Modeling the bystander effect during viral coinfection.

Viral coinfections are responsible for a significant portion of cases of patients hospitalized with influenza-like illness. As our awareness of viral coinfections has increased, researchers have started to experimentally examine some of the virus-virus interactions underlying these infections. One mechanism of interaction between viruses is through the innate immune response. This seems to occur primarily through the interferon response, which generates an antiviral state in nearby uninfected cells, a phenomenon know as the bystander effect. Here, we develop a mathematical model of two viruses interacting through the bystander effect. We find that when the rate of removal of cells to the protected state is high, growth of the first virus is suppressed, while the second virus enjoys sole access to the protected cells, enhancing its growth. Conversely, growth of the second virus can be fully suppressed if its ability to infect the protected cells is limited.

Effect of cellular regeneration and viral transmission mode on viral spread.

Illness negatively affects all aspects of life and one major cause of illness is viral infections. Some viral infections can last for weeks; others, like influenza (the flu), can resolve quickly. During infections, uninfected cells can replicate in order to replenish the cells that have died due to the virus. Many viral models, especially those for short-lived infections like influenza, tend to ignore cellular regeneration since many think that uncomplicated influenza resolves much faster than cells regenerate. This research accounts for cellular regeneration, using an agent-based framework, and varies the regeneration rate in order to understand how cell regeneration affects viral infection dynamics under assumptions of different modes of transmission. We find that although the general trends in peak viral load, time of viral peak, and chronic viral load as regeneration rate changes are the same for cell-free or cell-to-cell transmission, the changes are more extreme for cell-to-cell transmission due to limited access of infected cells to newly generated cells.

The role of syncytia during viral infections.

Respiratory syncytial virus (RSV) is a common, contagious infection of the lungs and the respiratory tract. RSV is characterized by syncytia, which are multinuclear cells created by cells that have fused together. We use a mathematical model to study how different assumptions about the viral production and lifespan of syncytia change the resulting infection time course. We find that the effect of syncytia on viral titer is only apparent when the basic reproduction number for infection via syncytia formation is similar to the reproduction number for cell free viral transmission. When syncytia fusion rate is high, we find the presence of syncytia can lead to slowly growing infections if viral production is suppressed in syncytia. Our model provides insight into how the presence of syncytia can affect the time course of a viral infection.

SARS-CoV-2 coinfections: Could influenza and the common cold be beneficial?

The novel coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has rapidly spread around the world, causing serious illness and death and creating a heavy burden on the healthcare systems of many countries. Since the virus first emerged in late November 2019, its spread has coincided with peak circulation of several seasonal respiratory viruses, yet some studies have noted limited coinfections between SARS-CoV-2 and other viruses. We use a mathematical model of viral coinfection to study SARS-CoV-2 coinfections, finding that SARS-CoV-2 replication is easily suppressed by many common respiratory viruses. According to our model, this suppression is because SARS-CoV-2 has a lower growth rate (1.8/d) than the other viruses examined in this study. The suppression of SARS-CoV-2 by other pathogens could have implications for the timing and severity of a second wave.

An approximate solution of the interferon-dependent viral kinetics model of influenza.

The analysis of viral kinetics models is mostly achieved by numerical methods. We present an approach via a Magnus expansion that allows us to give an approximate solution to the interferon-dependent viral infection model of influenza which is compared with numerical results. The time of peak viral load is calculated from the approximation and stays within 10% in the studied range of interferon (IFN) efficacy ϵ ∈ [0, 1000]. We utilize our solution to interpret the effect of varying IFN efficacy, suggesting a competition between virions and interferon that can cause an additional peak in the usually exponential increase in the viral load.

Effect of stochasticity on coinfection dynamics of respiratory viruses.

