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

A unifying model to explain high nirmatrelvir therapeutic efficacy against SARS-CoV-2, despite low post-exposure prophylaxis efficacy and frequent viral rebound

In a pivotal trial (EPIC-HR), a 5-day course of oral ritonavir-boosted nirmatrelvir, given early during symptomatic SARS-CoV-2 infection (within three days of symptoms onset), decreased hospitalization and death by 89.1% and nasal viral load by 0.87 log relative to placebo in high-risk individuals. Yet, nirmatrelvir/ritonavir failed as post-exposure prophylaxis in a trial, and frequent viral rebound has been observed in subsequent cohorts. We developed a mathematical model capturing viral-immune dynamics and nirmatrelvir pharmacokinetics that recapitulated viral loads from this and another clinical trial (PLATCOV). Our results suggest that nirmatrelvir's in vivo potency is significantly lower than in vitro assays predict. According to our model, a maximally potent agent would reduce the viral load by approximately 3.5 logs relative to placebo at 5 days. The model identifies that earlier initiation and shorter treatment duration are key predictors of post-treatment rebound. Extension of treatment to 10 days for Omicron variant infection in vaccinated individuals, rather than increasing dose or dosing frequency, is predicted to lower the incidence of viral rebound significantly.

Heterogeneous SARS-CoV-2 kinetics due to variable timing and intensity of immune responses

The viral kinetics of documented SARS-CoV-2 infections exhibit a high degree of interindividual variability. We identified 6 distinct viral shedding patterns, which differed according to peak viral load, duration, expansion rate, and clearance rate, by clustering data from 768 infections in the National Basketball Association cohort. Omicron variant infections in previously vaccinated individuals generally led to lower cumulative shedding levels of SARS-CoV-2 than other scenarios. We then developed a mechanistic mathematical model that recapitulated 1,510 observed viral trajectories, including viral rebound and cases of reinfection. Lower peak viral loads were explained by a more rapid and sustained transition of susceptible cells to a refractory state during infection as well as by an earlier and more potent late, cytolytic immune response. Our results suggest that viral elimination occurs more rapidly during Omicron infection, following vaccination, and following reinfection due to enhanced innate and acquired immune responses. Because viral load has been linked with COVID-19 severity and transmission risk, our model provides a framework for understanding the wide range of observed SARS-CoV-2 infection outcomes.

In silico identification of viral loads in cough-generated droplets - Seamless integrated analysis of CFPD-HCD-EWF

BACKGROUND AND OBJECTIVE

Respiratory diseases caused by respiratory viruses have significantly threatened public health worldwide. This study presents a comprehensive approach to predict viral dynamics and the generation of stripped droplets within the mucus layer of the respiratory tract during coughing using a larynx-trachea-bifurcation (LTB) model.

METHODS

This study integrates computational fluid-particle dynamics (CFPD), host-cell dynamics (HCD), and the Eulerian wall film (EWF) model to propose a potential means for seamless integrated analysis. The verified CFPD-HCD coupling model based on a 3D-shell model was used to characterize the severe acute respiratory syndrome, coronavirus 2 (SARS-CoV-2) dynamics in the LTB mucus layer, whereas the EWF model was employed to account for the interfacial fluid to explore the generation mechanism and trace the origin site of droplets exhaled during a coughing event of an infected host.

RESULTS

The results obtained using CFPD delineated the preferential deposition sites for droplets in the laryngeal and tracheal regions. Thus, the analysis of the HCD model showed that the viral load increased rapidly in the laryngeal region during the peak of infection, whereas there was a growth delay in the tracheal region (up to day 8 after infection). After two weeks of infection, the high viral load gradually migrated towards the glottic region. Interestingly, the EWF model demonstrated a high concentration of exhaled droplets originating from the larynx. The coupling technique indicated a concurrent high viral load in the mucus layer and site of origin of the exhaled droplets.

