A simplified model of the Human Immune System response to the COVID-19

Abstract

By November 2020, the Coronavirus disease 2019 has infected more than 50 million people worldwide, causing more than 1.2 million deaths. This new contagious disease is not well understood, and the scientific community is trying to comprehend better the interactions of the causative agent of the disease, SAR2-CoV-2, and the immune response to identify its weak points to develop new therapies to impair its lethal effects. Mathematical and computational tools can help in this task: the multiscale interactions among the various components of the human immune system and the pathogen are very complex. In this work, we present a simple system of five ordinary differential equations that can be used to model the immune response to SARS-CoV-2. The model parameters and initial conditions were adjusted to cohort studies that collected viremia and antibody data. The results have shown that the model was able to reproduce both viremia and antibodies dynamics successfully.

Spatially distributed infection increases viral load in a computational model of SARS-CoV-2 lung infection

“…Some earlier SARS-CoV-2 ODE TCL models included an implicit immune response incorporated in the cell clearance term and an explicit adaptive immune response, e.g. [8,[14][15][16]44], similar to the approach we took with SIMCoV. These models were tuned to fit the same lung viral load data from [33] that we fit here; however, because SIMCoV explicitly represents cell and virus movement, it mimics the highly variable dynamics by varying only a few key parameters.…”

Spatially distributed infection increases viral load in a computational model of SARS-CoV-2 lung infection

“…Some included an implicit immune response incorporated in the cell clearance term and an explicit adaptive immune response, e.g. [8,[14][15][16]49], similar to the approach we took with SIMCoV. SIMCoV complements these earlier ODE models but makes different predictions.…”

A Validated Mathematical Model of the Cytokine Release Syndrome in Severe COVID-19

“…The authors then present the Stability Analysis of their model (Almocera et al, 2020), which suggests that the SARS-CoV-2 virus replicates fast enough to overcome T cell response and cause infection. Xavier et al (2020) proposed a model based on five Ordinary Differential Equations to model the immune response to SARS-CoV-2. The model parameters and initial conditions were adjusted to cohort studies that collected viremia and antibody data.…”

“…A large number of works use mathematical and computational tools to model the Human Immune System (HIS) using distinct techniques, such as ordinary differential equations (ODEs) ( Perelson, 1989 ; Baker et al, 1997 ; Chang et al, 2005 ; Vodovotz et al, 2006 ; Jarrett et al, 2015 ; Bonin et al, 2016 ), partial differential equations (PDEs) ( Pettet et al, 1996 ; Su et al, 2009 ; Flegg et al, 2012 ; Pigozzo et al, 2013 ; Quintela et al, 2014 ), stochastic methods ( Chao et al, 2004 ; Xavier et al, 2017 ), cellular automaton and agents ( Celada and Seiden, 1992 ; Morpurgo et al, 1995 ; Kohler et al, 2000 ; Bernaschi and Castiglione, 2001 ; Pappalardo et al, 2018 ). On the other hand, very few papers were published describing the dynamics of SARS-CoV-2 ( Almocera et al, 2020 ; Du and Yuan, 2020 ; Hernandez-Vargas and Velasco-Hernandez, 2020 ; Xavier et al, 2020 ), although some additional non-peer-reviewed papers can also be found on the internet. Three out four published works ( Almocera et al, 2020 ; Du and Yuan, 2020 ; Hernandez-Vargas and Velasco-Hernandez, 2020 ) are based on the target cell-limited model proposed by Perelson (2002) : a system of three ODEs to model target cells, infected cells, and viruses.…”

“… Xavier et al (2020) proposed a model based on five Ordinary Differential Equations to model the immune response to SARS-CoV-2. The model parameters and initial conditions were adjusted to cohort studies that collected viremia and antibody data.…”