Modeling the Influenza Virus Dynamics Within a Host

Several mathematical models that describe the dynamics of a virus within a host have been proposed and analyzed. These studies are challenging as the viral dynamics interact with the host immune response. Influenza virus provides a good example of acute infections, which causes high morbidity and mortality in human and animal populations. The influenza virus spreads within a host by infecting epithelial cells of the respiratory tract. The infection elicits an immune response of the host, starting with the innate response as the first line of defense, that avoids the total cell depletion, followed by the adaptive response that clears the infection after a few days. Model development depends on the available data, which is usually limited to viral loads. Here, several models for the influenza virus dynamics within a host, with varying levels of detail with respect to the immune responses of the host (which are constraint by the available data), are proposed. The models are fitted to viral shedding and interferon data from experimental infections in horses. The parameter estimation is performed by means of the method of Markov Chains and Monte Carlo. The model fits are compared, and their merits and limitations are discussed.