CONCLUSIONS

This interdisciplinary research underscores the seamless analysis from initial exposure to virus-laden droplets, the dynamics of viral infection in the LTB mucus layer, and the re-emission from the coughing activities of an infected host. Our efforts aimed to address the complex challenges at the intersection of viral dynamics and respiratory health, which can contribute to a more detailed understanding and targeted prevention of respiratory diseases.

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

To mitigate the loss of lives during the COVID-19 pandemic, 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 variants susceptible to mAb therapy. 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 antiviral 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.

Within-host evolution of SARS-CoV-2: how often are de novo mutations transmitted from symptomatic infections?

Despite a relatively low mutation rate, the large number of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections has allowed for substantial genetic change, leading to a multitude of emerging variants. Using a recently determined mutation rate (per site replication), as well as within-host parameter estimates for symptomatic SARS-CoV-2 infection, we apply a stochastic transmission-bottleneck model to describe the survival probability of de novo SARS-CoV-2 mutations as a function of bottleneck size and selection coefficient. For narrow bottlenecks, we find that mutations affecting per-target-cell attachment rate (with phenotypes associated with fusogenicity and ACE2 binding) have similar transmission probabilities to mutations affecting viral load clearance (with phenotypes associated with humoral evasion). We further find that mutations affecting the eclipse rate (with phenotypes associated with reorganization of cellular metabolic processes and synthesis of viral budding precursor material) are highly favoured relative to all other traits examined. We find that mutations leading to reduced removal rates of infected cells (with phenotypes associated with innate immune evasion) have limited transmission advantage relative to mutations leading to humoral evasion. Predicted transmission probabilities, however, for mutations affecting innate immune evasion are more consistent with the range of clinically estimated household transmission probabilities for de novo mutations. This result suggests that although mutations affecting humoral evasion are more easily transmitted when they occur, mutations affecting innate immune evasion may occur more readily. We examine our predictions in the context of a number of previously characterized mutations in circulating strains of SARS-CoV-2. Our work offers both a null model for SARS-CoV-2 mutation rates and predicts which aspects of viral life history are most likely to successfully evolve, despite low mutation rates and repeated transmission bottlenecks.

Heterogeneous SARS-CoV-2 kinetics due to variable timing and intensity of immune responses

The viral kinetics of documented SARS-CoV-2 infections exhibit a high degree of inter-individual variability. We identified six distinct viral shedding patterns, which differed according to peak viral load, duration, expansion rate and clearance rate, by clustering data from 768 infections in the National Basketball Association cohort. Omicron variant infections in previously vaccinated individuals generally led to lower cumulative shedding levels of SARS-CoV-2 than other scenarios. We then developed a mechanistic mathematical model that recapitulated 1510 observed viral trajectories, including viral rebound and cases of reinfection. Lower peak viral loads were explained by a more rapid and sustained transition of susceptible cells to a refractory state during infection, as well as an earlier and more potent late, cytolytic immune response. Our results suggest that viral elimination occurs more rapidly during omicron infection, following vaccination, and following re-infection due to enhanced innate and acquired immune responses. Because viral load has been linked with COVID-19 severity and transmission risk, our model provides a framework for understanding the wide range of observed SARS-CoV-2 infection outcomes.

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.

Plasma SARS-CoV-2 RNA elimination and RAGE kinetics distinguish COVID-19 severity

Objectives

Identifying biomarkers causing differential SARS-CoV-2 infection kinetics associated with severe COVID-19 is fundamental for effective diagnostics and therapeutic planning.

Methods

In this work, we applied mathematical modelling to investigate the relationships between patient characteristics, plasma SARS-CoV-2 RNA dynamics and COVID-19 severity. Using a straightforward mathematical model of within-host viral kinetics, we estimated key model parameters from serial plasma viral RNA (vRNA) samples from 256 hospitalised COVID-19+ patients.

Results

Our model predicted that clearance rates distinguish key differences in plasma vRNA kinetics and severe COVID-19. Moreover, our analyses revealed a strong correlation between plasma vRNA kinetics and plasma receptor for advanced glycation end products (RAGE) concentrations (a plasma biomarker of lung damage), collected in parallel to plasma vRNA from patients in our cohort, suggesting that RAGE can substitute for viral plasma shedding dynamics to prospectively classify seriously ill patients.

