Causes and Consequences of Spatial Within-Host Viral Spread

Local and systemic replicative fitness for viruses in specialist, generalist, and non-specialist interactions with salmonid hosts

Host tissues represent diverse resources or barriers for pathogen replicative fitness. We tested whether viruses in specialist, generalist, and non-specialist interactions replicate differently in local entry tissue (fin), and systemic target tissue (kidney) using infectious hematopoietic necrosis virus (IHNV) and three salmonid fish hosts. Virus tissue replication was host specific, but one feature was shared by specialists and the generalist which was uncommon in the non-specialist interactions: high host entry and replication capacity in the local tissue after contact. Moreover, specialists showed increased replication in systemic target tissues early after host contact. By comparing ancestral and derived IHNV viruses, we also characterized replication tradeoffs associated with specialist and generalist evolution. Compared with the ancestral virus, a derived specialist gained early local replicative fitness in the new host but lost replicative fitness in the ancestral host. By contrast, a derived generalist showed small replication losses relative to the ancestral virus in the ancestral host but increased early replication in the local tissue of novel hosts. This study shows that the mechanisms of specialism and generalism are host specific and that local and systemic replication can contribute differently to overall within host replicative fitness for specialist and generalist viruses.

Choice of spatial discretisation influences the progression of viral infection within multicellular tissues

There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are simulated by discretising the viral surface and depending on the rate of viral diffusion and other considerations, a finer or coarser discretisation may be used. The impact that this choice may have on the behaviour of the system has not been studied. Here we demonstrate that under realistic parameter regimes - where viral diffusion is small enough to support the formation of familiar ring-shaped infection plaques - the choice of spatial discretisation of the viral surface can qualitatively change key model outcomes including the time scale of infection. Importantly, we show that the choice between implementing viral spread as a cell-scale process, or as a high-resolution converged PDE can generate distinct model outcomes, which raises important conceptual questions about the strength of assumptions underpinning the spatial structure of the model. We investigate the mechanisms driving these discretisation artefacts, the impacts they may have on model predictions, and provide guidance on the design and implementation of spatial and especially multicellular models of viral dynamics. We obtain our results using the simplest TIV construct for the viral dynamics, and therefore anticipate that the important effects we describe will also influence model predictions in more complex models of virus-cell-immune system interactions. This analysis will aid in the construction of models for robust and biologically realistic modelling and inference.

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

The COVID-19 pandemic has led to over 760 million cases and 6.9 million deaths worldwide. To mitigate the loss of lives, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with susceptible variants. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response anti-viral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

Making waves: Integrating wastewater surveillance with dynamic modeling to track and predict viral outbreaks

Wastewater surveillance has proved to be a valuable tool to track the COVID-19 pandemic. However, most studies using wastewater surveillance data revolve around establishing correlations and lead time relative to reported case data. In this perspective, we advocate for the integration of wastewater surveillance data with dynamic within-host and between-host models to better understand, monitor, and predict viral disease outbreaks. Dynamic models overcome emblematic difficulties of using wastewater surveillance data such as establishing the temporal viral shedding profile. Complementarily, wastewater surveillance data bypasses the issues of time lag and underreporting in clinical case report data, thus enhancing the utility and applicability of dynamic models. The integration of wastewater surveillance data with dynamic models can enhance real-time tracking and prevalence estimation, forecast viral transmission and intervention effectiveness, and most importantly, provide a mechanistic understanding of infectious disease dynamics and the driving factors. Dynamic modeling of wastewater surveillance data will advance the development of a predictive and responsive monitoring system to improve pandemic preparedness and population health.

Viral kinetics, stability and sensitivity analysis of the within-host COVID-19 model

This paper delves into the investigation of the COVID-19 dynamics within a host using the Target-Latent-Infected-Virus (TLIV) model, presenting a fresh approach compared to previous studies. Our model introduces a latent class and explores sensitivity analysis, aspects that have received limited attention in prior research. A significant contribution of this study is the analysis of both local and global stability of equilibrium states, subject to specific sufficient conditions based on the basic reproduction number [Formula: see text]. By examining these stability properties, we aim to gain insights into the factors underlying variations observed in the findings of different studies. Additionally, we identify the death rate of infected cells as the parameter most susceptible to influence in our model. To minimize its impact and facilitate recovery, it is crucial to implement appropriate medical therapies and consume immune-boosting foods. Some computer simulations are carried out to strengthen the theoretical results.

Semi-infectious particles contribute substantially to influenza virus within-host dynamics when infection is dominated by spatial structure

Influenza is an ribonucleic acid virus with a genome that comprises eight segments. Experiments show that the vast majority of virions fail to express one or more gene segments and thus cannot cause a productive infection on their own. These particles, called semi-infectious particles (SIPs), can induce virion production through complementation when multiple SIPs are present in an infected cell. Previous within-host influenza models did not explicitly consider SIPs and largely ignore the potential effects of coinfection during virus infection. Here, we constructed and analyzed two distinct models explicitly keeping track of SIPs and coinfection: one without spatial structure and the other implicitly considering spatial structure. While the model without spatial structure fails to reproduce key aspects of within-host influenza virus dynamics, we found that the model implicitly considering the spatial structure of the infection process makes predictions that are consistent with biological observations, highlighting the crucial role that spatial structure plays during an influenza infection. This model predicts two phases of viral growth prior to the viral peak: a first phase driven by fully infectious particles at the initiation of infection followed by a second phase largely driven by coinfections of fully infectious particles and SIPs. Fitting this model to two sets of data, we show that SIPs can contribute substantially to viral load during infection. Overall, the model provides a new interpretation of the in vivo exponential viral growth observed in experiments and a mechanistic explanation for why the production of large numbers of SIPs does not strongly impede viral growth. Being simple and predictive, our model framework serves as a useful tool to understand coinfection dynamics in spatially structured acute viral infections.

