Assessing Uncertainty in A2 Respiratory Syncytial Virus Viral Dynamics

A target-cell limited model can reproduce influenza infection dynamics in hosts with differing immune responses

We consider a hierarchy of ordinary differential equation models that describe the within-host viral kinetics of influenza infections: the IR model explicitly accounts for an immune response to the virus, while the simpler, target-cell limited TEIV and TV models do not. We show that when the IR model is fitted to pooled experimental murine data of the viral load, fraction of dead cells, and immune response levels, its parameters values can be determined. However, if, as is common, only viral load data are available, we can estimate parameters of the TEIV and TV models but not the IR model. These results are substantiated by a structural and practical identifiability analysis. We then use the IR model to generate synthetic data representing infections in hosts whose immune responses differ. We fit the TV model to these synthetic datasets and show that it can reproduce the characteristic exponential increase and decay of viral load generated by the IR model. Furthermore, the values of the fitted parameters of the TV model can be mapped from the immune response parameters in the IR model. We conclude that, if only viral load data are available, a simple target-cell limited model can reproduce influenza infection dynamics and distinguish between hosts with differing immune responses.

How Interactions During Viral-Viral Coinfection Can Shape Infection Kinetics

Respiratory virus infections are a leading cause of disease worldwide with multiple viruses detected in 20-30% of cases and several viruses simultaneously circulating. Some infections with viral copathogens have been shown to result in reduced pathogenicity while other virus pairings can worsen disease. The mechanisms driving these dichotomous outcomes are likely variable and have only begun to be examined in the laboratory and clinic. To better understand viral-viral coinfections and predict potential mechanisms that result in distinct disease outcomes, we first systematically fit mathematical models to viral load data from ferrets infected with respiratory syncytial virus (RSV) followed by influenza A virus (IAV) after 3 days. The results suggested that IAV reduced the rate of RSV production while RSV reduced the rate of IAV infected cell clearance. We then explored the realm of possible dynamics for scenarios not examined experimentally, including different infection order, coinfection timing, interaction mechanisms, and viral pairings. IAV coinfection with rhinovirus (RV) or SARS-CoV-2 (CoV2) was examined by using human viral load data from single infections together with murine weight loss data from IAV-RV, RV-IAV, and IAV-CoV2 coinfections to guide the interpretation of the model results. Similar to the results with RSV-IAV coinfection, this analysis showed that the increased disease severity observed during murine IAV-RV or IAV-CoV2 coinfection was likely due to slower clearance of IAV infected cells by the other viruses. On the contrary, the improved outcome when IAV followed RV could be replicated when the rate of RV infected cell clearance was reduced by IAV. Simulating viral-viral coinfections in this way provides new insights about how viral-viral interactions can regulate disease severity during coinfection and yields testable hypotheses ripe for experimental evaluation.

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.

Mathematical Modeling to Study Optimal Allocation of Vaccines against COVID-19 Using an Age-Structured Population

Vaccination against the coronavirus disease 2019 (COVID-19) started in early December of 2020 in the USA. The efficacy of the vaccines vary depending on the SARS-CoV-2 variant. Some countries have been able to deploy strong vaccination programs, and large proportions of their populations have been fully vaccinated. In other countries, low proportions of their populations have been vaccinated, due to different factors. For instance, countries such as Afghanistan, Cameroon, Ghana, Haiti and Syria have less than 10% of their populations fully vaccinated at this time. Implementing an optimal vaccination program is a very complex process due to a variety of variables that affect the programs. Besides, science, policy and ethics are all involved in the determination of the main objectives of the vaccination program. We present two nonlinear mathematical models that allow us to gain insight into the optimal vaccination strategy under different situations, taking into account the case fatality rate and age-structure of the population. We study scenarios with different availabilities and efficacies of the vaccines. The results of this study show that for most scenarios, the optimal allocation of vaccines is to first give the doses to people in the 55+ age group. However, in some situations the optimal strategy is to first allocate vaccines to the 15–54 age group. This situation occurs whenever the SARS-CoV-2 transmission rate is relatively high and the people in the 55+ age group have a transmission rate 50% or less that of those in the 15–54 age group. This study and similar ones can provide scientific recommendations for countries where the proportion of vaccinated individuals is relatively small or for future pandemics.

Modeling and Forecasting Cases of RSV Using Artificial Neural Networks

In this paper, we study and present a mathematical modeling approach based on artificial neural networks to forecast the number of cases of respiratory syncytial virus (RSV). The number of RSV-positive cases in most of the countries around the world present a seasonal-type behavior. We constructed and developed several multilayer perceptron (MLP) models that intend to appropriately forecast the number of cases of RSV, based on previous history. We compared our mathematical modeling approach with a classical statistical technique for the time-series, and we concluded that our results are more accurate. The dataset collected during 2005 to 2010 consisting of 312 weeks belongs to Bogotá D.C., Colombia. The adjusted MLP network that we constructed has a fairly high forecast accuracy. Finally, based on these computations, we recommend training the selected MLP model using 70% of the historical data of RSV-positive cases for training and 20% for validation in order to obtain more accurate results. These results are useful and provide scientific information for health authorities of Colombia to design suitable public health policies related to RSV.