Conclusion

Overall, our study identifies factors of COVID-19 severity, supports interventions to accelerate viral clearance and underlines the importance of mathematical modelling to better understand COVID-19.

Prediction of long-term humoral response induced by the two-dose heterologous Ad26.ZEBOV, MVA-BN-Filo vaccine against Ebola

The persistence of the long-term immune response induced by the heterologous Ad26.ZEBOV, MVA-BN-Filo two-dose vaccination regimen against Ebola has been investigated in several clinical trials. Longitudinal data on IgG-binding antibody concentrations were analyzed from 487 participants enrolled in six Phase I and Phase II clinical trials conducted by the EBOVAC1 and EBOVAC2 consortia. A model based on ordinary differential equations describing the dynamics of antibodies and short- and long-lived antibody-secreting cells (ASCs) was used to model the humoral response from 7 days after the second vaccination to a follow-up period of 2 years. Using a population-based approach, we first assessed the robustness of the model, which was originally estimated based on Phase I data, against all data. Then we assessed the longevity of the humoral response and identified factors that influence these dynamics. We estimated a half-life of the long-lived ASC of at least 15 years and found an influence of geographic region, sex, and age on the humoral response dynamics, with longer antibody persistence in Europeans and women and higher production of antibodies in younger participants.

Molnupiravir Revisited-Critical Assessment of Studies in Animal Models of COVID-19

Molnupiravir, a prodrug known for its broad antiviral activity, has demonstrated efficacy in animal models of COVID-19, prompting clinical trials, in which initial results indicated a significant effect against the disease. However, subsequent clinical studies did not confirm these findings, leading to the refusal of molnupiravir for permanent market authorization in many countries. This report critically assessed 22 studies published in 18 reports that investigated the efficacy of molnupiravir in animal models of COVID-19, with the purpose of determining how well the design of these models informed human studies. We found that the administered doses of molnupiravir in most studies involving animal COVID-19 models were disproportionately higher than the dose recommended for human use. Specifically, when adjusted for body surface area, over half of the doses of molnupiravir used in the animal studies exceeded twice the human dose. Direct comparison of reported drug exposure across species after oral administration of molnupiravir indicated that the antiviral efficacy of the dose recommended for human use was underestimated in some animal models and overestimated in others. Frequently, molnupiravir was given prophylactically or shortly after SARS-CoV-2 inoculation in these models, in contrast to clinical trials where such timing is not consistently achieved. Furthermore, the recommended five-day treatment duration for humans was exceeded in several animal studies. Collectively, we suggest that design elements in the animal studies under examination contributed to a preference favoring molnupiravir, and thus inflated expectations for its efficacy against COVID-19. Addressing these elements may offer strategies to enhance the clinical efficacy of molnupiravir for the treatment of COVID-19. Such strategies include dose increment, early treatment initiation, administration by inhalation, and use of the drug in antiviral combination therapy.

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.

Modelling how increased Cathepsin B/L and decreased TMPRSS2 usage for cell entry by the SARS-CoV-2 Omicron variant may affect the efficacy and synergy of TMPRSS2 and Cathepsin B/L inhibitors

The SARS-CoV-2 Omicron variant harbours many mutations in its spike protein compared to the original SARS-CoV-2 strain, which may alter its ability to enter cells, cell tropism, and response to interventions blocking virus entry. To elucidate these effects, we developed a mathematical model of SARS-CoV-2 entry into target cells and applied it to analyse recent in vitro data. SARS-CoV-2 can enter cells via two pathways, one using the host proteases Cathepsin B/L and the other using the host protease TMPRSS2. We found enhanced entry efficiency of the Omicron variant in cells where the original strain preferentially used Cathepsin B/L and reduced efficiency where it used TMPRSS2. The Omicron variant thus appears to have evolved to use the Cathepsin B/L pathway better but at the expense of its ability to use the TMPRSS2 pathway compared to the original strain. We estimated >4-fold enhanced efficiency of the Omicron variant in entry via the Cathepsin B/L pathway and >3-fold reduced efficiency via the TMPRSS2 pathway compared to the original or other strains in a cell type-dependent manner. Our model predicted that Cathepsin B/L inhibitors would be more efficacious and TMPRSS2 inhibitors less efficacious in blocking Omicron variant entry into cells than the original strain. Furthermore, model predictions suggested that drugs simultaneously targeting the two pathways would exhibit synergy. The maximum synergy and drug concentrations yielding it would differ for the Omicron variant compared to the original strain. Our findings provide insights into the cell entry mechanisms of the Omicron variant and have implications for intervention targeting these mechanisms.