Superinfection exclusion creates spatially distinct influenza virus populations

Interactions between viruses during coinfections can influence viral fitness and population diversity, as seen in the generation of reassortant pandemic influenza A virus (IAV) strains. However, opportunities for interactions between closely related viruses are limited by a process known as superinfection exclusion (SIE), which blocks coinfection shortly after primary infection. Using IAVs, we asked whether SIE, an effect which occurs at the level of individual cells, could limit interactions between populations of viruses as they spread across multiple cells within a host. To address this, we first measured the kinetics of SIE in individual cells by infecting them sequentially with 2 isogenic IAVs, each encoding a different fluorophore. By varying the interval between addition of the 2 IAVs, we showed that early in infection SIE does not prevent coinfection, but that after this initial lag phase the potential for coinfection decreases exponentially. We then asked how the kinetics of SIE onset controlled coinfections as IAVs spread asynchronously across monolayers of cells. We observed that viruses at individual coinfected foci continued to coinfect cells as they spread, because all new infections were of cells that had not yet established SIE. In contrast, viruses spreading towards each other from separately infected foci could only establish minimal regions of coinfection before reaching cells where coinfection was blocked. This created a pattern of separate foci of infection, which was recapitulated in the lungs of infected mice, and which is likely to be applicable to many other viruses that induce SIE. We conclude that the kinetics of SIE onset segregate spreading viral infections into discrete regions, within which interactions between virus populations can occur freely, and between which they are blocked.

Rapid transmission and tight bottlenecks constrain the evolution of highly transmissible SARS-CoV-2 variants

Transmission bottlenecks limit the spread of novel mutations and reduce the efficiency of selection along a transmission chain. While increased force of infection, receptor binding, or immune evasion may influence bottleneck size, the relationship between transmissibility and the transmission bottleneck is unclear. Here we compare the transmission bottleneck of non-VOC SARS-CoV-2 lineages to those of Alpha, Delta, and Omicron. We sequenced viruses from 168 individuals in 65 households. Most virus populations had 0-1 single nucleotide variants (iSNV). From 64 transmission pairs with detectable iSNV, we identify a per clade bottleneck of 1 (95% CI 1-1) for Alpha, Delta, and Omicron and 2 (95% CI 2-2) for non-VOC. These tight bottlenecks reflect the low diversity at the time of transmission, which may be more pronounced in rapidly transmissible variants. Tight bottlenecks will limit the development of highly mutated VOC in transmission chains, adding to the evidence that selection over prolonged infections may drive their evolution.

Human 3D Airway Tissue Models for Real-Time Microscopy: Visualizing Respiratory Virus Spreading

Our knowledge about respiratory virus spreading is mostly based on monolayer cultures that hardly reflect the complex organization of the airway epithelium. Thus, there is a strong demand for biologically relevant models. One possibility to study virus spreading at the cellular level is real-time imaging. In an attempt to visualize virus spreading under somewhat more physiological conditions, Calu-3 cells and human primary fibroblasts were co-cultured submerged or as air-liquid interface (ALI). An influenza A virus (IAV) replicating well in cell culture, and carrying a red fluorescent protein (RFP) reporter gene was used for real-time imaging. Our three-dimensional (3D) models exhibited important characteristics of native airway epithelium including a basement membrane, tight junctions and, in ALI models, strong mucus production. In submerged models, first fluorescence signals appeared between 9 and 12 h post infection (hpi) with a low multiplicity of infection of 0.01. Virus spreading further proceeded in the immediate vicinity of infected cells. In ALI models, RFP was found at 22 hpi and later. Consequently, the progression of infection was delayed, in contrast to the submerged model. With these features, we believe that our 3D airway models can deliver new insights in the spreading of IAV and other respiratory viruses.

Influenza A virus reassortment in mammals gives rise to genetically distinct within-host subpopulations

Influenza A virus (IAV) genetic exchange through reassortment has the potential to accelerate viral evolution and has played a critical role in the generation of multiple pandemic strains. For reassortment to occur, distinct viruses must co-infect the same cell. The spatio-temporal dynamics of viral dissemination within an infected host therefore define opportunity for reassortment. Here, we used wild type and synonymously barcoded variant viruses of a pandemic H1N1 strain to examine the within-host viral dynamics that govern reassortment in guinea pigs, ferrets and swine. The first two species are well-established models of human influenza, while swine are a natural host and a frequent conduit for cross-species transmission and reassortment. Our results show reassortment to be pervasive in all three hosts but less frequent in swine than in ferrets and guinea pigs. In ferrets, tissue-specific differences in the opportunity for reassortment are also evident, with more reassortants detected in the nasal tract than the lower respiratory tract. While temporal trends in viral diversity are limited, spatial patterns are clear, with heterogeneity in the viral genotypes detected at distinct anatomical sites revealing extensive compartmentalization of reassortment and replication. Our data indicate that the dynamics of viral replication in mammals allow diversification through reassortment but that the spatial compartmentalization of variants likely shapes their evolution and onward transmission.

