Simple scaling laws for influenza A rise time, duration, and severity

Simple scaling laws are developed for the severity and characteristic time scales of influenza A infection in man. The scaling laws are based on a model of the infection described by six coupled ordinary differential equations that describe the time courses of the numbers of infectious viral particles, activated cytotoxic T-lymphocytes, interferon molecules, infected cells, uninfected cells, and the subset of uninfected cells that are protected by interferon from viral infection. Computer simulations show that the disease can be regarded approximately as a two-stage process. In the first stage, the growth in the number of infected cells is determined primarily by the interferon-enhanced limitation in the available number of target cells. In the second stage, the bulk of the duration of the infection is determined mainly by the destruction of the infected cells by the cytotoxic T-lymphocytes. The severity and characteristic times of the infection are found to depend simply on the logarithm of the initial number of viruses.