Anti-inflammatory effects of dexamethasone in COVID-19 patients: Translational population PK/PD modeling and simulation

Dexamethasone (DEX) given at a dose of 6 mg once-daily for 10 days is a recommended dosing regimen in patients with coronavirus disease 2019 (COVID-19) requiring oxygen therapy. We developed a population pharmacokinetic and pharmacodynamic (PopPK/PD) model of DEX anti-inflammatory effects in COVID-19 and provide simulations comparing the expected efficacy of four dosing regimens of DEX. Nonlinear mixed-effects modeling and simulations were performed using Monolix Suite version 2021R1 (Lixoft, France). Published data for DEX PK in patients with COVID-19 exhibited moderate variability with a clearance of about half that in healthy adults. No accumulation of the drug was expected even with daily oral doses of 12 mg. Indirect effect models of DEX inhibition of TNFα, IL-6, and CRP plasma concentrations were enacted and simulations performed for DEX given at 1.5, 3, 6, and 12 mg daily for 10 days. The numbers of individuals that achieved specified reductions in inflammatory biomarkers were compared among the treatment groups. The simulations indicate the need for 6 or 12 mg daily doses of DEX for 10 days for simultaneous reductions in TNFα, IL-6, and CRP. Possibly beneficial is DEX given at a dose of 12 mg compared to 6 mg. The PopPK/PD model may be useful in the assessment of other anti-inflammatory compounds as well as drug combinations in the treatment of cytokine storms.

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.

Statistical Challenges When Analyzing SARS-CoV-2 RNA Measurements Below the Assay Limit of Quantification in COVID-19 Clinical Trials

Most clinical trials evaluating coronavirus disease 2019 (COVID-19) therapeutics include assessments of antiviral activity. In recently completed outpatient trials, changes in nasal severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA levels from baseline were commonly assessed using analysis of covariance (ANCOVA) or mixed models for repeated measures (MMRM) with single imputation for results below assay lower limits of quantification (LLoQ). Analyzing changes in viral RNA levels with singly imputed values can lead to biased estimates of treatment effects. In this article, using an illustrative example from the ACTIV-2 trial, we highlight potential pitfalls of imputation when using ANCOVA or MMRM methods, and illustrate how these methods can be used when considering values Collapse

Key Words

• COVID-19
• SARS-CoV-2 RNA
• linear regression for censored data
• randomized trial

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MESH Headings

• Humans
• Antiviral Agents
• Biological Assay
• COVID-19
• RNA, Viral
• SARS-CoV-2/genetics

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Grants

• UM1 AI069424 NIAID NIH HHS
• UM1 AI068634 NIH HHS
• UM1 AI069481 NIAID NIH HHS
• UM1 AI106701 NIAID NIH HHS
• U01 AI069424 NIAID NIH HHS
• UM1 AI069412 NIAID NIH HHS
• UM1 AI068634 NIAID NIH HHS
• UM1 AI068636 NIAID NIH HHS
• National Institute of Allergy and Infectious Diseases
• National Institutes of Health

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Affiliation(s)

