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

Abstract

By June 2021, a new contagious disease, the Coronavirus disease 2019 (COVID-19), has infected more than 172 million people worldwide, causing more than 3.7 million deaths. Many aspects related to the interactions of the disease’s causative agent, SAR2-CoV-2, and the immune response are not well understood: the multiscale interactions among the various components of the human immune system and the pathogen are very complex. Mathematical and computational tools can help researchers to answer these open questions about the disease. In this work, we present a system of fifteen ordinary differential equations that models the immune response to SARS-CoV-2. The model is used to investigate the hypothesis that the SARS-CoV-2 infects immune cells and, for this reason, induces high-level productions of inflammatory cytokines. Simulation results support this hypothesis and further explain why survivors have lower levels of cytokines levels than non-survivors.

Theoretical Explanation for the Rarity of Antibody-Dependent Enhancement of Infection (ADE) in COVID-19

“…The dynamics of neutral APSs and activated APSs in lungs and lymphoid organs can be described by the following equations: where χ b is the generation and degradation of neutral APSs in the absence of the virus (homeostasis rate of neutral APSs); Ap 0 and Ap are the initial and transient concentrations of neutral APSs; δ ap and δ apm are the rates of APS lung and APS lo deactivation, correspondingly; the terms β apm ∗ Ap ∗ V f /( φ + V f ) indicate the rate of APS lung activation, β apm is the maximal activation rate; and φ is the half-saturation constant for APS lung activation. φ was estimated from an existing model [ 49 , 50 ]. The terms k s 1 and k s −1 denote rates of APS transition between two compartments: lungs and lymphoid organs.…”

“…The following supporting information can be downloaded at: . References [ 1 , 34 , 35 , 36 , 38 , 49 , 51 , 52 , 53 , 57 , 58 , 59 , 60 , 61 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 ] are cited in the Supplementary Materials.…”

A Poroelastic Approach for Modelling Myocardial Oedema in Acute Myocarditis

“…The relevance of the contraction of cardiac myocytes in oedema formation also deserves further attention in future studies, as well as: the investigation of other constitutive relations for the hydraulic conductivity; the inclusion of lymphatic sinks for c p and c l ; modification of the model to include leukocyte’s decay as well as other cells of the immune system, in particular, those related to the adaptive immune system (T and B cells, antibodies, etc.) as proposed in Reis et al (2021) ; a more detailed description of the complex porous media ( Alves et al, 2019 ), since here we focused only on the interstitial space between cells; and a more quantitative validation of the model against patient-specific data.…”

Macrophage Boolean networks in the time of SARS-CoV-2

“…For instance, Reis et al. ( 29 ) developed a mathematical model of a set of fifteen ODEs comprising T and B cells, antibodies, and cytokines. Besides, the action of APC cells was included to mimic the innate immune response.…”