Rapid transmission and tight bottlenecks constrain the evolution of highly transmissible SARS-CoV-2 variants

Transmission bottlenecks limit the spread of novel mutations and reduce the efficiency of natural selection along a transmission chain. Many viruses exhibit tight bottlenecks, and studies of early SARS-CoV-2 lineages identified a bottleneck of 1-3 infectious virions. While increased force of infection, host receptor binding, or immune evasion may influence bottleneck size, the relationship between transmissibility and the transmission bottleneck is unclear. Here, we compare the transmission bottleneck of non-variant-of-concern (non-VOC) SARS-CoV-2 lineages to those of the Alpha, Delta, and Omicron variants. We sequenced viruses from 168 individuals in 65 multiply infected households in duplicate to high depth of coverage. In 110 specimens collected close to the time of transmission, within-host diversity was extremely low. At a 2% frequency threshold, 51% had no intrahost single nucleotide variants (iSNV), and 42% had 1-2 iSNV. In 64 possible transmission pairs with detectable iSNV, we identified a bottleneck of 1 infectious virion (95% CI 1-1) for Alpha, Delta, and Omicron lineages and 2 (95% CI 2-2) in non-VOC lineages. The latter was driven by a single iSNV shared in one non-VOC household. The tight transmission bottleneck in SARS-CoV-2 is due to low genetic diversity at the time of transmission, a relationship that may be more pronounced in rapidly transmissible variants. The tight bottlenecks identified here will limit the development of highly mutated VOC in typical transmission chains, adding to the evidence that selection over prolonged infections in immunocompromised patients may drive their evolution.

Heterogeneity in viral populations increases the rate of deleterious mutation accumulation

RNA viruses have high mutation rates, with the majority of mutations being deleterious. We examine patterns of deleterious mutation accumulation over multiple rounds of viral replication, with a focus on how cellular coinfection and heterogeneity in viral output affect these patterns. Specifically, using agent-based intercellular simulations we find, in agreement with previous studies, that coinfection of cells by viruses relaxes the strength of purifying selection, and thereby increases the rate of deleterious mutation accumulation. We further find that cellular heterogeneity in viral output exacerbates the rate of deleterious mutation accumulation, regardless of whether this heterogeneity in viral output is stochastic or is due to variation in cellular multiplicity of infection. These results highlight the need to consider the unique life histories of viruses and their population structure to better understand observed patterns of viral evolution.

Mathematical Modeling Suggests Cooperation of Plant-Infecting Viruses

Viruses are major pathogens of agricultural crops. Viral infections often start after the virus enters the outer layer of a tissue, and many successful viruses, after local replication in the infected tissue, are able to spread systemically. Quantitative details of virus dynamics in plants, however, are poorly understood, in part, because of the lack of experimental methods which allow the accurate measurement of the degree of infection in individual plant tissues. Recently, a group of researchers followed the kinetics of infection of individual cells in leaves of Nicotiana tabacum plants using Tobacco etch virus (TEV) expressing either Venus or blue fluorescent protein (BFP). Assuming that viral spread occurs from lower to upper leaves, the authors fitted a simple mathematical model to the frequency of cellular infection by the two viral variants found using flow cytometry. While the original model could accurately describe the kinetics of viral spread locally and systemically, we found that many alternative versions of the model, for example, if viral spread starts at upper leaves and progresses to lower leaves or when virus dissemination is stopped due to an immune response, fit the data with reasonable quality, and yet with different parameter estimates. These results strongly suggest that experimental measurements of the virus infection in individual leaves may not be sufficient to identify the pathways of viral dissemination between different leaves and reasons for viral control. We propose experiments that may allow discrimination between the alternatives. By analyzing the kinetics of coinfection of individual cells by Venus and BFP strains of TEV we found a strong deviation from the random infection model, suggesting cooperation between the two strains when infecting plant cells. Importantly, we showed that many mathematical models on the kinetics of coinfection of cells with two strains could not adequately describe the data, and the best fit model needed to assume (i) different susceptibility of uninfected cells to infection by two viruses locally in the leaf vs. systemically from other leaves, and (ii) decrease in the infection rate depending on the fraction of uninfected cells which could be due to a systemic immune response. Our results thus demonstrate the difficulty in reaching definite conclusions from extensive and yet limited experimental data and provide evidence of potential cooperation between different viral variants infecting individual cells in plants.

The evolution of cheating in viruses

The success of many viruses depends upon cooperative interactions between viral genomes. However, whenever cooperation occurs, there is the potential for 'cheats' to exploit that cooperation. We suggest that: (1) the biology of viruses makes viral cooperation particularly susceptible to cheating; (2) cheats are common across a wide range of viruses, including viral entities that are already well studied, such as defective interfering genomes, and satellite viruses. Consequently, the evolutionary theory of cheating could help us understand and manipulate viral dynamics, while viruses also offer new opportunities to study the evolution of cheating.

Generation of multicellular spatiotemporal models of population dynamics from ordinary differential equations, with applications in viral infection

BACKGROUND

The biophysics of an organism span multiple scales from subcellular to organismal and include processes characterized by spatial properties, such as the diffusion of molecules, cell migration, and flow of intravenous fluids. Mathematical biology seeks to explain biophysical processes in mathematical terms at, and across, all relevant spatial and temporal scales, through the generation of representative models. While non-spatial, ordinary differential equation (ODE) models are often used and readily calibrated to experimental data, they do not explicitly represent the spatial and stochastic features of a biological system, limiting their insights and applications. However, spatial models describing biological systems with spatial information are mathematically complex and computationally expensive, which limits the ability to calibrate and deploy them and highlights the need for simpler methods able to model the spatial features of biological systems.