Carlee B Moser Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Kara W Chew Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California, USA
Mark J Giganti Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Jonathan Z Li Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Cambridge, Massachusetts, USA
Evgenia Aga Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Justin Ritz Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Alexander L Greninger Department of Laboratory Medicine and Pathology, University of Washington, Seattle, Washington, USA
Arzhang Cyrus Javan National Institutes of Health, Rockville, Maryland, USA
Rachel Bender Ignacio Department of Medicine, University of Washington, Seattle, Washington, USA
Eric S Daar Lundquist Institute at Harbor-University of California, Los Angeles Medical Center, Torrance, California, USA
David A Wohl Department of Medicine, Chapel Hill School of Medicine, University of North Carolina, Chapel Hill, North Carolina, USA
Judith S Currier Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California, USA
Joseph J Eron Department of Medicine, Chapel Hill School of Medicine, University of North Carolina, Chapel Hill, North Carolina, USA
Davey M Smith Department of Medicine, University of California, San Diego, La Jolla, California, USA
Michael D Hughes Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA

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Modelling the viral dynamics of the SARS-CoV-2 Delta and Omicron variants in different cell types

We use viral kinetic models fitted to viral load data from in vitro studies to explain why the SARS-CoV-2 Omicron variant replicates faster than the Delta variant in nasal cells, but slower than Delta in lung cells, which could explain Omicron's higher transmission potential and lower severity. We find that in both nasal and lung cells, viral infectivity is higher for Omicron but the virus production rate is higher for Delta, with an estimated approximately 200-fold increase in infectivity and 100-fold decrease in virus production when comparing Omicron with Delta in nasal cells. However, the differences are unequal between cell types, and ultimately lead to the basic reproduction number and growth rate being higher for Omicron in nasal cells, and higher for Delta in lung cells. In nasal cells, Omicron alone can enter via a TMPRSS2-independent pathway, but it is primarily increased efficiency of TMPRSS2-dependent entry which accounts for Omicron's increased activity. This work paves the way for using within-host mathematical models to understand the transmission potential and severity of future variants.

COVID infection in 4 steps: Thermodynamic considerations reveal how viral mucosal diffusion, target receptor affinity and furin cleavage act in concert to drive the nature and degree of infection in human COVID-19 disease

We have developed a mechanistic model of SARS-CoV-2 and SARS-CoV infection, exploring the relationship between the viral diffusion in the mucosa and viral affinity for the angiotensin converting enzyme 2 (ACE2) target. Utilising the structural similarity of SARS-CoV and SARS-CoV-2 and a shared viral target receptor (ACE2), but a dramatic difference in upper or lower respiratory tract infectivity, we were able to generate insights into the linkage of mucosal diffusion and target receptor affinity in determining the pathophysiological pathways of these two viruses. Our analysis reveals that for SARS-CoV-2 the higher affinity of ACE2 binding, the faster and more complete the mucosal diffusion in its transport from the upper airway to the region of the ACE2 target on the epithelium. This diffusional process is essential for the presentation of this virus to the furin catalysed highly efficient entry and infection process in the upper respiratory tract epithelial cells. A failure of SARS-CoV to follow this path is associated with lower respiratory tract infection and decreased infectivity. Thus, our analysis supports the view that through tropism SARS-CoV-2 has evolved a highly efficient membrane entry process that can act in concert with a high binding affinity of this virus and its variants for its ACE2 which in turn promotes enhanced movement of the virus from airway to epithelium. In this way ongoing mutations yielding higher affinities of SARS-CoV-2 for the ACE2 target becomes the basis for higher upper respiratory tract infectivity and greater viral spread. It is concluded that SARS-CoV-2 is constrained in the extent of its activities by the fundamental laws of physics and thermodynamics. Laws that describe diffusion and molecular binding. Moreover it can be speculated that the very earliest contact of this virus with the human mucosa defines the pathogenesis of this infection.

Visual prediction and parameter optimization of viral dynamics in the mucus milieu of the upper airway based on CFPD-HCD analysis

BACKGROUND AND OBJECTIVE

Respiratory diseases caused by viruses are a major human health problem. To better control the infection and understand the pathogenesis of these diseases, this paper studied SARS-CoV-2, a novel coronavirus outbreak, as an example.