BACKGROUND: Respiratory viral infections are a leading cause of mortality worldwide. As many as 40% of patients hospitalized with influenza-like illness are reported to be infected with more than one type of virus. However, it is not clear whether these infections are more severe than single viral infections. Mathematical models can be used to help us understand the dynamics of respiratory viral coinfections and their impact on the severity of the illness. Most models of viral infections use ordinary differential equations (ODE) that reproduce the average behavior of the infection, however, they might be inaccurate in predicting certain events because of the stochastic nature of viral replication cycle. Stochastic simulations of single virus infections have shown that there is an extinction probability that depends on the size of the initial viral inoculum and parameters that describe virus-cell interactions. Thus the coinfection dynamics predicted by the ODE might be difficult to observe in reality. RESULTS: In this work, a continuous-time Markov chain (CTMC) model is formulated to investigate probabilistic outcomes of coinfections. This CTMC model is based on our previous coinfection model, expressed in terms of a system of ordinary differential equations. Using the Gillespie method for stochastic simulation, we examine whether stochastic effects early in the infection can alter which virus dominates the infection. CONCLUSIONS: We derive extinction probabilities for each virus individually as well as for the infection as a whole. We find that unlike the prediction of the ODE model, for similar initial growth rates stochasticity allows for a slower growing virus to out-compete a faster growing virus.

Superinfection and cell regeneration can lead to chronic viral coinfections.

Molecular diagnostic techniques have revealed that approximately 43% of the patients hospitalized with influenza-like illness are infected by more than one viral pathogen, sometimes leading to long-lasting infections. It is not clear how the heterologous viruses interact within the respiratory tract of the infected host to lengthen the duration of what are usually short, self-limiting infections. We develop a mathematical model which allows for single cells to be infected simultaneously with two different respiratory viruses (superinfection) to investigate the possibility of chronic coinfections. We find that a model with superinfection and cell regeneration has a stable chronic coinfection fixed point, while superinfection without cell regeneration produces only acute infections. This analysis suggests that both superinfection and cell regeneration are required to sustain chronic coinfection via this mechanism since coinfection is maintained by superinfected cells that allow slow-growing infections a chance to infect cells and continue replicating. This model provides a possible mechanism for chronic coinfection independent of any viral interactions via the immune response.

The rate of viral transfer between upper and lower respiratory tracts determines RSV illness duration.

Respiratory syncytial virus can lead to serious lower respiratory infection (LRI), particularly in children and the elderly. LRI can cause longer infections, lingering respiratory problems, and higher incidence of hospitalization. In this paper, we use a simplified ordinary differential equation model of viral dynamics to study the role of transport mechanisms in the occurrence of LRI. Our model uses two compartments to simulate the upper respiratory tract and the lower respiratory tract (LRT) and assumes two distinct types of viral transfer between the two compartments: diffusion and advection. We find that a range of diffusion and advection values lead to long-lasting infections in the LRT, elucidating a possible mechanism for the severe LRI infections observed in humans.

Intermittent treatment of severe influenza.

Severe, long-lasting influenza infections are often caused by new strains of the virus. The long duration of these infections leads to an increased opportunity for the emergence of drug resistant mutants. This is particularly problematic since for new strains there is often no vaccine, so drug treatment is the first line of defense. One strategy for trying to minimize drug resistance is to apply drugs periodically. During treatment phases the wild-type virus decreases, but resistant virus might increase; when there is no treatment, wild-type virus will hopefully out-compete the resistant virus, driving down the number of resistant virus. A stochastic model of severe influenza is combined with a model of drug resistance to simulate long-lasting infections and intermittent treatment with two types of antivirals: neuraminidase inhibitors, which block release of virions; and adamantanes, which block replication of virions. Each drug's ability to reduce emergence of drug resistant mutants is investigated. We find that cell regeneration is required for successful implementation of intermittent treatment and that the optimal cycling parameters change with regeneration rate.

Modeling of fusion inhibitor treatment of RSV in African green monkeys.

Respiratory syncytial virus (RSV) is a respiratory infection that can cause serious illness, particularly in infants. In this study, we test four different model implementations for the effect of a fusion inhibitor, including one model that combines different drug effects, by fitting the models to data from a study of TMC353121 in African green monkeys. We use mathematical modeling to estimate the drug efficacy parameters, εmax, the maximum efficacy of the drug, and EC50, the drug concentration needed to achieve half the maximum effect. We find that if TMC353121 is having multiple effects on viral kinetics, more detailed data, using different treatment delays, is needed to detect this effect.

The impact of cell regeneration on the dynamics of viral coinfection.

