Quantifying rotavirus kinetics in the REH tumor cell line using in vitro data

The reproduction number and its probability distribution for stochastic viral dynamics

We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.

Mathematical Modeling of Virus-Mediated Syncytia Formation: Past Successes and Future Directions

Many viruses have the ability to cause cells to fuse into large multi-nucleated cells, known as syncytia. While the existence of syncytia has long been known and its importance in helping spread viral infection within a host has been understood, few mathematical models have incorporated syncytia formation or examined its role in viral dynamics. This review examines mathematical models that have incorporated virus-mediated cell fusion and the insights they have provided on how syncytia can change the time course of an infection. While the modeling efforts are limited, they show promise in helping us understand the consequences of syncytia formation if future modeling efforts can be coupled with appropriate experimental efforts to help validate the models.

Culture of Human Rotaviruses in Relevant Models Shows Differences in Culture-Adapted and Nonculture-Adapted Strains

Rotavirus (RV) is the leading cause of acute gastroenteritis (AGE) in children under 5 years old worldwide, and several studies have demonstrated that histo-blood group antigens (HBGAs) play a role in its infection process. In the present study, human stool filtrates from patients diagnosed with RV diarrhea (genotyped as P[8]) were used to infect differentiated Caco-2 cells (dCaco-2) to determine whether such viral strains of clinical origin had the ability to replicate in cell cultures displaying HBGAs. The cell culture-adapted human RV Wa model strain (P[8] genotype) was used as a control. A time-course analysis of infection was conducted in dCaco-2 at 1, 24, 48, 72, and 96 h. The replication of two selected clinical isolates and Wa was further assayed in MA104, undifferentiated Caco-2 (uCaco-2), HT29, and HT29-M6 cells, as well as in monolayers of differentiated human intestinal enteroids (HIEs). The results showed that the culture-adapted Wa strain replicated more efficiently in MA104 cells than other utilized cell types. In contrast, clinical virus isolates replicated more efficiently in dCaco-2 cells and HIEs. Furthermore, through surface plasmon resonance analysis of the interaction between the RV spike protein (VP8*) and its glycan receptor (the H antigen), the V7 RV clinical isolate showed 45 times better affinity compared to VP8* from the Wa strain. These findings support the hypothesis that the differences in virus tropism between clinical virus isolates and RV Wa could be a consequence of the different HBGA contents on the surface of the cell lines employed. dCaco-2, HT29, and HT29M6 cells and HIEs display HBGAs on their surfaces, whereas MA104 and uCaco-2 cells do not. These results indicate the relevance of using non-cell culture-adapted human RV to investigate the replication of rotavirus in relevant infection models.

The effect of random virus failure following cell entry on infection outcome and the success of antiviral therapy

A virus infection can be initiated with very few or even a single infectious virion, and as such can become extinct, i.e. stochastically fail to take hold or spread significantly. There are many ways that a fully competent infectious virion, having successfully entered a cell, can fail to cause a productive infection, i.e. one that yields infectious virus progeny. Though many stochastic models (SMs) have been developed and used to estimate a virus infection's establishment probability, these typically neglect infection failure post virus entry. The SM presented herein introduces parameter [Formula: see text] which corresponds to the probability that a virion's entry into a cell will result in a productive cell infection. We derive an expression for the likelihood of infection establishment in this new SM, and find that prophylactic therapy with an antiviral reducing [Formula: see text] is at least as good or better at decreasing the establishment probability, compared to antivirals reducing the rates of virus production or virus entry into cells, irrespective of the SM parameters. We investigate the difference in the fraction of cells consumed by so-called extinct versus established virus infections, and find that this distinction becomes biologically meaningless as the probability of establishment approaches zero. We explain why the release of virions continuously over an infectious cell's lifespan, rather than as a single burst at the end of the cell's lifespan, does not result in an increased risk of infection extinction. We show, instead, that the number of virus released, not the timing of the release, affects infection establishment and associated critical antiviral efficacy.

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.

Dynamics of toxoplasmosis in the cat's population with an exposed stage and a time delay

We propose a new mathematical model to investigate the effect of the introduction of an exposed stage for the cats who become infected with the T. gondii parasite, but that are not still able to produce oocysts in the environment. The model considers a time delay in order to represent the duration of the exposed stage. Besides the cat population the model also includes the oocysts related to the T. gondii in the environment. The model includes the cats since they are the only definitive host and the oocysts, since they are relevant to the dynamics of toxoplasmosis. The model considers lifelong immunity for the recovered cats and vaccinated cats. In addition, the model considers that cats can get infected through an effective contact with the oocysts in the environment. We find conditions such that the toxoplasmosis disease becomes extinct. We analyze the consequences of considering the exposed stage and the time delay on the stability of the equilibrium points. We numerically solve the constructed model and corroborated the theoretical results.

A study of the effects of age on the dynamics of RSV in animal models

Respiratory syncytial virus can cause severe illness and even death, particularly in infants. The increased severity of disease in young children is thought to be due to a lack of previous exposure to the virus as well as the limited immune response in infants. While studies have examined the clinical differences in disease between infants and adults, there has been limited examination of how the viral dynamics differ as infants develop. In this study, we apply a mathematical model to data from cotton rats and ferrets of different ages to assess how viral kinetics parameters change as the animals age. We find no clear trend in the viral decay rate, infecting time, and basic reproduction number as the animals age. We discuss possible reasons for the null result including the limited data, lack of detail of the mathematical model, and the limitations of animal models.

