scholarly journals Mathematical Modeling of Immune Responses against SARS-CoV-2 Using an Ensemble Kalman Filter

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2427
Author(s):  
Rabih Ghostine ◽  
Mohamad Gharamti ◽  
Sally Hassrouny ◽  
Ibrahim Hoteit
Keyword(s):  
Kalman Filter ◽  
Viral Load ◽  
Immune Responses ◽  
Ensemble Kalman Filter ◽  
Plasma Cells ◽  
Equilibrium Points ◽  
Infected Cells ◽  
Many Sources ◽  
Antibody Levels ◽  
Assimilation System

In this paper, a mathematical model was developed to simulate SARS-CoV-2 dynamics in infected patients. The model considers both the innate and adaptive immune responses and consists of healthy cells, infected cells, viral load, cytokines, natural killer cells, cytotoxic T-lymphocytes, B-lymphocytes, plasma cells, and antibody levels. First, a mathematical analysis was performed to discuss the model’s equilibrium points and compute the basic reproduction number. The accuracy of such mathematical models may be affected by many sources of uncertainties due to the incomplete representation of the biological process and poorly known parameters. This may strongly limit their performance and prediction skills. A state-of-the-art data assimilation technique, the ensemble Kalman filter (EnKF), was then used to enhance the model’s behavior by incorporating available data to determine the best possible estimate of the model’s state and parameters. The proposed assimilation system was applied on the real viral load datasets of six COVID-19 patients. The results demonstrate the efficiency of the proposed assimilation system in improving the model predictions by up to 40%.

An ensemble Kalman filter data assimilation system for the martian atmosphere: Implementation and simulation experiments

Icarus ◽  
2010 ◽  
Vol 209 (2) ◽  
pp. 470-481 ◽  
Author(s):  
Matthew J. Hoffman ◽  
Steven J. Greybush ◽  
R. John Wilson ◽  
Gyorgyi Gyarmati ◽  
Ross N. Hoffman ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Martian Atmosphere ◽  
Simulation Experiments ◽  
Data Assimilation System ◽  
Assimilation System

scholarly journals A Global Carbon Assimilation System using a modified EnKF assimilation method

2014 ◽  
Vol 7 (5) ◽  
pp. 6519-6547
Author(s):  
S. Zhang ◽  
X. Zheng ◽  
Z. Chen ◽  
B. Dan ◽  
J. M. Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Carbon Assimilation ◽  
Terrestrial Ecosystem ◽  
Carbon Fluxes ◽  
Ecosystem Model ◽  
Atmospheric Co2 ◽  
Forecast Errors ◽  
Global Carbon ◽  
Assimilation System

Abstract. A Global Carbon Assimilation System based on Ensemble Kalman filter (GCAS-EK) is developed for assimilating atmospheric CO2 abundance data into an ecosystem model to simultaneously estimate the surface carbon fluxes and atmospheric CO2 distribution. This assimilation approach is based on the ensemble Kalman filter (EnKF), but with several new developments, including using analysis states to iteratively estimate ensemble forecast errors, and a maximum likelihood estimation of the inflation factors of the forecast and observation errors. The proposed assimilation approach is tested in observing system simulation experiments and then used to estimate the terrestrial ecosystem carbon fluxes and atmospheric CO2 distributions from 2002 to 2008. The results showed that this assimilation approach can effectively reduce the biases and uncertainties of the carbon fluxes simulated by the ecosystem model.

scholarly journals Sensitivity tests for an ensemble Kalman filter for aerosol assimilation

2010 ◽  
Vol 10 (3) ◽  
pp. 5947-5997
Author(s):  
N. A. J. Schutgens ◽  
T. Miyoshi ◽  
T. Takemura ◽  
T. Nakajima
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Patch Size ◽  
Initial Conditions ◽  
Grid Cell ◽  
Ensemble Size ◽  
Sensitivity Tests ◽  
Local Patch ◽  
The Impact ◽  
Assimilation System

Abstract. We present sensitivity tests for a global aerosol assimilation system utilizing AERONET observations of AOT (aerosol optical thickness) and AAE (aerosol Ångström exponent). The assimilation system employs an ensemble Kalman filter which requires optimization of three numerical parameters: ensemble size nens, local patch size npatch and inflation factor ρ. In addition, experiments are performed to test the impact of various implementations of the system. For instance, we use a different prescription of the emission ensemble or a different combination of observations. The various experiments are compared against one-another and against independent AERONET andMODIS/Aqua observations. The assimilation leads to significant improvements in modelled AOT and AAE fields. Moreover remaining errors are mostly random while they are mostly systematic for an experiment without assimilation. In addition, these results do not depend much on our parameter or design choices. It appears that the value of the local patch size has by far the biggest impact on the assimilation, which has sufficiently converged for an ensemble size of nens=20. Assimilating AOT and AAE is clearly preferential to assimilating AOT at two different wavelengths. In contrast, initial conditions or a description of aerosol beyond two modes (coarse and fine) have only little effect. We also discuss the use of the ensemble spread as an error estimate of the analysed AOT and AAE fields. We show that a very common prescription of the emission ensemble (independent random modification in each grid cell) can have trouble generating sufficient spread in the forecast ensemble.

