Special Issue “Mathematical Modeling of Viral Infections”

How an infection will progress in the body is dependent on myriad factors: the rate of spread of the agent, the immune response, what treatment may be applied, .... Clinically following the progression of the disease is limited to snapshots at discrete time points (longitudinally in an individual or in an in vitro/animal model if that is available, but most often from cross-sectional data over cohorts of individuals), and in many cases the data obtained are from a body compartment that is not the site of replication of the disease. We then infer disease progression by putting these discrete data together based on our biological knowledge of the systems involved. However, based on these snapshots, it is not straightforward to work out important disease properties, such as the rate of progression, pathogenicity, and treatment and immune response effects. Mathematical modelling provides a scientifically sound, reproducible method to describe the underlying dynamics that produce these data, as well as a means to investigate new scenarios, such as the effect of a new drug. Its impact has been demonstrated on a number of diseases, for example, contributing to a better understanding of the speed with which human immunodeficiency virus (HIV) replicates [1,2], the dynamics of different drug classes for HIV [3], the main mode of action of interferon in hepatitis C virus (HCV) [4], the effects of direct-acting antivirals in HCV [5], potential effects of the immune response [6], and many others [7,8,9,10,11]