Quantifying mechanistic traits of influenza viral dynamics using in vitro data

When analysing in vitro data, growth kinetics of influenza virus strains are often compared by computing their growth rates, which are sometimes used as proxies for fitness. However, analogous to mathematical models for epidemics, the growth rate can be defined as a function of mechanistic traits: the basic reproduction number (the average number of cells each infected cell infects) and the mean generation time (the average length of a replication cycle). Fitting a model to previously published and newly generated data from experiments in human lung cells, we compared estimates of growth rate, reproduction number and generation time for six influenza A strains. Of four strains in previously published data, A/Canada/RV733/2003 (seasonal H1N1) had the lowest basic reproduction number, followed by A/Mexico/INDRE4487/2009 (pandemic H1N1), then A/Indonesia/05/2005 (spill-over H5N1) and A/Anhui/1/2013 (spill-over H7N9). This ordering of strains was preserved for both generation time and growth rate, suggesting a positive biological correlation between these quantities which have not been previously observed. We further investigated these potential correlations using data from reassortant viruses with different internal proteins (from A/England/195/2009 (pandemic H1N1) and A/Turkey/05/2005 (H5N1)), and the same surface proteins (from A/Puerto Rico/8/34 (lab-adapted H1N1)). Similar correlations between traits were observed for these viruses, confirming our initial findings and suggesting that these patterns were related to the degree of human adaptation of internal genes. Also, the model predicted that strains with a smaller basic reproduction number, shorter generation time and slower growth rate underwent more replication cycles by the time of peak viral load, potentially accumulating mutations more quickly. These results illustrate the utility of mathematical models in inferring traits driving observed differences in in vitro growth of influenza strains.

Energy Requirements for Loss of Viral Infectivity

Outside the host, viruses will eventually lose their ability to infect cells due to conformational changes that occur to proteins on the viral capsid. In order to undergo a conformational change, these proteins require energy to activate the chemical reaction that leads to the conformational change. In this study, data from the literature is used to calculate the energy required for viral inactivation for a variety of different viruses by means of the Arrhenius equation. We find that some viruses (rhinovirus, poliovirus, human immunodeficiency virus, Alkhumra hemorrhagic fever virus, and hepatitis A virus) have high inactivation energies, indicative of breaking of a chemical double bond. We also find that several viruses (respiratory syncytial virus, poliovirus, and norovirus) have nonlinear Arrhenius plots, suggesting that there is more than a single pathway for inactivation of these viruses.

Quantification of Ebola virus replication kinetics in vitro

Mathematical modelling has successfully been used to provide quantitative descriptions of many viral infections, but for the Ebola virus, which requires biosafety level 4 facilities for experimentation, modelling can play a crucial role. Ebola virus modelling efforts have primarily focused on in vivo virus kinetics, e.g., in animal models, to aid the development of antivirals and vaccines. But, thus far, these studies have not yielded a detailed specification of the infection cycle, which could provide a foundational description of the virus kinetics and thus a deeper understanding of their clinical manifestation. Here, we obtain a diverse experimental data set of the Ebola virus infection in vitro, and then make use of Bayesian inference methods to fully identify parameters in a mathematical model of the infection. Our results provide insights into the distribution of time an infected cell spends in the eclipse phase (the period between infection and the start of virus production), as well as the rate at which infectious virions lose infectivity. We suggest how these results can be used in future models to describe co-infection with defective interfering particles, which are an emerging alternative therapeutic.

Optimization of the Controls against the Spread of Zika Virus in Populations

In this paper, we study and explore two control strategies to decrease the spread of Zika virus in the human and mosquito populations. The control strategies that we consider in this study are awareness and spraying campaigns. We solve several optimal control problems relying on a mathematical epidemic model of Zika that considers both human and mosquito populations. The first control strategy is broad and includes using information campaigns, encouraging people to use bednetting, wear long-sleeve shirts, or similar protection actions. The second control is more specific and relies on spraying insecticides. The control system relies on a Zika mathematical model with control functions. To develop the optimal control problem, we use Pontryagins’ maximum principle, which is numerically solved as a boundary value problem. For the mathematical model of the Zika epidemic, we use parameter values extracted from real data from an outbreak in Colombia. We study the effect of the costs related to the controls and infected populations. These costs are important in real life since they can change the outcomes and recommendations for health authorities dramatically. Finally, we explore different options regarding which control measures are more cost-efficient for society.

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.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2793-6) contains supplementary material, which is available to authorized users.

Superinfection and cell regeneration can lead to chronic viral coinfections

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Clinical researchers have found that coinfection of the respiratory tract can cause distinct disease outcome, sometimes leading to long-lasting infection, compared to single viral infection.

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The impact of coinfections in human respiratory tract have not yet been evaluated in either theoretical or experimental studies on a large scale.

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A few experiments confirm that different respiratory viruses can infect the same cell (superinfection).

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Superinfection alone cannot cause long-lasting viral coinfections.

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The combined mechanism of superinfection and cell regeneration provides a plausible mechanism for 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.