Many mathematical models of respiratory viral infections do not include regeneration of cells within the respiratory tract, arguing that the infection is resolved before there is significant cellular regeneration. However, recent studies have found that ∼40% of patients hospitalized with influenza-like illness are infected with at least two different viruses, which could potentially lead to longer-lasting infections. In these longer infections, cell regeneration might affect the infection dynamics, in particular, allowing for the possibility of chronic coinfections. Several mathematical models have been used to describe cell regeneration in infection models, though the effect of model choice on the predicted time course of viral coinfections is not clear. We investigate four mathematical models incorporating different mechanisms of cell regeneration during respiratory viral coinfection to determine the effect of cell regeneration on infection dynamics. We perform linear stability analysis for each of the models and find the steady states analytically. The analysis suggests that chronic illness is possible but only with one viral species; chronic coexistence of two different viral species is not possible with the regeneration models considered here.

Differences in predictions of ODE models of tumor growth: a cautionary example.

BACKGROUND: While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer. METHODS: We examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model. RESULTS: We find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used. CONCLUSION: Our results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

Different routes of infection of H5N1 lead to changes in infecting time.

Influenza virus infection can result in a wide range of clinical outcomes from asymptomatic infection to severe disease and death. While there are undoubtedly many factors that contribute to the severity of disease, one possible contributing factor that needs more investigation is the route of infection. In this study, we use previously published data from cynomolgus macaques infected with A/Vietnam/1203/04 (H5N1) via either aerosol (with and without bronchoalveolar lavages (BAL)) or a combined intrabronchial, oral, and intranasal route. We fit a mathematical model of within host viral kinetics to the data and find that when the macaques are infected via the aerosol route with subsequent BAL, the infecting time is significantly lower than for the other two groups. A lower infecting time indicates that the virus spreads from cell to cell more rapidly for aerosol infection with BAL than for the combined deposition or aerosol deposition alone. This study helps elucidate the mechanism behind different infection outcomes caused by differences in routes of infection.

Virus-mediated cell fusion of SARS-CoV-2 variants.

SARS-CoV-2 has the ability to form large multi-nucleated cells known as syncytia. Little is known about how syncytia affect the dynamics of the infection or severity of the disease. In this manuscript, we extend a mathematical model of cell-cell fusion assays to estimate both the syncytia formation rate and the average duration of the fusion phase for five strains of SARS-CoV-2. We find that the original Wuhan strain has the slowest rate of syncytia formation (6.4×10-4/h), but takes only 4.0 h to complete the fusion process, while the Alpha strain has the fastest rate of syncytia formation (0.36 /h), but takes 7.6 h to complete the fusion process. The Beta strain also has a fairly fast syncytia formation rate (9.7×10-2/h), and takes the longest to complete fusion (8.4 h). The D614G strain has a fairly slow syncytia formation rate (2.8×10-3/h), but completes fusion in 4.0 h. Finally, the Delta strain is in the middle with a syncytia formation rate of 3.2×10-2/h and a fusing time of 6.1 h. We note that for these SARS-CoV-2 strains, there appears to be a tradeoff between the ease of forming syncytia and the speed at which they complete the fusion process.

Mathematical Modeling of Oncolytic Virus Therapy Reveals Role of the Immune Response.

Oncolytic adenoviruses (OAds) present a promising path for cancer treatment due to their selectivity in infecting and lysing tumor cells and their ability to stimulate the immune response. In this study, we use an ordinary differential equation (ODE) model of tumor growth inhibited by oncolytic virus activity to parameterize previous research on the effect of genetically re-engineered OAds in A549 lung cancer tumors in murine models. We find that the data are best fit by a model that accounts for an immune response, and that the immune response provides a mechanism for elimination of the tumor. We also find that parameter estimates for the most effective OAds share characteristics, most notably a high infection rate and low viral clearance rate, that might be potential reasons for these viruses' efficacy in delaying tumor growth. Further studies observing E1A and P19 recombined viruses in different tumor environments may further illuminate the extent of the effects of these genetic modifications.

Modeling of oncolytic viruses in a heterogeneous cell population to predict spread into non-cancerous cells.

