In-host Mathematical Modelling of COVID-19 in Humans

Abstract

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. Considering different starting times of infection, mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Based on the target cell limited model, the within-host reproductive number for SARS-CoV-2 is consistent with the broad values of human influenza infection. The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post-onset of symptoms. The model with the eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, all models predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and viral load could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work. These models can serve for future evaluation of control theoretical approaches to tailor new potential drugs against COVID-19.

Mechanistic Modeling of SARS‐CoV‐2 and Other Infectious Diseases and the Effects of Therapeutics

“…the antiviral remdesivir 58 . With the availability of clinical and experimental data, many mathematical models have been developed and calibrated with data 43,44,45,46,47,48,49,50,51,52,53 . Overall, these studies greatly advanced our quantitative understanding of SARS-CoV-2 infection in both humans and NHPs, the immune responses and the impact of therapeutics.…”

“…Viral dynamic models for chronic infections above can be adapted to quantify dynamics of acute infections, such as influenza, 24,40 West Nile virus, 41 respiratory synctial virus, 42 Zika, 26 and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). 43,44,45,46,47,48,49,50,51,52,53 In particular, extensive modeling efforts have been made towards understanding influenza infection and the immune response against it. These studies often serve as the basis for modeling other acute infections.…”

A modular framework for multiscale, multicellular, spatiotemporal modeling of acute primary viral infection and immune response in epithelial tissues and its application to drug therapy timing and effectiveness

“…Mathematical modeling methods integrate the available host- and pathogen-level data on disease dynamics that are required to understand the complex biology of infection and immune response to optimize therapeutic interventions [ 3 – 5 ]. Mathematical models and computer simulations built on spatial and ODE frameworks have been extensively used to study in-host progression of viral infection [ 6 ], with a recent acceleration in the development of spatial COVID-19 viral infection models in response to the global pandemic [ 7 , 8 ].…”

Structure and Hierarchy of SARS-CoV-2 Infection Dynamics Models Revealed by Reaction Network Analysis

“…Models of the infection dynamics can help understand SARS-CoV-2 pathogenesis, develop optimal treatments, and introduce appropriate measures to prevent the spread of the virus. There are a multitude of modeling approaches with different properties, applications and aims that can be classed into categories of in-host models (e.g., [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ]) versus host-to-host models (such as [ 9 , 10 , 11 , 12 ]), discrete versus continuous models and ODE versus PDE models (for an overview we refer to [ 13 , 14 , 15 , 16 ]). There is an accumulating body of literature on SARS-CoV-2 infection dynamics that make use of these various tools and provide datasets that can be analyzed retrospectively once consensus modeling strategies have been derived [ 17 , 18 ].…”