RESULTS

In this work, we develop a formal method for deriving cell-based, spatial, multicellular models from ODE models of population dynamics in biological systems, and vice versa. We provide examples of generating spatiotemporal, multicellular models from ODE models of viral infection and immune response. In these models, the determinants of agreement of spatial and non-spatial models are the degree of spatial heterogeneity in viral production and rates of extracellular viral diffusion and decay. We show how ODE model parameters can implicitly represent spatial parameters, and cell-based spatial models can generate uncertain predictions through sensitivity to stochastic cellular events, which is not a feature of ODE models. Using our method, we can test ODE models in a multicellular, spatial context and translate information to and from non-spatial and spatial models, which help to employ spatiotemporal multicellular models using calibrated ODE model parameters. We additionally investigate objects and processes implicitly represented by ODE model terms and parameters and improve the reproducibility of spatial, stochastic models.

CONCLUSION

We developed and demonstrate a method for generating spatiotemporal, multicellular models from non-spatial population dynamics models of multicellular systems. We envision employing our method to generate new ODE model terms from spatiotemporal and multicellular models, recast popular ODE models on a cellular basis, and generate better models for critical applications where spatial and stochastic features affect outcomes.

Rab11a mediates cell-cell spread and reassortment of influenza A virus genomes via tunneling nanotubes

Influenza A virus [IAV] genomes comprise eight negative strand RNAs packaged into virions in the form of viral ribonucleoproteins [vRNPs]. Rab11a plays a crucial role in the transport of vRNPs from the nucleus to the plasma membrane via microtubules, allowing assembly and virus production. Here, we identify a novel function for Rab11a in the inter-cellular transport of IAV vRNPs using tunneling nanotubes [TNTs]as molecular highways. TNTs are F-Actin rich tubules that link the cytoplasm of nearby cells. In IAV-infected cells, Rab11a was visualized together with vRNPs in these actin-rich intercellular connections. To better examine viral spread via TNTs, we devised an infection system in which conventional, virion-mediated, spread was not possible. Namely, we generated HA-deficient reporter viruses which are unable to produce progeny virions but whose genomes can be replicated and trafficked. In this system, vRNP transfer to neighboring cells was observed and this transfer was found to be dependent on both actin and Rab11a. Generation of infectious virus via TNT transfer was confirmed using donor cells infected with HA-deficient virus and recipient cells stably expressing HA protein. Mixing donor cells infected with genetically distinct IAVs furthermore revealed the potential for Rab11a and TNTs to serve as a conduit for genome mixing and reassortment in IAV infections. These data therefore reveal a novel role for Rab11a in the IAV life cycle, which could have significant implications for within-host spread, genome reassortment and immune evasion.

Dynamically linking influenza virus infection kinetics, lung injury, inflammation, and disease severity

Influenza viruses cause a significant amount of morbidity and mortality. Understanding host immune control efficacy and how different factors influence lung injury and disease severity are critical. We established and validated dynamical connections between viral loads, infected cells, CD8⁺ T cells, lung injury, inflammation, and disease severity using an integrative mathematical model-experiment exchange. Our results showed that the dynamics of inflammation and virus-inflicted lung injury are distinct and nonlinearly related to disease severity, and that these two pathologic measurements can be independently predicted using the model-derived infected cell dynamics. Our findings further indicated that the relative CD8⁺ T cell dynamics paralleled the percent of the lung that had resolved with the rate of CD8⁺ T cell-mediated clearance rapidly accelerating by over 48,000 times in 2 days. This complimented our analyses showing a negative correlation between the efficacy of innate and adaptive immune-mediated infected cell clearance, and that infection duration was driven by CD8⁺ T cell magnitude rather than efficacy and could be significantly prolonged if the ratio of CD8⁺ T cells to infected cells was sufficiently low. These links between important pathogen kinetics and host pathology enhance our ability to forecast disease progression, potential complications, and therapeutic efficacy.

The Social Life of Viruses

Despite their simplicity, viruses exhibit certain types of social interactions. Situations in which a given virus achieves higher fitness in combination with other members of the viral population have been described at the level of transmission, replication, suppression of host immune responses, and host killing, enabling the evolution of viral cooperation. Although cellular coinfection with multiple viral particles is the typical playground for these interactions, cooperation between viruses infecting different cells is also established through cellular and viral-encoded communication systems. In general, the stability of cooperation is compromised by cheater genotypes, as best exemplified by defective interfering particles. As predicted by social evolution theory, cheater invasion can be avoided when cooperators interact preferentially with other cooperators, a situation that is promoted in spatially structured populations. Processes such as transmission bottlenecks, organ compartmentalization, localized spread of infection foci, superinfection exclusion, and even discrete intracellular replication centers promote multilevel spatial structuring in viruses. Expected final online publication date for the Annual Review of Virology, Volume 8 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Fitness Estimation for Viral Variants in the Context of Cellular Coinfection

Animal models are frequently used to characterize the within-host dynamics of emerging zoonotic viruses. More recent studies have also deep-sequenced longitudinal viral samples originating from experimental challenges to gain a better understanding of how these viruses may evolve in vivo and between transmission events. These studies have often identified nucleotide variants that can replicate more efficiently within hosts and also transmit more effectively between hosts. Quantifying the degree to which a mutation impacts viral fitness within a host can improve identification of variants that are of particular epidemiological concern and our ability to anticipate viral adaptation at the population level. While methods have been developed to quantify the fitness effects of mutations using observed changes in allele frequencies over the course of a host’s infection, none of the existing methods account for the possibility of cellular coinfection. Here, we develop mathematical models to project variant allele frequency changes in the context of cellular coinfection and, further, integrate these models with statistical inference approaches to demonstrate how variant fitness can be estimated alongside cellular multiplicity of infection. We apply our approaches to empirical longitudinally sampled H5N1 sequence data from ferrets. Our results indicate that previous studies may have significantly underestimated the within-host fitness advantage of viral variants. These findings underscore the importance of considering the process of cellular coinfection when studying within-host viral evolutionary dynamics.