METHODS

Based on coupled computational fluid and particle dynamics (CFPD) and host-cell dynamics (HCD) analyses, we studied the viral dynamics in the mucus layer of the human nasal cavity-nasopharynx. To reproduce the effect of mucociliary movement on the diffusive and convective transport of viruses in the mucus layer, a 3D-shell model was constructed using CT data of the upper respiratory tract (URT) of volunteers. Considering the mucus environment, the HCD model was established by coupling the target cell-limited model with the convection-diffusion term. Parameter optimization of the HCD model is the key problem in the simulation. Therefore, this study focused on the parameter optimization of the viral dynamics model, divided the geometric model into multiple compartments, and used Monolix to perform the nonlinear mixed effects (NLME) of pharmacometrics to discuss the influence of factors such as the number of mucus layers, number of compartments, diffusion rate, and mucus flow velocity on the prediction results.

RESULTS

The findings showed that sufficient experimental data can be used to estimate the corresponding parameters of the HCD model. The optimized convection-diffusion case with a two-layer multi-compartment low-velocity model could accurately predict the viral dynamics.

CONCLUSIONS

Its visualization process could explain the symptoms of the disease in the nose and contribute to the prevention and targeted treatment of respiratory diseases.

Dynamics of a cross-superdiffusive SIRS model with delay effects in transmission and treatment

We investigate the dynamics of a SIRS epidemiological model taking into account cross-superdiffusion and delays in transmission, Beddington-DeAngelis incidence rate and Holling type II treatment. The superdiffusion is induced by inter-country and inter-urban exchange. The linear stability analysis for the steady-state solutions is performed, and the basic reproductive number is calculated. The sensitivity analysis of the basic reproductive number is presented, and we show that some parameters strongly influence the dynamics of the system. A bifurcation analysis to determine the direction and stability of the model is carried out using the normal form and center manifold theorem. The results reveal a proportionality between the transmission delay and the diffusion rate. The numerical results show the formation of patterns in the model, and their epidemiological implications are discussed.

Multiple cohort study of hospitalized SARS-CoV-2 in-host infection dynamics: Parameter estimates, identifiability, sensitivity and the eclipse phase profile

Within-host SARS-CoV-2 modelling studies have been published throughout the COVID-19 pandemic. These studies contain highly variable numbers of individuals and capture varying timescales of pathogen dynamics; some studies capture the time of disease onset, the peak viral load and subsequent heterogeneity in clearance dynamics across individuals, while others capture late-time post-peak dynamics. In this study, we curate multiple previously published SARS-CoV-2 viral load data sets, fit these data with a consistent modelling approach, and estimate the variability of in-host parameters including the basic reproduction number, R₀, as well as the best-fit eclipse phase profile. We find that fitted dynamics can be highly variable across data sets, and highly variable within data sets, particularly when key components of the dynamic trajectories (e.g. peak viral load) are not represented in the data. Further, we investigated the role of the eclipse phase time distribution in fitting SARS-CoV-2 viral load data. By varying the shape parameter of an Erlang distribution, we demonstrate that models with either no eclipse phase, or with an exponentially-distributed eclipse phase, offer significantly worse fits to these data, whereas models with less dispersion around the mean eclipse time (shape parameter two or more) offered the best fits to the available data across all data sets used in this work. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Determination of significant immunological timescales from mRNA-LNP-based vaccines in humans

A compartment model for an in-host liquid nanoparticle delivered mRNA vaccine is presented. Through non-dimensionalisation, five timescales are identified that dictate the lifetime of the vaccine in-host: decay of interferon gamma, antibody priming, autocatalytic growth, antibody peak and decay, and interleukin cessation. Through asymptotic analysis we are able to obtain semi-analytical solutions in each of the time regimes which allows us to predict maximal concentrations and better understand parameter dependence in the model. We compare our model to 22 data sets for the BNT162b2 and mRNA-1273 mRNA vaccines demonstrating good agreement. Using our analysis, we estimate the values for each of the five timescales in each data set and predict maximal concentrations of plasma B-cells, antibody, and interleukin. Through our comparison, we do not observe any discernible differences between vaccine candidates and sex. However, we do identify an age dependence, specifically that vaccine activation takes longer and that peak antibody occurs sooner in patients aged 55 and greater.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