New cancer treatment modalities that limit patient discomfort need to be developed. One possible new therapy is the use of oncolytic (cancer-killing) viruses. It is only recently that our ability to manipulate viral genomes has allowed us to consider deliberately infecting cancer patients with viruses. One key consideration is to ensure that the virus exclusively targets cancer cells and does not harm nearby non-cancerous cells. Here, we use a mathematical model of viral infection to determine the characteristics a virus would need to have in order to eradicate a tumor, but leave non-cancerous cells untouched. We conclude that the virus must differ in its ability to infect the two different cell types, with the infection rate of non-cancerous cells needing to be less than one hundredth of the infection rate of cancer cells. Differences in viral production rate or infectious cell death rate alone are not sufficient to protect non-cancerous cells.

Quantifying the effect of defective viral genomes in respiratory syncytial virus infections.

Defective viral genomes (DVGs) are viral genomes that contain only a partial viral RNA and so cannot replicate within cells on their own. If a cell containing DVGs is subsequently infected with a complete viral genome, the DVG can then use the missing proteins expressed by the full genome in order to replicate itself. Since the cell is producing defective genomes, it has less resources to produce fully functional virions and thus release of complete virions is often suppressed. Here, we use data from challenge studies of respiratory syncytial virus (RSV) in healthy adults to quantify the effect of DVGs. We use a mathematical model to fit the data, finding that late onset of DVGs and prolonged DVG detection are associated with lower infection rates and higher clearance rates. This result could have implications for the use of DVGs as a therapeutic.

Epidemiological Consequences of Viral Interference: A Mathematical Modeling Study of Two Interacting Viruses.

Some viruses have the ability to block or suppress growth of other viruses when simultaneously present in the same host. This type of viral interference or viral block has been suggested as a potential interaction between some respiratory viruses including SARS-CoV-2 and other co-circulating respiratory viruses. We explore how one virus' ability to block infection with another within a single host affects spread of the viruses within a susceptible population using a compartmental epidemiological model. We find that population-level effect of viral block is a decrease in the number of people infected with the suppressed virus. This effect is most pronounced when the viruses have similar epidemiological parameters. We use the model to simulate co-circulating epidemics of SARS-CoV-2 and influenza, respiratory syncytial virus (RSV), and rhinovirus, finding that co-circulation of SARS-CoV-2 and RSV causes the most suppression of SARS-CoV-2. Paradoxically, co-circulation of SARS-CoV-2 and influenza or rhinovirus results in almost no change in the SARS-CoV-2 epidemic, but causes a shift in the timing of the influenza and rhinovirus epidemics.

Treatment of Respiratory Viral Coinfections.

With the advent of rapid multiplex PCR, physicians have been able to test for multiple viral pathogens when a patient presents with influenza-like illness. This has led to the discovery that many respiratory infections are caused by more than one virus. Antiviral treatment of viral coinfections can be complex because treatment of one virus will affect the time course of the other virus. Since effective antivirals are only available for some respiratory viruses, careful consideration needs to be given on the effect treating one virus will have on the dynamics of the other virus, which might not have available antiviral treatment. In this study, we use mathematical models of viral coinfections to assess the effect of antiviral treatment on coinfections. We examine the effect of the mechanism of action, relative growth rates of the viruses, and the assumptions underlying the interaction of the viruses. We find that high antiviral efficacy is needed to suppress both infections. If high doses of both antivirals are not achieved, then we run the risk of lengthening the duration of coinfection or even of allowing a suppressed virus to replicate to higher viral titers.

Estimation of virus-mediated cell fusion rate of SARS-CoV-2.

Several viruses have the ability to form large multinucleated cells known as syncytia. Many properties of syncytia and the role they play in the evolution of a viral infection are not well understood. One basic question that has not yet been answered is how quickly syncytia form. We use a novel mathematical model of cell-cell fusion assays and apply it to experimental data from SARS-CoV-2 fusion assays to provide the first estimates of virus-mediated cell fusion rate. We find that for SARS-CoV2, the fusion rate is in the range of 6 × 10-4-12×10-4/h. We also use our model to compare fusion rates when the protease TMPRSS2 is overexpressed (2-4 times larger fusion rate), when the protease furin is removed (one third the original fusion rate), and when the spike protein is altered (1/10th the original fusion rate). The use of mathematical models allows us to provide additional quantitative information about syncytia formation.