Influenza Virus Infection Model With Density Dependence Supports Biphasic Viral Decay

Abstract

Mathematical models that describe infection kinetics help elucidate the time scales, effectiveness, and mechanisms underlying viral growth and infection resolution. For influenza A virus (IAV) infections, the standard viral kinetic model has been used to investigate the effect of different IAV proteins, immune mechanisms, antiviral actions, and bacterial coinfection, among others. We sought to further define the kinetics of IAV infections by infecting mice with influenza A/PR8 and measuring viral loads with high frequency and precision over the course of infection. The data highlighted dynamics that were not previously noted, including viral titers that remain elevated for several days during mid-infection and a sharp 4–5 log10 decline in virus within 1 day as the infection resolves. The standard viral kinetic model, which has been widely used within the field, could not capture these dynamics. Thus, we developed a new model that could simultaneously quantify the different phases of viral growth and decay with high accuracy. The model suggests that the slow and fast phases of virus decay are due to the infected cell clearance rate changing as the density of infected cells changes. To characterize this model, we fit the model to the viral load data, examined the parameter behavior, and connected the results and parameters to linear regression estimates. The resulting parameters and model dynamics revealed that the rate of viral clearance during resolution occurs 25 times faster than the clearance during mid-infection and that small decreases to this rate can significantly prolong the infection. This likely reflects the high efficiency of the adaptive immune response. The new model provides a well-characterized representation of IAV infection dynamics, is useful for analyzing and interpreting viral load dynamics in the absence of immunological data, and gives further insight into the regulation of viral control.

Host‐pathogen kinetics during influenza infection and coinfection: insights from predictive modeling

“…With these data, even the larger, more comprehensive models can be calibrated to data . In addition, efforts to improve parameter estimation algorithms and employ analytical techniques have significantly advanced our ability to generate robust predictions about the underlying biology . Model results are now undergoing rigorous testing in the laboratory, which has confirmed their predictive capability and importance in identifying regulatory mechanisms driving influenza virus infections.…”

“…Viral Kinetic Model and Dynamics. A schematic of the standard viral kinetic model, associated equations, fit to data from mice infected with influenza A/Puerto Rico/34/8 ( PR 8), and timeline of major host responses are shown. The model tracks susceptible “target” cells (), two classes of infected cells ( and ), and virus ().…”

“…Until recently, it was relatively well accepted that the choice of estimation scheme is not critical. However, contrasting parameter estimates may result and some evidence suggests that ASA or GP methods can outperform MCMC and MLE methods in terms of accuracy, convergence, and run time . Further investigation is needed to ensure robust results, particularly because MCMC methods are popular.…”

“…In most studies, the values of the eclipse phase parameter ( k ) and initial target cells ( T 0 ) are fixed because their values can be calculated . However, these can be left free without compromising the predictive capability. One problematic parameter has been the virus clearance rate ( c ), which often estimates to large values that may not be biologically relevant .…”

“…However, these can be left free without compromising the predictive capability. One problematic parameter has been the virus clearance rate ( c ), which often estimates to large values that may not be biologically relevant . This is because the model attempts to capture the rapid decrease in free virus shortly after the infection is initiated as virus infects cells (~0‐4 hours).…”