Influenza a infections in the host : modeling and control approaches
Authors:   , Hernandez Mejia Gustavo 
Published: January 2024

Influenza is a contagious respiratory disease caused by influenza A and influenza B viruses. The World Health Organisation (WHO) reports that annual influenza epidemics result in approximately 1 billion infections, 3 to 5 million severe cases, and 300 to 650 thousand deaths. Understanding hidden mechanisms that lead to optimal vaccine efficacy and improvement antiviral treatment strategies remain continuous and central tasks. First, regarding the immune response to vaccines and natural infections, the antibody response echoes the dynamics of diverse immune elements such as B-cells, and plasma cells. Also, responses reflect the processes for B-cells to gain and adapt affinity for the virus. Antibodies (Abs) that respond to the virus surface proteins, particularly to the hemagglutinin (HA), have been identified to protect against infection. The Abs responses binding to HA can be broadly protective as this protein is considerably accessible on the virion. When following sequential infections with similar influenza strains, i.e. two infections with different strains of a subtype, an enhanced breadth and magnitude of Abs response is developed, mainly after the second infection. The effect of being effective to new strains is called Abs cross-reaction. On the other hand, as for antiviral treatment, the WHO currently approves the use of neuraminidase inhibitors (NIs) such as zanamivir and oseltamivir. Diverse research areas such as system biology, learning-based methods, control theory, and systems pharmacology have guided the development of modern treatment schemes. To do so, mathematical models are used to describe a wide range of phenomena such as viral pathogenesis, immune responses, and the drug's dynamics in the body. Drug dynamics are usually expressed in two phases, pharmacokinetics (PK) and pharmacodynamics (PD) - the PK/PD approach. These schemes leverage pre-clinical and clinical data through modeling and simulation of infection and drug effects at diverse levels. Under such a framework, control-based scheduling systems seek to tailor optimal antiviral treatment for infectious diseases. Thus, influenza treatment can be theoretically studied as a control-based optimization duty (about systems stability, bounded inputs, and optimality). Finally, towards real-world implementation, learning-based methods such as neural networks (NNs) can guide solving issues on the control-based performance. Using NNs as identifiers provide a setting to deal with infrequent measures and uncertain parameters for the control systems. This thesis theoretically explores central mechanisms in influenza infection via modeling and control approaches. In the first project, we explore how and to what extent antibody-antigen affinity flexibility could guide the Abs cross-reaction in two sequential infections using a hypothetical family of antigens. The set of antigens generally represent strains of influenza, such as those of a subtype. Each antigen is composed of a variable and a conserved area, generically representing the structures of the HA, head, and stalk, respectively. We test diverse scenarios of affinity thresholds in the conserved and variable areas of the antigens. The Abs response reaches a high magnitude when using equivalent affinity thresholds in the conserved and variable areas during the first infection. However, improved cross-reaction is developed when slightly increasing the affinity threshold of the variable area for the second infection. Key mutations via affinity maturation is a feature that, together with affinity flexibility between infections, guides Abs cross-reaction in the model outcome. These results could correlate with studies pointing out that broad responses might be dependent on reaching specific mutations for getting affinity to a newly presented antigen while broadly reaching related antigens. The general platform may serve as a proof-of-concept for exploring fundamental mechanisms that favor the Abs cross-reaction. In a second project, theoretical schemes are developed to combine impulsive and inverse optimal control strategies to address antiviral treatment scheduling. We present results regarding stability, passivity, bounded inputs, and optimality using impulsive action. The study is founded on mathematical models of the influenza virus (target-cell limited model) adjusted to data from clinical trials. In these studies, participants were experimentally infected with influenza H1N1 and treated with NIs. Results show that control-based strategies could tailor dosage and reduce the amount of medication by up to 44%. Also, control-based treatment reaches the efficacy (98%) of the current treatment recommendations by the WHO. Monte Carlo simulations (MCS) disclose the robustness of the proposed control-based techniques. Using MCS, we also explore the applicability to the individualized treatment of infectious diseases through virtual clinical trials. Furthermore, bounded control strategies are applied directly in drug dose estimation accounting for overdose prevention. Finally, due to the limitations of the available technology intended for clinical practice, we emphasize the necessity of developing system identifiers and observers for real-world applications. In the third project, the problem of data scarcity and infrequent measures in the real world is handled by means of learning-based methods. System identification is derived using a Recurrent High Order Neural Network (RHONN) trained with the Extended Kalman filter (EKF). Lessons learned from impulsive control frameworks are taken to develop a neural inverse optimal impulsive control --neurocontrol. The treatment efficacy is tested for early (one day post-infection) and late (2 to 3 days post-infection) treatment initiation. The neurocontrol reaches an efficacy of up to 95% while saving almost 40% of the total drug in the early treatment. Robustness is tested via virtual clinical trials using MCS. Lastly, taking all together, the schemes developed in this thesis for modeling the Abs cross-reaction and control-based treatment tailoring can be extended and adapted to explore similar phenomena in different respiratory pathogens, such as SARS-CoV-2.