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.

Analysis of Delayed Vaccination Regimens: A Mathematical Modeling Approach

The first round of vaccination against coronavirus disease 2019 (COVID-19) began in early December of 2020 in a few countries. There are several vaccines, and each has a different efficacy and mechanism of action. Several countries, for example, the United Kingdom and the USA, have been able to develop consistent vaccination programs where a great percentage of the population has been vaccinated (May 2021). However, in other countries, a low percentage of the population has been vaccinated due to constraints related to vaccine supply and distribution capacity. Countries such as the USA and the UK have implemented different vaccination strategies, and some scholars have been debating the optimal strategy for vaccine campaigns. This problem is complex due to the great number of variables that affect the relevant outcomes. In this article, we study the impact of different vaccination regimens on main health outcomes such as deaths, hospitalizations, and the number of infected. We develop a mathematical model of COVID-19 transmission to focus on this important health policy issue. Thus, we are able to identify the optimal strategy regarding vaccination campaigns. We find that for vaccines with high efficacy (>70%) after the first dose, the optimal strategy is to delay inoculation with the second dose. On the other hand, for a low first dose vaccine efficacy, it is better to use the standard vaccination regimen of 4 weeks between doses. Thus, under the delayed second dose option, a campaign focus on generating a certain immunity in as great a number of people as fast as possible is preferable to having an almost perfect immunity in fewer people first. Therefore, based on these results, we suggest that the UK implemented a better vaccination campaign than that in the USA with regard to time between doses. The results presented here provide scientific guidelines for other countries where vaccination campaigns are just starting, or the percentage of vaccinated people is small.

Analysis of Key Factors of a SARS-CoV-2 Vaccination Program: A Mathematical Modeling Approach

The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the availability of the vaccine. In this article, we study the impact of the pace of vaccination and the intrinsic efficacy of the vaccine on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. Then we study different potential scenarios regarding the burden of the COVID-19 pandemic in the near future. We construct a compartmental mathematical model and use computational methodologies to study these different scenarios. Thus, we are able to identify some key factors to reach the aims of the vaccination programs. We use some metrics related to the outcomes of the COVID-19 pandemic in order to assess the impact of the efficacy of the vaccine and the pace of the vaccine inoculation. We found that both factors have a high impact on the outcomes. However, the rate of vaccine administration has a higher impact in reducing the burden of the COVID-19 pandemic. This result shows that health institutions need to focus on increasing the vaccine inoculation pace and create awareness in the population about the importance of COVID-19 vaccines.

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.

Impact of a New SARS-CoV-2 Variant on the Population: A Mathematical Modeling Approach

Several SARS-CoV-2 variants have emerged around the world, and the appearance of other variants depends on many factors. These new variants might have different characteristics that can affect the transmissibility and death rate. The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020 and in some countries the vaccines will not soon be widely available. For this article, we studied the impact of a new more transmissible SARS-CoV-2 strain on prevalence, hospitalizations, and deaths related to the SARS-CoV-2 virus. We studied different scenarios regarding the transmissibility in order to provide a scientific support for public health policies and bring awareness of potential future situations related to the COVID-19 pandemic. We constructed a compartmental mathematical model based on differential equations to study these different scenarios. In this way, we are able to understand how a new, more infectious strain of the virus can impact the dynamics of the COVID-19 pandemic. We studied several metrics related to the possible outcomes of the COVID-19 pandemic in order to assess the impact of a higher transmissibility of a new SARS-CoV-2 strain on these metrics. We found that, even if the new variant has the same death rate, its high transmissibility can increase the number of infected people, those hospitalized, and deaths. The simulation results show that health institutions need to focus on increasing non-pharmaceutical interventions and the pace of vaccine inoculation since a new variant with higher transmissibility, such as, for example, VOC-202012/01 of lineage B.1.1.7, may cause more devastating outcomes in the population.

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.

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.

