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A stochastic model of bacterial infection associated with neutrophils. (English) Zbl 1433.92017

Summary: We study stochastic phenomena for a model of bacterial infection and neutrophils defense. Sufficient conditions of stochastic permanence and extinction for the random model are discussed. To explore the effect of different noises on the bacteria dynamics, we estimate the confidence intervals by the Stochastic Sensitivity Function (SSF) technique. Numerical simulations show the dramatic change of bacterial concentration induced by noises, that is, the solution with initial value near the positive deterministic equilibrium can shift into the extinct zone due to the effect of noises.

MSC:

92C42 Systems biology, networks
92D40 Ecology
92D30 Epidemiology
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[1] Li, Y.; Karlin, A.; Loike, J. D.; Silverstein, S. C., A critical concentration of neutrophils is required for effective bacterial killing in suspension, PNAS, 99, 12, 8289-8294 (2002)
[2] Malka, R.; Wolach, B.; Gavrieli, R.; Shochat, E.; Rom-Kedar, V., Evidence for bistable bacteria-neutrophil interaction and its clinical implications, J. Clin. Invest., 122, 8, 3002-3011 (2012)
[3] Crawford, J.; Dale, D. C.; Lyman, G. H., Chemotherapy-induced neutropenia: risks, consequences, and new directions for its management, Cancer, 100, 2, 228-237 (2004)
[4] Malka, R.; Shochat, E.; Rom-Kedar, V., Bistability and bacterial infections, PLoS One, 5, 5, e10010 (2010)
[5] Malka, R.; Rom-Kedar, V., Bacteria-phagocyte dynamics, axiomatic modelling and mass-action kinetics, Math. Biosci. Eng., 8, 2, 475-502 (2011) · Zbl 1260.92119
[6] N. Frenkel, R.S. Dover, E. Titon, Y. Shai, V. Rom-Kedar, Bistable bacterial growth dynamics in the presence of antimicrobial agents, bioRxiv (2018) 330035, https://doi.org/10.1101/330035.
[7] Coates, J.; Park, B. R.; Le, D.; Şimşek, E.; Chaudhry, W.; Kim, M., Antibiotic-induced population fluctuations and stochastic clearance of bacteria, Elife, 7, e32976 (2018)
[8] Alonso, A. A.; Molina, I.; Theodoropoulos, C., Modeling bacterial population growth from stochastic single cell dynamics, Appl. Environ. Microbiol., AEM-01423 (2014)
[9] Elowitz, M. B.; Levine, A. J.; Siggia, E. D.; Swain, P. S., Stochastic gene expression in a single cell, Science, 297, 5584, 1183-1186 (2002)
[10] Miekisz, J.; Poleszczuk, J.; Bodnar, M.; Foryś, U., Stochastic models of gene expression with delayed degradation, Bulletin of Mathematical Biology, 73, 9, 2231-2247 (2011) · Zbl 1225.92018
[11] Baker, C.; Jia, T.; Kulkarni, R. V., Stochastic modeling of regulation of gene expression by multiple small RNAS, Phys. Rev. E, 85, 6, 061915 (2012)
[12] Ribeiro, A. S., Stochastic and delayed stochastic models of gene expression and regulation, Math. Biosci., 223, 1, 1-11 (2010) · Zbl 1180.92033
[13] Paulsson, J., Models of stochastic gene expression, Phys. Life Rev., 2, 2, 157-175 (2005)
[14] Yu, X.; Yuan, S.; Zhang, T., Asymptotic properties of stochastic nutrient-plankton food chain models with nutrient recycling, Nonlinear Anal. Hybrid Syst., 34, 209-225 (2019) · Zbl 1435.34056
[15] Yu, X.; Yuan, S.; Zhang, T., Persistence and ergodicity of a stochastic single species model with allee effect under regime switching, Commun. Nonlinear Sci. Numer. Simulat., 59, 359-374 (2018) · Zbl 1524.37084
[16] Lorens, I.; Sebastian, W., Exclusion and persistence in deterministic and stochastic chemostat models, J. Differ. Equ., 217, 1, 26-53 (2005) · Zbl 1089.34041
[17] Durrett, R., Stochastic Calculus: A Practical Introduction (1996), CRC Press · Zbl 0856.60002
[18] Zhang, S.; Meng, X.; Feng, T.; Zhang, T., Dynamics analysis and numerical simulations of a stochastic non-autonomous predator-prey system with impulsive effects, Nonlinear Anal. Hybrid Syst., 26, 19-37 (2017) · Zbl 1376.92057
[19] Yu, X.; Yuan, S.; Zhang, T., Survival and ergodicity of a stochastic phytoplankton-zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment, Appl. Math. Comput., 347, 249-264 (2019) · Zbl 1428.92097
[20] Tang, Y.; Yuan, R.; Wang, G.; Zhu, X.; Ao, P., Potential landscape of high dimensional nonlinear stochastic dynamics with large noise, Scientific Rep., 7, 1, 15762 (2017)
[21] Yuan, R.; Ao, P., Beyond itô versus stratonovich, J. Statist. Mech. Theory Exper., 2012, 07, P07010 (2012) · Zbl 1456.60168
[22] Mao, X.; Yuan, C., Stochastic Differential Equations with Markovian Switching (2006), Imperial College Press · Zbl 1126.60002
[23] Bashkirtseva, I.; Ryashko, L., Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with Allee effect, Chaos Interdisci. J. Nonlinear Sci., 21, 4, 047514 (2011) · Zbl 1317.92075
[24] Xu, C.; Yuan, S.; Zhang, T., Stochastic sensitivity analysis for a competitive turbidostat model with inhibitory nutrients, Int. J. Bifurcat. Chaos, 26, 10, 1650173 (2016) · Zbl 1352.34079
[25] Mil’Shtein, G.; Ryashko, L., A first approximation of the quasipotential in problems of the stability of systems with random non-degenerate perturbations, J. Appl. Math. Mech., 59, 1, 47-56 (1995) · Zbl 0880.34059
[26] Bashkirtseva, I.; Ryashko, L., Stochastic bifurcations and noise-induced chaos in a dynamic prey-predator plankton system, Int. J. Bifurcat. Chaos, 24, 09, 1450109 (2014) · Zbl 1301.34061
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