Spatio-Temporal Modeling of Immune Response to SARS-CoV-2 Infection

Abstract

COVID-19 is a disease occurring as a result of infection by a novel coronavirus called SARS-CoV-2. Since the WHO announced COVID-19 as a global pandemic, mathematical works have taken place to simulate infection scenarios at different scales even though the majority of these models only consider the temporal dynamics of SARS-COV-2. In this paper, we present a new spatio-temporal within-host mathematical model of COVID-19, accounting for the coupled dynamics of healthy cells, infected cells, SARS-CoV-2 molecules, chemokine concentration, effector T cells, regulatory T cells, B-lymphocytes cells and antibodies. We develop a computational framework involving discretisation schemes for diffusion and chemotaxis terms using central differences and midpoint approximations within two dimensional space combined with a predict–evaluate–correct mode for time marching. Then, we numerically investigate the model performance using a list of values simulating the baseline scenario for viral infection at a cellular scale. Moreover, we explore the model sensitivity via applying certain conditions to observe the model validity in a comparison with clinical outcomes collected from recent studies. In this computational investigation, we have a numerical range of 104 to 108 for the viral load peak, which is equivalent to what has been obtained from throat swab samples for many patients.

A Hybrid Local Radial Basis Function Method for the Numerical Modeling of Mixed Diffusion and Wave-Diffusion Equations of Fractional Order Using Caputo’s Derivatives

“…Successful implementation of such a framework could pave the way for further mathematical and biological applications. In future work, we will aim to extend our numerical method to include multiple components of the differential operator of order 2, as introduced in [57]. This will allow us to compare the impact of the errors of the proposed method and the validity of the model with clinical outcomes, thereby facilitating the understanding of complex phenomena.…”

A General Approach to Modeling Covid-19

“…The immune response that is triggered in people as a result of infection by SARS-CoV-2 virions has been described in various models in the scientific literature [21,22],but most posts solve it numerically.Furthermore, recent studies have associated a storm of cytokines generated by SARS-CoV-2 such that it leads lymphocytes to the lungs in search of infection, and thus maintains the replication and transmission of the virus [23].…”

A General Approach to Modeling Covid-19

“…The immune response that is triggered in people as a result of infection by SARSCoV-2 virions has been described in various models in the scientific literature [21,22], but most posts solve it numerically. Furthermore, recent studies have associated a storm of cytokines generated by SARS-CoV-2 such that it leads lymphocytes to the lungs in search of infection, and thus maintains the replication and transmission of the virus [23].…”