Mathematical modelling identifies the role of adaptive immunity as a key controller of respiratory syncytial virus in cotton rats

Respiratory syncytial virus (RSV) is a common virus that can have varying effects ranging from mild cold-like symptoms to mortality depending on the age and immune status of the individual. We combined mathematical modelling using ordinary differential equations (ODEs) with measurement of RSV infection kinetics in primary well-differentiated human bronchial epithelial cultures in vitro and in immunocompetent and immunosuppressed cotton rats to glean mechanistic details that underlie RSV infection kinetics in the lung. Quantitative analysis of viral titre kinetics in our mathematical model showed that the elimination of infected cells by the adaptive immune response generates unique RSV titre kinetic features including a faster timescale of viral titre clearance than viral production, and a monotonic decrease in the peak RSV titre with decreasing inoculum dose. Parameter estimation in the ODE model using a nonlinear mixed effects approach revealed a very low rate (average single-cell lifetime > 10 days) of cell lysis by RSV before the adaptive immune response is initiated. Our model predicted negligible changes in the RSV titre kinetics at early times post-infection (less than 5 dpi) but a slower decay in RSV titre in immunosuppressed cotton rats compared to that in non-suppressed cotton rats at later times (greater than 5 dpi) in silico. These predictions were in excellent agreement with the experimental results. Our combined approach quantified the importance of the adaptive immune response in suppressing RSV infection in cotton rats, which could be useful in testing RSV vaccine candidates.

Targeting Intracellular Ion Homeostasis for the Control of Respiratory Syncytial Virus

Respiratory syncytial virus (RSV) is a leading cause of mortality in infants and young children. Despite the RSV disease burden, no vaccine is available, and treatment remains nonspecific. New drug candidates are needed to combat RSV. Toward this goal, we screened over 2,000 compounds to identify approved drugs with novel anti-RSV activity. Cardiac glycosides, inhibitors of the membrane-bound Na⁺/K⁺-ATPase, were identified to have anti-RSV activity. Cardiac glycosides diminished RSV infection in human epithelial type 2 cells and in primary human airway epithelial cells grown at an air-liquid interface. Digoxin, a U.S. Food and Drug Administration-approved cardiac glycoside, was also able to inhibit infection of primary nasal epithelial cells with community isolates of RSV. Our results suggest that the antiviral effects of cardiac glycosides may be dependent on changes in the intracellular Na⁺ and K⁺ composition. Consistent with this mechanism, we demonstrated that the ionophoric antibiotics salinomycin, valinomycin, and monensin inhibited RSV in human epithelial type 2 cells and primary nasal epithelial cells. Our data indicate that the K⁺/Na⁺-sensitive steps in the RSV life cycle occur within the initial 4 hours of viral infection but do not include virus binding/entry. Rather, our findings demonstrated a negative effect on the RSV transcription and/or replication process. Overall, this work suggests that targeting intracellular ion concentrations offers a novel antiviral strategy.

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.

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.

A quantitative assessment of dynamical differences of RSV infections in vitro and in vivo

Experimental results in vitro and in animal models are used to guide researchers in testing vaccines or treatment in humans. However, viral kinetics are different in vitro, in animals, and in humans, so it is sometimes difficult to translate results from one system to another. In this study, we use a mathematical model to fit experimental data from multiple cycle respiratory syncytial virus (RSV) infections in vitro, in african green monkey (AGM), and in humans in order to quantitatively compare viral kinetics in the different systems. We find that there are differences in viral clearance rate, productively infectious cell lifespan, and eclipse phase duration between in vitro and in vivo systems and among different in vivo systems. We show that these differences in viral kinetics lead to different estimates of drug effectiveness of fusion inhibitors in vitro and in AGM than in humans.

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, ε_max, 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.

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

Globally, rotavirus is the most common cause of diarrhea in children younger than 5 years of age, however, a quantitative understanding of the infection dynamics is still lacking. In this paper, we present the first study to extract viral kinetic parameters for in vitro rotavirus infections in the REH cell tumor line. We use a mathematical model of viral kinetics to extract parameter values by fitting the model to data from rotavirus infection of REH cells. While accurate results for some of the parameters of the mathematical model were not achievable due to its global non-identifiability, we are able to quantify approximately the time course of the infection for the first time. We also find that the basic reproductive number of rotavirus, which gives the number of secondary infections from a single infected cell, is much greater than one. Quantifying the kinetics of rotavirus leads not only to a better understanding of the infection process, but also provides a method for quantitative comparison of kinetics of different strains or for quantifying the effectiveness of antiviral treatment.

Coinfections of the Respiratory Tract: Viral Competition for Resources

Studies have shown that simultaneous infection of the respiratory tract with at least two viruses is common in hospitalized patients, although it is not clear whether these infections are more or less severe than single virus infections. We use a mathematical model to study the dynamics of viral coinfection of the respiratory tract in an effort to understand the kinetics of these infections. Specifically, we use our model to investigate coinfections of influenza, respiratory syncytial virus, rhinovirus, parainfluenza virus, and human metapneumovirus. Our study shows that during coinfections, one virus can block another simply by being the first to infect the available host cells; there is no need for viral interference through immune response interactions. We use the model to calculate the duration of detectable coinfection and examine how it varies as initial viral dose and time of infection are varied. We find that rhinovirus, the fastest-growing virus, reduces replication of the remaining viruses during a coinfection, while parainfluenza virus, the slowest-growing virus is suppressed in the presence of other viruses.