Homogenization of a reaction diffusion equation can explain influenza A virus load data

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L^-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. We present new data on the virus load infection of Ube1L^-/-, which have been micro-printed in a checker board pattern of different sizes of the inner squares. Surprisingly, the total viral load at one day after inoculation significantly depends on the sizes of the inner squares. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities. If the individual patches are large, then the growth rate and the carrying capacity will be the arithmetic means of the patches. For finer and finer patches the average growth rate is still the arithmetic mean, however, the carrying capacity uses the harmonic mean. While fitting the PDE to the experimental data, we also predict that a discrepancy in virus load would be unobservable after only half a day. Furthermore, we predict the viral load in different inner squares that had not been measured in our experiment and the travelling distance the virions can reach after one day.

Mechanistic Modeling of SARS-CoV-2 and Other Infectious Diseases and the Effects of Therapeutics

Modern viral kinetic modeling and its application to therapeutics is a field that attracted the attention of the medical, pharmaceutical, and modeling communities during the early days of the AIDS epidemic. Its successes led to applications of modeling methods not only to HIV but a plethora of other viruses, such as hepatitis C virus (HCV), hepatitis B virus and cytomegalovirus, which along with HIV cause chronic diseases, and viruses such as influenza, respiratory syncytial virus, West Nile virus, Zika virus, and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which generally cause acute infections. Here we first review the historical development of mathematical models to understand HIV and HCV infections and the effects of treatment by fitting the models to clinical data. We then focus on recent efforts and contributions of applying these models towards understanding SARS-CoV-2 infection and highlight outstanding questions where modeling can provide crucial insights and help to optimize nonpharmaceutical and pharmaceutical interventions of the coronavirus disease 2019 (COVID-19) pandemic. The review is written from our personal perspective emphasizing the power of simple target cell limited models that provided important insights and then their evolution into more complex models that captured more of the virology and immunology. To quote Albert Einstein, "Everything should be made as simple as possible, but not simpler," and this idea underlies the modeling we describe below.

Autocrine and paracrine interferon signalling as 'ring vaccination' and 'contact tracing' strategies to suppress virus infection in a host

The innate immune response, particularly the interferon response, represents a first line of defence against viral infections. The interferon molecules produced from infected cells act through autocrine and paracrine signalling to turn host cells into an antiviral state. Although the molecular mechanisms of IFN signalling have been well characterized, how the interferon response collectively contribute to the regulation of host cells to stop or suppress viral infection during early infection remain unclear. Here, we use mathematical models to delineate the roles of the autocrine and the paracrine signalling, and show that their impacts on viral spread are dependent on how infection proceeds. In particular, we found that when infection is well-mixed, the paracrine signalling is not as effective; by contrast, when infection spreads in a spatial manner, a likely scenario during initial infection in tissue, the paracrine signalling can impede the spread of infection by decreasing the number of susceptible cells close to the site of infection. Furthermore, we argue that the interferon response can be seen as a parallel to population-level epidemic prevention strategies such as ‘contact tracing’ or ‘ring vaccination’. Thus, our results here may have implications for the outbreak control at the population scale more broadly.

Cross-scale dynamics and the evolutionary emergence of infectious diseases

When emerging pathogens encounter new host species for which they are poorly adapted, they must evolve to escape extinction. Pathogens experience selection on traits at multiple scales, including replication rates within host individuals and transmissibility between hosts. We analyze a stochastic model linking pathogen growth and competition within individuals to transmission between individuals. Our analysis reveals a new factor, the cross-scale reproductive number of a mutant virion, that quantifies how quickly mutant strains increase in frequency when they initially appear in the infected host population. This cross-scale reproductive number combines with viral mutation rates, single-strain reproductive numbers, and transmission bottleneck width to determine the likelihood of evolutionary emergence, and whether evolution occurs swiftly or gradually within chains of transmission. We find that wider transmission bottlenecks facilitate emergence of pathogens with short-term infections, but hinder emergence of pathogens exhibiting cross-scale selective conflict and long-term infections. Our results provide a framework to advance the integration of laboratory, clinical, and field data in the context of evolutionary theory, laying the foundation for a new generation of evidence-based risk assessment of emergence threats.

Cellular co-infection can modulate the efficiency of influenza A virus production and shape the interferon response

During viral infection, the numbers of virions infecting individual cells can vary significantly over time and space. The functional consequences of this variation in cellular multiplicity of infection (MOI) remain poorly understood. Here, we rigorously quantify the phenotypic consequences of cellular MOI during influenza A virus (IAV) infection over a single round of replication in terms of cell death rates, viral output kinetics, interferon and antiviral effector gene transcription, and superinfection potential. By statistically fitting mathematical models to our data, we precisely define specific functional forms that quantitatively describe the modulation of these phenotypes by MOI at the single cell level. To determine the generality of these functional forms, we compare two distinct cell lines (MDCK cells and A549 cells), both infected with the H1N1 strain A/Puerto Rico/8/1934 (PR8). We find that a model assuming that infected cell death rates are independent of cellular MOI best fits the experimental data in both cell lines. We further observe that a model in which the rate and efficiency of virus production increase with cellular co-infection best fits our observations in MDCK cells, but not in A549 cells. In A549 cells, we also find that induction of type III interferon, but not type I interferon, is highly dependent on cellular MOI, especially at early timepoints. This finding identifies a role for cellular co-infection in shaping the innate immune response to IAV infection. Finally, we show that higher cellular MOI is associated with more potent superinfection exclusion, thus limiting the total number of virions capable of infecting a cell. Overall, this study suggests that the extent of cellular co-infection by influenza viruses may be a critical determinant of both viral production kinetics and cellular infection outcomes in a host cell type-dependent manner.

