Modelling viral and immune system dynamics

Viruses are extraordinarily diverse in shape and size, but they all have several structural features in common. All viruses have a core that contains a DNA- or RNA-based genome. The core is surrounded by a protective coat of proteins called the capsid. The capsid is composed of subunits called capsomeres. The capsid and genome-containing core are together known as the nucleocapsid.

The immune system's response to viral infections is a complex and coordinated process involving natural killer (NK) cells, T cell-mediated responses, and antibody-mediated responses.
NK Cells
NK cells are a crucial part of our innate immune system, acting as the first line of defense against viral infections. These cells can recognize and kill infected cells without prior exposure to the virus, effectively slowing down the spread of infection. Additionally, NK cells produce proinflammatory...

The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A higher...

Viral genomes exhibit remarkable diversity in size, structure, and composition, influencing their replication strategies and interactions with host cells. These genomes consist of either DNA or RNA and may be linear or circular. Additionally, they can be single-stranded or double-stranded, with each configuration affecting how the virus propagates within a host. RNA viruses, for instance, generally have smaller genomes than DNA viruses, a factor that contributes to their high mutation rates and...

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...

The human body harbors a vast and diverse viral community known as the human virome. The virome includes bacteriophages that infect bacteria, and eukaryotic viruses that infect human cells. Transient dietary and environmental viruses also contribute to this dynamic ecosystem. Estimates suggest the human body may contain on the order of 10¹³ viral particles, though abundance varies widely by body site and detection method.Comprehensive characterization of the virome has become possible only with...