Mathematical models tackle Covid infection dynamics

Even years after the emergence of the COVID-19 global pandemic, the workings of SARS-CoV-2 infection inside the human body, including the early activity of the virus and the role of the body’s immune response, has proved difficult to precisely ascertain. Using data from a human challenge study, researchers from Los Alamos National Laboratory have developed a mathematical approach that models the dynamics of viral infection, shedding light on the early activity of the virus, immune responses and avenues for drug treatments.

“Mathematical models are really useful for COVID-19 dynamics because they help us disentangle different biological processes, with infection and immune responses being important to understand,” said Los Alamos researcher Ruian Ke. “Understanding these dynamics improves our knowledge of acute infections and aids us in developing more realistic models of viral transmission in human populations. In the long term, research like this can build toward using models to understand the effective design and impact of drugs and treatment strategies.”

Published in the Proceedings of the National Academy of Sciences, the team’s research focuses on the amount of virus in the upper respiratory tract and its relationship to the body’s immune response. The researchers track viral kinetics: how much of the virus actually infects cells, how the innate immune response (the body’s first, general response to infection) and the adaptive immune response (the body’s specialized, targeted immune system) respond to the infection.

“Viral kinetics take into account the events that occur after the body’s first encounter with the virus, from infection onset to clearance,” said Alan Perelson, Laboratory fellow and researcher on the mathematical modeling. “The dynamic models we proposed feature increasing complexity to dissect how the observed viral kinetics are determined by target cell limitation, innate immunity and adaptive immunity.  We fit our models to viral load and measures of infectious virus concentrations from all the untreated infected participants in the study simultaneously.”

Human challenge study

The models were developed on data from a landmark, 2021 human challenge study in which 36 healthy volunteers, with no record of previous infection or vaccination, were inoculated with the COVID-19 virus. (The study was conducted in the United Kingdom without the involvement of Los Alamos National Laboratory.) A subset of the challenge group was given the therapeutic drug remdesivir; however, the Laboratory team based their modeling only on the participants not treated with remdesivir. The progression of the virus in the participants was tracked in real time to observe the dynamics of infection.

The Los Alamos team used the data from the study to build corresponding mathematical models. The team found a power-law, or an expression of a functional relationship, between infectious virus and viral load. That is, they were able to mathematically model the rate of change of the amount of infectious virus particles — those that cause further viral replication — among the overall amount of virus present in the participant.

The team’s models uncovered rapid viral replication at the early stage of infection, with viral RNA doubling approximately every two hours, and infectious virus doubling approximately every three hours. The modeling also explores the initiation of the adaptive immune response as the body builds antibodies that attack the virus, approximately seven to 10 days after infection, with an impact on viral decline for some study participants.

For some participants, the virus rebounded. The mathematical modeling suggests that such rebounds are consistent with a decline in the body’s innate immunity, specifically the interferon response. Because viral rebounds could lead to renewed symptoms and the ability to transmit the virus, understanding that dynamic is important for designing effective treatments.

Paper: “The kinetics of SARS-CoV-2 infection based on a human challenge study.” Proceedings of the National Academy of Sciences. DOI: 10.1073/pnas.2406303121

Funding: The work was supported by the National Institutes of Health, the National Science Foundation and the Laboratory Directed Research and Development program at Los Alamos.

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