During influenza A virus (IAV) infection, the number of virions to enter individual cells can be highly variable. Cellular co-infection appears to be common and plays an essential role in facilitating reassortment for IAV, yet little is known about how cellular co-infection influences infection outcomes at the cellular level. Here, we combine quantitative in vitro infection experiments with statistical model fitting to precisely define the phenotypic consequences of cellular co-infection in two cell lines. We reveal that cellular co-infection can increase and accelerate the efficiency of IAV production in a cell line-dependent fashion, identifying it as a potential determinant of viral replication kinetics. We also show that induction of type III, but not type I, interferon is highly dependent upon the number of virions that infect a given cell, implicating cellular co-infection as an important determinant of the host innate immune response to infection. Altogether, our findings show that cellular co-infection plays a crucial role in determining infection outcome. The integration of experimental and statistical modeling approaches detailed here represents a significant advance in the quantitative study of influenza virus infection and should aid ongoing efforts focused on the construction of mathematical models of IAV infection.

Cell-to-Cell Spread of Dengue Viral RNA in Mosquito Cells

Dengue virus (DENV) is an important mosquito-borne arbovirus that is particularly prevalent in tropical and subtropical areas of the world. The virus is generally ingested with a blood meal, replicates in host tissues, and disseminates into salivary glands for transmission to the next host. Membrane-bound vacuoles carrying DENV particles have been documented in mosquito cells and play a role in the cell-to-cell transmission of DENV2. C189 is one member of the tetraspanin family and generally increases its expression as one component of the vacuoles (C189-VCs) within C6/36 cells infected with DENV2. In the present study, we have further demonstrated via sucrose gradient centrifugation as well as magnetic immune isolation (MI) that the RNA of DENV2 was eventually carried by C189-VCs. In addition, viral RNA was shown to spread from donor to recipient cells in a coculture assay even when 20 mM NH₄Cl was added to inhibit virus replication in the culture. In an alternate assay using the transwell system, viral RNA was only detected in recipient cells in the absence of 40 mM NH₄Cl, suggesting that cell-cell contact is required for the intercellular spread of DENV2. In turn, the formation of viral synapse (VS) derived from aggregates of viral particles was frequently observed at sites of cell contact. Taken together, the formation of C189-VCs in C6/36 cells is induced by DENV2 infection, which may serve as a vehicle for transferring virions and also viral RNA to neighboring cells by cell-to-cell transmission after cell-cell contact. This finding provides insight into the understanding of viral spread between mosquito cells. It may also elucidate the benign persistent infection in mosquito cells and efficient dissemination of DENV infection within a mosquito vector.

Stochastic dynamics of Francisella tularensis infection and replication

We study the pathogenesis of Francisella tularensis infection with an experimental mouse model, agent-based computation and mathematical analysis. Following inhalational exposure to Francisella tularensis SCHU S4, a small initial number of bacteria enter lung host cells and proliferate inside them, eventually destroying the host cell and releasing numerous copies that infect other cells. Our analysis of disease progression is based on a stochastic model of a population of infectious agents inside one host cell, extending the birth-and-death process by the occurrence of catastrophes: cell rupture events that affect all bacteria in a cell simultaneously. Closed expressions are obtained for the survival function of an infected cell, the number of bacteria released as a function of time after infection, and the total bacterial load. We compare our mathematical analysis with the results of agent-based computation and, making use of approximate Bayesian statistical inference, with experimental measurements carried out after murine aerosol infection with the virulent SCHU S4 strain of the bacterium Francisella tularensis, that infects alveolar macrophages. The posterior distribution of the rate of replication of intracellular bacteria is consistent with the estimate that the time between rounds of bacterial division is less than 6 hours in vivo.

Infecting a host cell is required for the replication of many types of bacteria and viruses. In some cases, infected cells release new infectious agents continuously over their lifetime. In others, such as the Francisella tularensis bacterium studied here, they are released in a single burst that coincides with the cell’s death. We show how a stochastic model, the birth-and-death process with catastrophe, can be used to characterise infection in a single cell, thereby allowing us to account for burst events and quantify the kinetics of pathogenesis in the lung, the initial site of infection, as well as in other organs that the infection spreads to. We learn about the parameters of the mathematical model of Francisella tularensis infection making use of the experimental measurements of bacterial loads, together with approximate Bayesian statistical inference methods. The most important parameter describing the pathogenesis is the rate of replication of intracellular bacteria.

A mathematical model describing the localization and spread of influenza A virus infection within the human respiratory tract

Within the human respiratory tract (HRT), virus diffuses through the periciliary fluid (PCF) bathing the epithelium. But virus also undergoes advection: as the mucus layer sitting atop the PCF is pushed along by the ciliated cell's beating cilia, the PCF and its virus content are also pushed along, upwards towards the nose and mouth. While many mathematical models (MMs) have described the course of influenza A virus (IAV) infections in vivo, none have considered the impact of both diffusion and advection on the kinetics and localization of the infection. The MM herein represents the HRT as a one-dimensional track extending from the nose down towards the lower HRT, wherein stationary cells interact with IAV which moves within (diffusion) and along with (advection) the PCF. Diffusion was found to be negligible in the presence of advection which effectively sweeps away IAV, preventing infection from disseminating below the depth at which virus first deposits. Higher virus production rates (10-fold) are required at higher advection speeds (40 μm/s) to maintain equivalent infection severity and timing. Because virus is entrained upwards, upper parts of the HRT see more virus than lower parts. As such, infection peaks and resolves faster in the upper than in the lower HRT, making it appear as though infection progresses from the upper towards the lower HRT, as reported in mice. When the spatial MM is expanded to include cellular regeneration and an immune response, it reproduces tissue damage levels reported in patients. It also captures the kinetics of seasonal and avian IAV infections, via parameter changes consistent with reported differences between these strains, enabling comparison of their treatment with antivirals. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viral infections within the HRT.