scholarly journals A global carbon assimilation system using a modified ensemble Kalman filter

2015 ◽  
Vol 8 (3) ◽  
pp. 805-816 ◽  
Author(s):  
S. Zhang ◽  
X. Zheng ◽  
J. M. Chen ◽  
Z. Chen ◽  
B. Dan ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Carbon Assimilation ◽  
Terrestrial Ecosystem ◽  
Carbon Fluxes ◽  
Ecosystem Model ◽  
Atmospheric Co2 ◽  
Forecast Errors ◽  
Global Carbon ◽  
Assimilation System

Abstract. A Global Carbon Assimilation System based on the ensemble Kalman filter (GCAS-EK) is developed for assimilating atmospheric CO2 data into an ecosystem model to simultaneously estimate the surface carbon fluxes and atmospheric CO2 distribution. This assimilation approach is similar to CarbonTracker, but with several new developments, including inclusion of atmospheric CO2 concentration in state vectors, using the ensemble Kalman filter (EnKF) with 1-week assimilation windows, using analysis states to iteratively estimate ensemble forecast errors, and a maximum likelihood estimation of the inflation factors of the forecast and observation errors. The proposed assimilation approach is used to estimate the terrestrial ecosystem carbon fluxes and atmospheric CO2 distributions from 2002 to 2008. The results show that this assimilation approach can effectively reduce the biases and uncertainties of the carbon fluxes simulated by the ecosystem model.

scholarly journals Preliminary Test of a Data Assimilation System with a Regional High-Resolution Atmosphere–Ocean Coupled Model Based on an Ensemble Kalman Filter

2017 ◽  
Vol 145 (2) ◽  
pp. 565-581 ◽  
Author(s):  
Masaru Kunii ◽  
Kosuke Ito ◽  
Akiyoshi Wada
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Coupled Model ◽  
Sea Surface ◽  
Intensity Change ◽  
Near Surface ◽  
Data Assimilation System ◽  
Atmospheric Variables ◽  
Assimilation System

An ensemble Kalman filter (EnKF) that uses a regional mesoscale atmosphere–ocean coupled model was preliminarily examined to provide realistic sea surface temperature (SST) estimates and to represent the uncertainties of SST in ensemble data assimilation strategies. The system was evaluated through data assimilation cycle experiments over a one-month period from July to August 2014, during which time a tropical cyclone (TC) as well as severe rainfall events occurred. The results showed that the data assimilation cycle with the coupled model reproduced SST distributions realistically even without assimilating SST and sea surface salinity observations, and atmospheric variables provided to ocean models can, therefore, control oceanic variables physically to some extent. The forecast error covariance calculated in the EnKF with the coupled model showed dependency on oceanic vertical mixing for near-surface atmospheric variables due to the difference of variability between the atmosphere and the ocean as well as the influence of SST variations on the atmospheric boundary layer. The EnKF with the coupled model reproduced the intensity change of Typhoon Halong (2014) during the mature phase more realistically than with an uncoupled atmosphere model, although there remained a degradation of the SST estimate, particularly around the Kuroshio region. This suggests that an atmosphere–ocean coupled data assimilation system should be developed that is able to physically control both atmospheric and oceanic variables.

Activated PI3Kδ signals compromise plasma cell survival via limiting autophagy and increasing ER stress

2021 ◽  
Vol 218 (12) ◽  
Author(s):  
Fahd Al Qureshah ◽  
Sara Sagadiev ◽  
Christopher D. Thouvenel ◽  
Shuozhi Liu ◽  
Zhaolin Hua ◽  
...  
Keyword(s):  
B Cells ◽  
Immune Responses ◽  
Plasma Cell ◽  
Cell Biology ◽  
Plasma Cells ◽  
Critical Role ◽  
Secondary Response ◽  
Mtorc1 Signaling ◽  
Humoral Responses ◽  
Antibody Levels

While phosphatidylinositide 3-kinase delta (PI3Kδ) plays a critical role in humoral immunity, the requirement for PI3Kδ signaling in plasma cells remains poorly understood. Here, we used a conditional mouse model of activated PI3Kδ syndrome (APDS), to interrogate the function of PI3Kδ in plasma cell biology. Mice expressing a PIK3CD gain-of-function mutation (aPIK3CD) in B cells generated increased numbers of memory B cells and mounted an enhanced secondary response but exhibited a rapid decay of antibody levels over time. Consistent with these findings, aPIK3CD expression markedly impaired plasma cell generation, and expression of aPIK3CD intrinsically in plasma cells was sufficient to diminish humoral responses. Mechanistically, aPIK3CD disrupted ER proteostasis and autophagy, which led to increased plasma cell death. Notably, this defect was driven primarily by elevated mTORC1 signaling and modulated by treatment with PI3Kδ-specific inhibitors. Our findings establish an essential role for PI3Kδ in plasma cell homeostasis and suggest that modulating PI3Kδ activity may be useful for promoting and/or thwarting specific immune responses.

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