A quantitative systems pharmacology model of the pathophysiology and treatment of COVID-19 predicts optimal timing of pharmacological interventions

A quantitative systems pharmacology (QSP) model of the pathogenesis and treatment of SARS-CoV-2 infection can streamline and accelerate the development of novel medicines to treat COVID-19. Simulation of clinical trials allows in silico exploration of the uncertainties of clinical trial design and can rapidly inform their protocols. We previously published a preliminary model of the immune response to SARS-CoV-2 infection. To further our understanding of COVID-19 and treatment, we significantly updated the model by matching a curated dataset spanning viral load and immune responses in plasma and lung. We identified a population of parameter sets to generate heterogeneity in pathophysiology and treatment and tested this model against published reports from interventional SARS-CoV-2 targeting mAb and antiviral trials. Upon generation and selection of a virtual population, we match both the placebo and treated responses in viral load in these trials. We extended the model to predict the rate of hospitalization or death within a population. Via comparison of the in silico predictions with clinical data, we hypothesize that the immune response to virus is log-linear over a wide range of viral load. To validate this approach, we show the model matches a published subgroup analysis, sorted by baseline viral load, of patients treated with neutralizing Abs. By simulating intervention at different time points post infection, the model predicts efficacy is not sensitive to interventions within five days of symptom onset, but efficacy is dramatically reduced if more than five days pass post symptom onset prior to treatment.

Statistical Challenges when Analyzing SARS-CoV-2 RNA Measurements Below the Assay Limit of Quantification in COVID-19 Clinical Trials

Most clinical trials evaluating COVID-19 therapeutics include assessments of antiviral activity. In recently completed outpatient trials, changes in nasal SARS-CoV-2 RNA levels from baseline were commonly assessed using analysis of covariance (ANCOVA) or mixed models for repeated measures (MMRM) with single-imputation for results below assay lower limits of quantification (LLoQ). Analyzing changes in viral RNA levels with singly-imputed values can lead to biased estimates of treatment effects. In this paper, using an illustrative example from the ACTIV-2 trial, we highlight potential pitfalls of imputation when using ANCOVA or MMRM methods, and illustrate how these methods can be used when considering values Collapse

Key Words

• sars-cov-2 rna
• covid-19
• linear regression for censored data
• randomized trial

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MESH Headings Collapse

Grants

• UM1 AI068634 NIAID NIH HHS
• UM1 AI068636 NIAID NIH HHS
• UM1 AI106701 NIAID NIH HHS

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Affiliation(s)

Carlee B Moser Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Kara W Chew Department of Medicine, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, 90024, USA
Mark J Giganti Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Jonathan Z Li Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Cambridge, 02139, USA
Evgenia Aga Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Justin Ritz Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Alexander L Greninger Department of Laboratory Medicine & Pathology, University of Washington, Seattle, 98195, USA
Arzhang Cyrus Javan National Institutes of Health, Rockville, 20852, USA Rachel Bender Ignacio, MD, MPH, Department of Medicine, University of Washington, Seattle, 98195, USA
Eric S Daar Lundquist Institute at Harbor-UCLA Medical Center, Torrance, 90502, USA David A Wohl, MD, Department of Medicine, University of North Carolina at Chapel Hill School of Medicine, Chapel Hill, 27599, USA
Judith S Currier Department of Medicine, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, 90024, USA
Joseph J Eron Department of Medicine, University of North Carolina at Chapel Hill School of Medicine, Chapel Hill, 27599, USA
Davey M Smith Department of Medicine, University of California, San Diego, La Jolla, 92093, USA
Michael D Hughes Department of Biostatistics and Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA For the ACTIV-2/A5401 Study Team

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Drug Cocktail Formulation via Circuit Design