The impact of long-range dispersal on gene surfing

Range expansions lead to distinctive patterns of genetic variation in populations, even in the absence of selection. These patterns and their genetic consequences have been well studied for populations advancing through successive short-ranged migration events. However, most populations harbor some degree of long-range dispersal, experiencing rare yet consequential migration events over arbitrarily long distances. Although dispersal is known to strongly affect spatial genetic structure during range expansions, the resulting patterns and their impact on neutral diversity remain poorly understood. Here, we systematically study the consequences of long-range dispersal on patterns of neutral variation during range expansion in a class of dispersal models which spans the extremes of local (effectively short-ranged) and global (effectively well-mixed) migration. We find that sufficiently long-ranged dispersal leaves behind a mosaic of monoallelic patches, whose number and size are highly sensitive to the distribution of dispersal distances. We develop a coarse-grained model which connects statistical features of these spatial patterns to the evolution of neutral diversity during the range expansion. We show that growth mechanisms that appear qualitatively similar can engender vastly different outcomes for diversity: Depending on the tail of the dispersal distance distribution, diversity can be either preserved (i.e., many variants survive) or lost (i.e., one variant dominates) at long times. Our results highlight the impact of spatial and migratory structure on genetic variation during processes as varied as range expansions, species invasions, epidemics, and the spread of beneficial mutations in established populations.

A Turkey-origin H9N2 Avian Influenza Virus Shows Low Pathogenicity but Different Within-Host Diversity in Experimentally Infected Turkeys, Quail and Ducks

Avian influenza virus (AIV) is a highly diverse and widespread poultry pathogen. Its evolution and adaptation may be affected by multiple host and ecological factors, which are still poorly understood. In the present study, a turkey-origin H9N2 AIV was used as a model to investigate the within-host diversity of the virus in turkeys, quail and ducks in conjunction with the clinical course, shedding and seroconversion. Ten birds were inoculated oculonasally with a dose of 10⁶ EID₅₀ of the virus and monitored for 14 days. Virus shedding, transmission and seroconversion were evaluated, and swabs collected at selected time-points were characterized in deep sequencing to assess virus diversity. In general, the virus showed low pathogenicity for the examined bird species, but differences in shedding patterns, seroconversion and clinical outcome were noted. The highest heterogeneity of the virus population as measured by the number of single nucleotide polymorphisms and Shannon entropy was found in oropharyngeal swabs from quail, followed by turkeys and ducks. This suggests a strong bottleneck was imposed on the virus during replication in ducks, which can be explained by its poor adaptation and stronger selection pressure in waterfowl. The high within-host virus diversity in quail with high level of respiratory shedding and asymptomatic course of infection may contribute to our understanding of the role of quail as an intermediate host for adaptation of AIV to other species of poultry. In contrast, low virus complexity was observed in cloacal swabs, mainly from turkeys, showing that the within-host diversity may vary between different replication sites. Consequences of these observations on the virus evolution and adaptation require further investigation.

A Parameter Estimation Method for Multiscale Models of Hepatitis C Virus Dynamics

Mathematical models that are based on differential equations require detailed knowledge about the parameters that are included in the equations. Some of the parameters can be measured experimentally while others need to be estimated. When the models become more sophisticated, such as in the case of multiscale models of hepatitis C virus dynamics that deal with partial differential equations (PDEs), several strategies can be tried. It is possible to use parameter estimation on an analytical approximation of the solution to the multiscale model equations, namely the long-term approximation, but this limits the scope of the parameter estimation method used and a long-term approximation needs to be derived for each model. It is possible to transform the PDE multiscale model to a system of ODEs, but this has an effect on the model parameters themselves and the transformation can become problematic for some models. Finally, it is possible to use numerical solutions for the multiscale model and then use canned methods for the parameter estimation, but the latter is making the user dependent on a black box without having full control over the method. The strategy developed here is to start by working directly on the multiscale model equations for preparing them toward the parameter estimation method that is fully coded and controlled by the user. It can also be adapted to multiscale models of other viruses. The new method is described, and illustrations are provided using a user-friendly simulator that incorporates the method.

Incomplete influenza A virus genomes occur frequently but are readily complemented during localized viral spread

Segmentation of viral genomes into multiple RNAs creates the potential for replication of incomplete viral genomes (IVGs). Here we use a single-cell approach to quantify influenza A virus IVGs and examine their fitness implications. We find that each segment of influenza A/Panama/2007/99 (H3N2) virus has a 58% probability of being replicated in a cell infected with a single virion. Theoretical methods predict that IVGs carry high costs in a well-mixed system, as 3.6 virions are required for replication of a full genome. Spatial structure is predicted to mitigate these costs, however, and experimental manipulations of spatial structure indicate that local spread facilitates complementation. A virus entirely dependent on co-infection was used to assess relevance of IVGs in vivo. This virus grows robustly in guinea pigs, but is less infectious and does not transmit. Thus, co-infection allows IVGs to contribute to within-host spread, but complete genomes may be critical for transmission.

