Mathematical models of immune responses during external challenges and autoimmunity

Abstract

Characterizing the mechanisms of the immune system and its response to infection and autoimmunity is crucial for understanding and predicting disease outcomes and evaluating potential interventions at multiple scales. While data provide a snapshot of certain biological phenomena, they cannot capture the underlying dynamics. Despite technological advancements, data limitations—arising from ethical, technical, and financial constraints—continue to hinder the precise quantification of key biological processes involved in disease progression and transmission at both individual and population levels. Mathematical models have been used with data at multiple scales to investigate the underlying complex systems of the body's natural molecular, cellular, and systemic processes, its response to external challenges or immunodeficiencies, and subsequent impacts on disease, treatment, and transmission outcomes. This dissertation uses mathematical modeling, mathematical analysis, and parameter estimation tools to uncover mechanisms of immune responses and immune system dysfunction during autoimmunity and viral infections. The immunological and viral dynamic models were validated against longitudinal virus or immune cell and marker data.

The immune response is the body's mechanism for protecting itself against foreign pathogens (e.g., viruses, bacteria, fungi, toxins) or substances it deems harmful. It consists of the innate (non-specific) immune response and the adaptive (specialized) immune response. The innate immune response serves as one of the body's first lines of defense, responding rapidly and uniformly to all foreign substances. This pathogen-induced innate immune response operates through inflammatory immune mechanisms and the removal of foreign particles by immune cells. In the case of SARS-CoV-2, virus-induced persistent inflammation and tissue damage are associated with increased COVID-19 severity and disease progression. To better understand the mechanisms underlying persistent inflammation in severe COVID-19 cases, we developed a mathematical model of the innate immune response following SARS-CoV-2 infection. After fitting the model to immune cell and immune marker data from COVID-19 patients, we estimated key parameters for both mild and severe clinical cases. Analytical, bifurcation, and numerical techniques were used to investigate how changes in immune function affect long-term immune dynamics and to identify potential mechanisms needed for immune resolution.

If the innate immune response fails to eliminate the pathogen, the adaptive immune response takes over. Although it is slow to activate, the adaptive immune response employs specialized immune cells and antibodies that specifically target and eliminate foreign pathogens while generating memory cells that allow for a faster response upon reinfection. Immune memory can also be induced through vaccination, as demonstrated by the global vaccination efforts during the COVID-19 pandemic. However, we observed that vaccine-induced immunity to SARS-CoV-2 waned over time as mutations in the virus emerged, necessitating booster vaccinations to maintain protection. Accurately predicting the strength and durability of the adaptive immune response requires understanding diverse immune profiles. In the case of SARS-CoV-2, immune profile heterogeneity arises from prior infection with multiple variants, the severity of previous infections, and the timing and order of natural infection and vaccination. We developed mathematical models of antibody responses following vaccination against SARS-CoV-2, fitting them to longitudinal antibody data to determine the long-term dynamics and composition of the antibody-mediated immune response in individuals with varying immune landscapes.

When functioning correctly, the adaptive immune response can last weeks, months, or even years, depending on the context. However, in some cases, the adaptive immune response fails to distinguish between foreign and self-antigens, leading to an immune response against the body's own tissues. One example is systemic lupus erythematosus (SLE), a chronic autoimmune disease with no single known cause, though evidence suggests that dysregulated immune responses—driven by a combination of genetic predisposition and environmental factors—may contribute to its development. One emerging area of interest in immunotherapy is centered around harnessing the anti-inflammatory properties of Aryl hydrocarbon receptor (AhR), a flexible ligand-activated transcription factor that acts as an environmental sensor, activation. Using mathematical modelling and data from an animal study, we developed a framework for identifying cellular and molecular factors that contribute to physiological outcomes observed in Lupus. We developed a novel model to describe dynamics of immunosuppressive and follicular T cell phenotypes and predicted the T cell balance over time.

Lastly, we developed a multiscale model to describe disease dynamics in an emerging zoonotic disease, Usutu virus, which spreads between birds and mosquitoes with occasional spillover humans causing neurological disease. The multiscale model was fit to data at three biological scales: infectious Usutu virus titers in canaries, bird-to-mosquito transmission data, as well as reported susceptible and infected birds. The model was used to predict disease dynamics at multiple scales. Since during data fitting, the model and type of data being used has significant effect on reliability of parameter estimates and predicted disease dynamics, we conduct identifiability analyses to determine the reliability of parameters estimated from our model.