE viral infection model incorporating cell-to-cell transmission, J. Math. Anal. Appl., 444, 1542-1564 (2016) · Zbl 1362.37165 [42] Wu, Y.; Zou, X., Dynamics and profiles of a diffusive host-pathogen system with distinct dispersal rates, J. Differential Equations, 264, 4989-5024 (2018) · Zbl 1387.35362 [43] Wang, F.; Huang, Y.; Zou, X., Global dynamics of a PDE in-host viral model, Appl. Anal., 93, 2312-2329 (2014) · Zbl 1307.35054 [44] Bai, Z.; Peng, R.; Zhao, X., A reaction-diffusion malaria model with seasonality and incubation period, J. Math. Biol., 77, 201-228 (2018) · Zbl 1390.35145 [45] Wu, R.; Zhao, X., A reaction-diffusion model of vector-borne disease with periodic delays, J. Nonlinear Sci., 29, 29-64 (2019) · Zbl 1411.35170 [46] Zhang, L.; Wang, Z.; Zhao, X., Threshold dynamics of a time periodic reaction-diffusion epidemic model with latent period, J. Differential Equations, 258, 3011-3036 (2015) · Zbl 1408.35088 [47] Markowitz, M.; Louie, M.; Hurley, A., A novel antiviral intervention results in more accurate assessment of human immunodeficiency virus type 1 replication dynamics and T-cell decay in vivo, J. Virol., 77, 5037-5038 (2003), PMID: 12663814 [48] Hazuda, D.; Lee, J.; Young, P., The kinetics of interleukin 1 secretion from activated monocytes. Diffferences between interleukin 1 alpha and interleukin 1 beta, J. Biol. Chem., 263, 8473-8479 (1988) [49] Hellerstein, M.; Hanley, M.; Cesar, D., Directly measured kinetics of circulating T lymphocytes in normal and HIV-1-infected humans, Nat. Med., 5, 83-89 (1999) [50] Yamazaki, K., Global well-posedness of infectious disease models without life-time immunity: the cases of cholera and avian influenza, Math. Med. Biol., 35, 428-445 (2018) · Zbl 1410.92144 [51] Wang, F.; Shi, J.; Zou, X., Dynamics of a host-pathogen system on a bounded spatial domain, Commun. Pure Appl. Anal., 14, 2535-2560 (2015) · Zbl 1328.35104 [52] Yamazaki, K., Zika virus dynamics partial differential equations model with sexual transmission route, Nonlinear Anal. RWA, 50, 290-315 (2019) · Zbl 1430.92116 [53] Daners, D.; Medina, P., (Abstract Evolution Equations, Periodic Problems and Applications. Abstract Evolution Equations, Periodic Problems and Applications, Pitman Res. Notes Math. Ser., vol. 279 (1992), Longman: Longman Harlow, UK) · Zbl 0789.35001 [54] Martin, R.; Smith, H., Abstract functional differential equations and reaction-diffusion systems, Trans. Amer. Math. Soc., 321, 1-44 (1990) · Zbl 0722.35046 [55] Smith, H., (Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, Math. Surveys Monogr., vol. 41 (1995), American Mathematical Society: American Mathematical Society Providence, Rhode Island) · Zbl 0821.34003 [56] Wu, J., Theory and Applications of Partial Functional Differential Equations (1996), Springer-Verlag: Springer-Verlag New York [57] Hale, J. K., (Asymptotic Behavior of Dissipative Systems. Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25 (1988), American Mathematical Society: American Mathematical Society Providence, RI) · Zbl 0642.58013 [58] Magal, P.; Zhao, X., Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37, 251-275 (2005) · Zbl 1128.37016 [59] Zhao, X., Dynamical Systems in Population Biology (2017), Springer: Springer New York · Zbl 1393.37003 [60] Hess, P., Periodic-Parabolic Boundary Value Problems and Positivity (1991), Longman Scientific and Technical: Longman Scientific and Technical Harlow, UK · Zbl 0731.35050 [61] Thieme, H., Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM J. Appl. Math., 70, 188-211 (2009) · Zbl 1191.47089 [62] Diekmann, O.; Heesterbeek, J.; Metz, J., On the definition and the computation of the basic reproduction ratio \(R_0\) in models of infectious disease in heterogeneous populations, J. Math. Biol., 28, 365-382 (1990) · Zbl 0726.92018 [63] Wang, W.; Zhao, X., Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst., 11, 1652-1673 (2012) · Zbl 1259.35120 [64] Zhao, X., Basic reproduction ratios for periodic compartmental models with time delay, J. Dynam. Differential Equations, 29, 67-82 (2017) · Zbl 1365.34145 [65] Liang, X.; Zhao, X., Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60, 1-40 (2007) · Zbl 1106.76008 [66] Cantrell, R.; Cosner, C., (Spatial Ecology Via Reaction-Diffusion Equations. Spatial Ecology Via Reaction-Diffusion Equations, Wiley Series in Mathematical and Computational Biology (2003), John Wiley Sons, Ltd.: John Wiley Sons, Ltd. Chichester) · Zbl 1059.92051 [67] Smith, H.; Zhao, X., Robust persistence for semidynamical systems, Nonlinear Anal., 47, 6169-6179 (2001) · Zbl 1042.37504 [68] Liu, S.; Lou, Y.; Peng, R.; Zhou, M., Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator, Proc. Amer. Math. Soc., 147, 5291-5302 (2019) · Zbl 1423.35278 [69] Tang, S.; Xiao, Y.; Wang, N.; Wu, H., Piecewise HIV virus dynamic model with CD4+ T cell count-guided therapy: I, J. Theoret. Biol., 308, 123-134 (2012) · Zbl 1411.92180 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.