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

Rabih Ghostine, Mohamad Gharamti, Sally Hassrouny and Ibrahim Hoteit
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Rabih Ghostine: Department of Mathematics, Kuwait College of Science and Technology, Doha 35001, Kuwait
Mohamad Gharamti: National Center for Atmospheric Research, Boulder, CO 80305, USA
Sally Hassrouny: School of Engineering, American International University, Doha 35001, Kuwait
Ibrahim Hoteit: Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia

Mathematics, 2021, vol. 9, issue 19, 1-13

Abstract: 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 % .

Keywords: mathematical modeling; SARS-CoV-2; immune response; ensemble Kalman filter; joint state–parameters estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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