Hana M. Dobrovolny

Favipiravir, an antiviral that inhibits viral RNA-dependent RNA polymerase, has demonstrated promise as a therapeutic for RNA viral infections such as SARS-CoV-2. Mathematical modeling of viral kinetics provides a tool for analyzing the progression of viral infections and the action of antiviral drugs. In the present investigation, the viral kinetics of SARS-CoV-2 infection in cynomolgus macaques treated with the antiviral drug favipiravir were analyzed using a target-cell-limited mathematical model of viral infection. The model parameters were estimated by fitting the model independently to each of the 30 individual animals across four treatment groups (untreated control, 100 mg/kg, 150 mg/kg, and 180 mg/kg). Bootstrap resampling was applied to quantify the parameter uncertainty, and Mann–Whitney U tests were used to compare the group-level parameter estimates between the control and each treated group. Despite broad trends in several parameters, no statistically significant differences were detected between the control and any favipiravir-dose group. We also fit the model to the group-averaged viral titer curves, which led to statistically significant differences in some of the parameters. These results highlight the danger in using averaged viral titers when there is substantial inter-animal variability in individual viral kinetics data, and they suggest that larger cohorts may be required to detect drug effects with statistical confidence at the individual animal level.

Syncytia are multinucleated cells created by fusion of normal cells. Some viruses are known to induce syncytia formation as a consequence of infected cells expressing viral surface proteins. The role of syncytia in the spread of viral infections and the resulting disease is still poorly understood. Researchers have developed cell-cell fusion assays to help study the fusion process. These assays use cells transfected to express viral surface proteins to study the fusion process without an active viral infection. Recently, mathematical models have been developed to simulate the dynamics of these assays and have been used to estimate parameters that characterize the fusion process. This review examines the cell-cell fusion assay and the mathematical models that have been developed to reproduce assay dynamics. While modeling of these systems is still in its early stages, further extension of these models will help improve our understanding of the syncytia formation process.

Oncolytic viruses, specifically Sindbis virus (SINV), combined with cytokines show promising results in slowing glioma progression, but a quantitative understanding of their effects remains limited. In this study, we use an ordinary differential equation (ODE) model to examine the effect of adding cytokines to oncolytic SINV therapy. We fit the mathematical model to data extracted from published tumor growth curves to estimate key model parameters. We find that there are statistically significant differences between the infection rates of SINV and cytokine‐bearing SINV, as well as differences in the cytokine's ability to reduce viral production. Model simulations show that the addition of cytokines causes an almost immediate reduction in the tumor size caused by the increased viral infection rate. The simultaneous reduction in viral production caused by the cytokines results in oscillations in virus, cytokines, and tumor volume. By providing parameter estimates for key biological processes, our model can help optimize treatment strategies and guide future research in oncolytic virotherapy.

The most common viral dynamics models for analyzing viral infections assume a well-mixed spatial distribution between viral particles and uninfected target cells. However, throughout an infection, the spatial distribution of virus and cells changes. Initially, virus and infected cells are localized so that a target cell in an area with lower virus presence will be less likely to be infected than a cell close to a location of viral production. A density-dependent infection rate has the potential to improve models that treat the cellular infection probability as a constant. Building on previous work that used epidemiological models, which introduced Saturated Incidence, Beddington-DeAngelis, and Crowley Martin models to simulate spatial heterogeneity in population-level models, we implemented these density-dependent models in within-host viral kinetics models to understand how a density dependent infection rate might impact the predicted severity of an influenza infection. The parameter values that govern the strength of density dependence were varied to understand the implications of density dependent infection rate on disease severity and the potential impacts on patient treatment. For low density dependence, a steeper increase in the virus and a higher viral peak was predicted. We find that the initial localization of infected cells slows the progression of the infection, thus suggesting that accounting for density dependence when analyzing influenza infection severity can result in an altered expectation for viral progression.

Oncolytic vaccinia viruses (OVVs) present a promising approach for melanoma treatment due to their ability to selectively infect and lyse tumour cells. However, OVV therapy has shown poor long-term outcomes. In this study, we use an ordinary differential equation model of tumour growth inhibited by OVV activity to characterize the effect of neutrophil depletion in B16-F10 melanoma tumours in mice. We find that the data can be fit by a model that accounts for neutrophil-mediated viral clearance. The model allows for two fixed points: a disease-free equilibrium, where the tumour is eradicated, and chronic infection, where the tumour is controlled but not eliminated. The model correctly predicts enhanced OVV effectiveness in the presence of chemotherapeutic neutrophil modulation, with OVV treatment in combination with neutrophil depletion driving the system from the chronic infection equilibrium to the disease-free equilibrium. We also find that parameter estimates for the most effective OVV regime share characteristics, most notably a low viral clearance rate, suggesting that improved outcomes are due to longer-lasting viral infections. Further studies examining the impact of neutrophil modulation across different tumour models can help elucidate the extent to which these findings generalize and inform the design of novel OVV-based cancer therapies.

Syncytia formation occurs when viruses fuse cells together, creating multinucleated cells. By spreading through fusion, the virus avoids the extracellular environment, protecting it from antibodies that can neutralize the virus. To investigate the effect of this protection, we used a mathematical model to simulate viral infections that spread via both cell-free transmission and syncytia formation and included the effect of antibodies. We compared infections with high, low, and no syncytia fusion, finding that even a low rate of syncytia formation affects infection dynamics and can hinder antibody effectiveness. Specifically, we find that the presence of syncytia increases the viral load, delays the time of peak, and increases the number of cells infected by the virus as compared to infections without syncytia formation. This mathematical model sheds light on how syncytia formation shields viruses from antibodies, aiding in spread of the virus in spite of a robust immune response.

Human Immunodeficiency Virus (HIV) Type-1 has been studied heavily for decades, yet one area that is still poorly understood is the virus’ ability to cause cell–cell fusion. In HIV, the fusion process is mediated by viral surface glycoproteins that bind to CD4 cell receptors. This virus-mediated cell fusion creates multi-nucleated cells called syncytia that can affect infection dynamics. Syncytia formation is often studied using a cell–cell fusion assay, in which donor cells expressing the viral surface protein fuse with acceptor cells expressing the cell receptor. A mathematical model capable of reproducing the dynamics of the cell–cell fusion assay was recently developed and can be used to quantify changes in syncytia formation. In this study, we use this mathematical model to quantify the changes in syncytia formation in HIV as the surface density of the glycoproteins is varied. We find that we need to modify the model to explicitly include a density-dependent syncytia formation rate that allows us to capture the dynamics of the cell–cell fusion assay as the density of the glycoproteins changes. With this modification, we find that cell–cell fusion of the HXB2 strain, which uses the CXCR4 coreceptor, shows a threshold-like behavior, while cell–cell fusion of the Sf162 strain, which uses the CCR5 co-receptor, shows a more gradual change as surface density decreases.