Bayesian estimation of parameters in viral dynamics models with antiviral effect of interferons in a cell culture

The goal of this work is to estimate the efficacy of interferon therapy in the inhibition of infection by the human immunodeficiency virus type 1 (HIV-1) in a cell culture. For this purpose, three viral dynamics models with the antiviral effect of interferons are presented; the dynamics of cell growth differ among the models, and a variant with Gompertz-type cell dynamics is proposed. A Bayesian statistics approach is used to estimate the cell dynamics parameters, viral dynamics and interferon efficacy. The models are fitted to sets of experimental data on cell growth, HIV-1 infection without interferon therapy and HIV-1 infection with interferon therapy, respectively. The Watanabe-Akaike information criterion (WAIC) is used to determine the model that best fits the experimental data. In addition to the estimated model parameters, the average lifespan of the infected cells and the basic reproductive number are calculated.