Mathematical modelling of the coronavirus disease

Vitaly Volpert

(CNRS, University Lyon, France)

"Introduction to the pathophysiology of the coronavirus disease"

A short overview of the current knowledge on the disease progression and its possible complications will be presented.

Anass Bouchnita

(Department of Integrative Biology, University of Texas at Austin, USA)

"Multiscale modelling of SARS-CoV-2 infection to study the role of innate and adaptive immune responses in healthy and immunocompromised individuals"

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection causes mild to severe outcomes depending on the balance of host immune response. The interaction between SARS-CoV-2 and the immune response is complex because it involves processes that span across several scales of biological hierarchy such as cells, tissues, organs, and the host. In this talk, we present a multiscale model that describes the interaction between SARS-CoV-2 and the immune response. In this model, dendritic cells are considered as individual objects that move within a section of the epithelial tissue and can be used by the virus to replicate and spread. They also secrete type I IFN which downregulates the production of the virus. At the same time, the model simulates the production of antigen-specific by lymph nodes as well as their interaction with infected cells and virions in the infection site. After model validation, we show that a moderately weak type I IFN could elicit a solid adaptive response that accelerates the virus's clearance. Numerical simulations suggest that the deficiency of naïve lymphocytes in immunocompromised individuals increases the persistence of the virus and exacerbates the disease's outcome.

Bogdan Kazmierczak

(Institute of Fundamental Technological Research, Polish Academy of Sciences, Poland)

"Infection spreading in cell culture as a reaction-diffusion wave"

We formulate a reaction-diffusion system of equations modeling the progression of viral infection, e.g. of SARS-Cov viruses. Analytical and numerical results obtained in the framework of the model are in agreement with the 'in vitro' experimental findings.

Alexey Tokarev

(S.M. Nikolskii Mathematical Institute, Рeoples’ Friendship University of Russia (RUDN University), Russia)

"Nonlinear dynamics in the homogeneous model of immune responses to SARS-CoV-2 virus"

Antiviral immune response is a highly nonlinear process governed by the cooperative behavior of variegated constituents of immune system. Depending on nature of virus, initial viral load, and patient peculiarities, infection can pass diversely and result from recovery to death. In the current pandemic of COVID-19 infection, in the part of patients the disease is complicated by abnormal inflammation response (hypercytokinemia, cytokine storm). We study the immune response to the SARS-CoV-2 virus by constructing the series of ODE-based mathematical models of different phases of this infection: (1) innate immune response, (2) innate plus adaptive immune response, (3) inflammation response. The innate immune response model shows the bistability and threshold properties, as well as possible oscillatory regime. The higher the initial viral load, the shorter is the incubation period and the higher is the maximal transient virus concentration. Depending on the effectiveness of antibodies production, the adaptive immune response can either fully eliminate the virus, or substantially postpone virus concentration burst with following higher virus concentration comparing to the case of innate response only. Inflammation response model also shows bistability and oscillatory behavior. We compare prediction of these models with clinical and epidemiological data. Finally, we study the duration of vaccine protection against the SARS-CoV-2 virus. This work was supported by the Ministry of Science and Higher Education of Russian Federation: agreement no. 075-03-2020-223/3 (FSSF-2020-0018).