The influenza A virus causes annually recurring epidemic outbreaks, most people become infected multiple times over their lifetime [1
]. The virus also has the propensity to cause occasional pandemics with potentially high death tolls [2
]. Influenza infection results in the desquamation of the epithelial cells lining the nasal mucosa, the larynx, and the tracheobronchial tree. In the case of typical, uncomplicated influenza in humans, the infection will involve only the upper respiratory tract and the upper divisions of bronchi [4
]. In very severe, and often fatal cases of influenza, the infection will spread to the lower lungs as observed, for example, in some infections with avian influenza strains [5
]. The site of infection, namely the airway epithelium, consists of a single layer of cells everywhere except in the trachea [7
] and is composed of four major cell types: basal (progenitor), ciliated, goblet, and Clara cells [8
]. While human-adapted, seasonal strains of influenza tend to preferentially bind and infect nonciliated cells, avian-adapted strains appear to prefer ciliated cells, which could explain these strain’s propensity to infect the lower respiratory tract [6
An influenza A infection is typically initiated following the inhalation of respiratory droplets from infected persons. These droplets containing influenza virions (virus particles) first land on the mucus blanket lining the respiratory tract [7
]. While many virions are destroyed by non-specific clearance such as mucus binding, the remaining virions escape the mucus and attach to receptors on the surface of target epithelial cells. The incubation time for influenza is typically about 48 h, but will typically vary between 24–96 h, possibly owing to the size of the initial inoculum [7
]. Cell infection is initiated by adsorption of the virions to the cell surface. The influenza virus hemagglutinin (HA) is responsible for binding the sialic acid receptors on the surface of epithelial cells providing a strong bond, facilitating the virion’s adsorption into the cell. This results in receptor-mediated endocytosis of the virus particles approximately 20 min after infection [7
]. Once inside the cell, the virions begin replicating, using the machinery and building materials that would normally be used by the host cell to maintain its functions. Virus budding, which takes place only at the apical surface membrane of infected cells [13
], can be detected 5–6 hours post-infection (hpi), and is maximal 7–8 hpi (see Table ). The period between successful infection of the cell and the productive release of viral progeny is often called the “eclipse phase”. Just as it did upon cell entry, the HA on the surface of the virions will again bind the sialic acid receptors. The virus neuraminidase (NA) is responsible for cleaving the sialic acid receptors on the surface of the cells to allow the newly-produced influenza virions to break free of the cell that has produced it and go on to infect other cells. Successive cycles of cell infection quickly result in an exponential growth of viral titer, which peaks around 2–3 days post-infection (dpi). The infection typically resolves in 3–5 dpi, and virus can typically be isolated between 1–7 dpi [7
]. In a primary infection with influenza, pathogen-specific antibodies (Abs) and CD8+
cytotoxic T lymphocytes (CTL) are first observed around 5 dpi, peaking around 7 dpi, whereas in a secondary infection Abs and CTLs can respond as early as 3 dpi [14
]. Cellular regeneration of the epithelium begins 5–7 dpi but complete resolution can take up to one month [15
]. Figure illustrates the kinetic of the course of an influenza infection within a host.
Kinetic parameters for influenza obtained from both fitting mathematical models to data and by direct estimation from experimental data.
Course of an influenza infection within a host. The timings of the adaptive immune response, namely Antibodies (Abs) and cytotoxic T lymphocytes (CTL), for both a primary (PR) and secondary (SR) response to an influenza infection are indicated.
Several aspects of influenza infections are still unresolved. For instance, the contributions of strain-specific cell tropism, pre-existing immunity, and host genetic factors in shaping the virulence and transmissibility of a particular influenza strain are not well understood [16
]. There is much to be learned about how a strain’s genotype shapes complex phenotypes such as virulence and transmissibility. Most of these unresolved aspects will require a quantitative analysis of the key players and of the significance of their respective contribution. As we enter the era of quantitative virology and immunology, with ever more sophisticated experimental tools collecting ever increasing amounts of data, there is more than ever a need for greater synergy between experiments and analysis.
Much work has been done on attempting to capture the dynamics of influenza A using mathematical models; almost all of these models are on the host population level and are concerned with transmission between infected hosts. These models can be used as tools to inform public health decisions with respect to pandemic planning: whom, how and when to quarantine, vaccinate, treat with antivirals, and how much and what to stockpile [18
Here, we focus on a lesser known application of mathematical modeling to the study of influenza kinetics, that aimed at understanding and quantifying the processes involved in determining the severity, duration, and outcome of the progression of the infection within a host or a cell culture. These types of models provide information of a different nature, but, as we will outline below, the information they provide can be equally critical for better treatment and management of the disease. Furthermore, the development of reliable within-host models is critical to improving epidemiological models since the latter relies on the former to more accurately capture the diversity of infection severity, latency, and symptoms.
We first present a survey of the published literature on within-host and in vitro modeling of influenza infections (see also [27
] for a recent review of some of those modeling efforts). We then discuss in general terms both the contributions made by those models and the lessons learned, as well as the challenges that remain as we seek to further our understanding of influenza kinetics within a host or cell culture. We close by highlighting the importance of the models to public health and promising directions for additional modeling studies.