Mathematical models of Influenza A virus infections in vitro: Investigating defective interfering particles and virus release

In this work, two studies were performed where mathematical models (MM) were used to re-examine and refine quantitative methods based on in vitro assays of influenza A virus infections. In the first study, we investigated the standard experimental method for counting defective interfering particles (DIPs) based on the reduction in standard virus (STV) yield (Bellett & Cooper, 1959). We found the method is valid for counting DIPs provided that: (1) a STV-infected cell’s co-infection window is approximately half its eclipse phase (it blocks infection by other virions before it begins producing progeny virions); (2) a cell co-infected by STV and DIP produces less than 1 STV per 1,000 DIPs; and (3) a high MOI of STV stock (>4 plaque-forming units/cell) is added to perform the assay. Prior work makes no mention of these criteria such that the counting method has been applied incorrectly in several publications discussed herein. We determined influenza A virus meets these criteria, making the method suitable for counting influenza A DIPs. In the second study, we compared a MM with an explicit representation of viral release to a simple MM without explicit release, and investigated whether parameter estimation and the estimation of neuraminidase inhibitor (NAI) efficacy were affected by the use of a simple MM. Since the release rate of influenza A virus is not well-known, a broad range of release rates were considered. If the virus release rate is greater than ∼0.1 h−1, the simple MM provides accurate estimates of infection parameters, but underestimates NAI efficacy, which could lead to underdosing and the emergence of NAI resistance. In contrast, when release is slower than ∼0.1 h−1, the simple MM accurately estimates NAI efficacy, but it can significantly overestimate the infectious lifespan (i.e., the time a cell remains infectious and producing free virus), and it will significantly underestimate the total virus yield and thus the likelihood of resistance emergence. We discuss the properties of, and a possible lower bound for, the influenza A virus release rate. Overall, MMs are a valuable tool in the exploration of the known unknowns (i.e., DIPs, virus release) of influenza A virus infection.