Principles of Effective and Robust Innate Immune Response to Viral Infections: A Multiplex Network Analysis

The human innate immune response, particularly the type-I interferon (IFN) response, is highly robust and effective first line of defense against virus invasion. IFN molecules are produced and secreted from infected cells upon virus infection and recognition. They then act as signaling/communication molecules to activate an antiviral response in neighboring cells so that those cells become refractory to infection. Previous experimental studies have identified the detailed molecular mechanisms for the IFN signaling and response. However, the principles underlying how host cells use IFN to communicate with each other to collectively and robustly halt an infection is not understood. Here we take a multiplex network modeling approach to provide a theoretical framework to identify key factors that determine the effectiveness of the IFN response against virus infection of a host. In this approach, we consider the virus spread among host cells and the interferon signaling to protect host cells as a competition process on a two-layer multiplex network. We focused on two types of network topology, i.e., the Erdős-Rényi (ER) network and the Geometric Random (GR) network, which represent the scenarios when infection of cells is mostly well mixed (e.g., in the blood) and when infection is spatially segregated (e.g., in tissues), respectively. We show that in general, the IFN response works effectively to stop viral infection when virus infection spreads spatially (a most likely scenario for initial virus infection of a host at the peripheral tissue). Importantly, we show that the effectiveness of the IFN response is robust against large variations in the distance of IFN diffusion as long as IFNs diffuse faster than viruses and they can effectively induce antiviral responses in susceptible host cells. This suggests that the effectiveness of the IFN response is insensitive to the specific arrangement of host cells in peripheral tissues. Thus, our work provides a quantitative explanation of why the IFN response can serve an effective and robust response in different tissue types to a wide range of viral infections of a host.

Recombinant vector vaccine evolution

Replicating recombinant vector vaccines consist of a fully competent viral vector backbone engineered to express an antigen from a foreign transgene. From the perspective of viral replication, the transgene is not only dispensable but may even be detrimental. Thus vaccine revertants that delete or inactivate the transgene may evolve to dominate the vaccine virus population both during the process of manufacture of the vaccine as well as during the course of host infection. A particular concern is that this vaccine evolution could reduce its antigenicity—the immunity elicited to the transgene. We use mathematical and computational models to study vaccine evolution and immunity. These models include evolution arising during the process of manufacture, the dynamics of vaccine and revertant growth, plus innate and adaptive immunity elicited during the course of infection. Although the selective basis of vaccine evolution is easy to comprehend, the immunological consequences are not. One complication is that the opportunity for vaccine evolution is limited by the short period of within-host growth before the viral population is cleared. Even less obvious, revertant growth may only weakly interfere with vaccine growth in the host and thus have a limited effect on immunity to vaccine. Overall, we find that within-host vaccine evolution can sometimes compromise vaccine immunity, but only when the extent of evolution during vaccine manufacture is severe, and this evolution can be easily avoided or mitigated.

Recombinant vector vaccines are live replicating viruses that are engineered to carry extra genes derived from a pathogen—and these extra genes produce proteins against which we want to generate immunity. These vaccine genomes may evolve to lose the extra genes during the process of manufacture of the vaccine or during replication within an individual, and there is a concern that this evolution might severely limit the vaccine’s efficacy. The dynamics of this process are studied here with mathematical models. The potential for vaccine evolution within the host is somewhat limited by the short-term growth of the vaccine population before it is suppressed by the immune response. We find that evolution is a problem only when the process of manufacture results in the majority of the vaccine virus being revertant. We show that increasing the vaccine inoculum size or reducing the level of revertant in the vaccine inoculum can largely avoid the loss of immunity arising from evolution.

Within-host infectious disease models accommodating cellular coinfection, with an application to influenza

Within-host models are useful tools for understanding the processes regulating viral load dynamics. While existing models have considered a wide range of within-host processes, at their core these models have shown remarkable structural similarity. Specifically, the structure of these models generally consider target cells to be either uninfected or infected, with the possibility of accommodating further resolution (e.g. cells that are in an eclipse phase). Recent findings, however, indicate that cellular coinfection is the norm rather than the exception for many viral infectious diseases, and that cells with high multiplicity of infection are present over at least some duration of an infection. The reality of these cellular coinfection dynamics is not accommodated in current within-host models although it may be critical for understanding within-host dynamics. This is particularly the case if multiplicity of infection impacts infected cell phenotypes such as their death rate and their viral production rates. Here, we present a new class of within-host disease models that allow for cellular coinfection in a scalable manner by retaining the low-dimensionality that is a desirable feature of many current within-host models. The models we propose adopt the general structure of epidemiological ‘macroparasite’ models that allow hosts to be variably infected by parasites such as nematodes and host phenotypes to flexibly depend on parasite burden. Specifically, our within-host models consider target cells as ‘hosts’ and viral particles as ‘macroparasites’, and allow viral output and infected cell lifespans, among other phenotypes, to depend on a cell’s multiplicity of infection. We show with an application to influenza that these models can be statistically fit to viral load and other within-host data, and demonstrate using model selection approaches that they have the ability to outperform traditional within-host viral dynamic models. Important in vivo quantities such as the mean multiplicity of cellular infection and time-evolving reassortant frequencies can also be quantified in a straightforward manner once these macroparasite models have been parameterized. The within-host model structure we develop here provides a mathematical way forward to address questions related to the roles of cellular coinfection, collective viral interactions, and viral complementation in within-host viral dynamics and evolution.

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.