Mathematical Modeling of Virus Dynamics in Immunology

A simplified dynamical model of immune response to uncomplicated influenza virus infection is presented, which focuses on the control of the infection by the innate and adaptive immunity. Innate immunity is represented by interferon-induced resistance to infection of respiratory epithelial cells and by removal of infected cells by effector cells. Adaptive immunity is represented by virus-specific antibodies. Similar in spirit to the recent model of Bocharov & Romanyukha (Bocharov and Romanyukha, 1994), the model is constructed as a system of 10 ordinary differential equations with 27 parameters. In the first part, parameter values for the model are obtained either from published experimental data or by estimation based on fitting available data about the time course of IAV infection in a naïve host. Sensitivity analysis is performed on the model parameters. To account for the variability and speed of adaptation, a variable is introduced that quantifies the antigenic compatibility between the virus and the antibodies. It is found that for small initial viral load the disease progresses through an asymptomatic course, for intermediate value it takes a typical course with constant duration and severity of infection but variable onset, and for large initial viral load the disease becomes severe. The absence of antibody response leads to recurrence of disease and appearance of a chronic state with nontrivial constant viral load. In the second part, an ensemble model of immune response is developed, which consists of multiple ODE models that are identical in form but differ in parameter values. A probabilistic measure of goodness of fit of the ODE model is used to derive an a posteriori probability density on the space of parameter values. This probability density is sampled using the Metropolis Monte Carlo method and sampling is enhanced using parallel tempering algorithm. The ensemble model is employed to compute probabilistic estimates on trajectory of the immune response, duration of disease, maximum damage, likelihood of rebound in the disease and the probability of occurrence of superspreaders. The effectiveness of using antiviral drug to treat the infection is addressed and optimal treatment scenarios are discussed