Electronic circuits intuitively visualize and quantitatively simulate biological systems with nonlinear differential equations that exhibit complicated dynamics. Drug cocktail therapies are a powerful tool against diseases that exhibit such dynamics. We show that just six key states, which are represented in a feedback circuit, enable drug-cocktail formulation: 1) healthy cell number; 2) infected cell number; 3) extracellular pathogen number; 4) intracellular pathogenic molecule number; 5) innate immune system strength; and 6) adaptive immune system strength. To enable drug cocktail formulation, the model represents the effects of the drugs in the circuit. For example, a nonlinear feedback circuit model fits measured clinical data, represents cytokine storm and adaptive autoimmune behavior, and accounts for age, sex, and variant effects for SARS-CoV-2 with few free parameters. The latter circuit model provided three quantitative insights on the optimal timing and dosage of drug components in a cocktail: 1) antipathogenic drugs should be given early in the infection, but immunosuppressant timing involves a tradeoff between controlling pathogen load and mitigating inflammation; 2) both within and across-class combinations of drugs have synergistic effects; 3) if they are administered sufficiently early in the infection, anti-pathogenic drugs are more effective at mitigating autoimmune behavior than immunosuppressant drugs.

Computational framework to understand the clinical stages of COVID-19 and visualization of time course for various treatment strategies

Coronavirus disease 2019 is known to be regulated by multiple factors such as delayed immune response, impaired T cell activation, and elevated levels of proinflammatory cytokines. Clinical management of the disease remains challenging due to interplay of various factors as drug candidates may elicit different responses depending on the staging of the disease. In this context, we propose a computational framework which provides insights into the interaction between viral infection and immune response in lung epithelial cells, with an aim of predicting optimal treatment strategies based on infection severity. First, we formulate the model for visualizing the nonlinear dynamics during the disease progression considering the role of T cells, macrophages and proinflammatory cytokines. Here, we show that the model is capable of emulating the dynamic and static data trends of viral load, T cell, macrophage levels, interleukin (IL)-6 and TNF-α levels. Second, we demonstrate the ability of the framework to capture the dynamics corresponding to mild, moderate, severe, and critical condition. Our result shows that, at late phase (>15 days), severity of disease is directly proportional to pro-inflammatory cytokine IL6 and tumor necrosis factor (TNF)-α levels and inversely proportional to the number of T cells. Finally, the simulation framework was used to assess the effect of drug administration time as well as efficacy of single or multiple drugs on patients. The major contribution of the proposed framework is to utilize the infection progression model for clinical management and administration of drugs inhibiting virus replication and cytokine levels as well as immunosuppressant drugs at various stages of the disease.

Modulating Immune Response in Viral Infection for Quantitative Forecasts of Drug Efficacy

The antiretroviral drug, the total level of viral production, and the effectiveness of immune responses are the main topics of this review because they are all dynamically interrelated. Immunological and viral processes interact in extremely complex and non-linear ways. For reliable analysis and quantitative forecasts that may be used to follow the immune system and create a disease profile for each patient, mathematical models are helpful in characterizing these non-linear interactions. To increase our ability to treat patients and identify individual differences in disease development, immune response profiling might be useful. Identifying which patients are moving from mild to severe disease would be more beneficial using immune system parameters. Prioritize treatments based on their inability to control the immune response and prevent T cell exhaustion. To increase treatment efficacy and spur additional research in this field, this review intends to provide examples of the effects of modelling immune response in viral infections, as well as the impact of pharmaceuticals on immune response.

A simple in-host model for COVID-19 with treatments: model prediction and calibration

In this paper, we provide a simple ODEs model with a generic nonlinear incidence rate function and incorporate two treatments, blocking the virus binding and inhibiting the virus replication to investigate the impact of calibration on model predictions for the SARS-CoV-2 infection dynamics. We derive conditions of the infection eradication for the long-term dynamics using the basic reproduction number, and complement the characterization of the dynamics at short-time using the resilience and reactivity of the virus-free equilibrium are considered to inform on the average time of recovery and sensitivity to perturbations in the initial virus free stage. Then, we calibrate the treatment model to clinical datasets for viral load in mild and severe cases and immune cells in severe cases. Based on the analysis, the model calibrated to these different datasets predicts distinct scenarios: eradication with a non reactive virus-free equilibrium, eradication with a reactive virus-free equilibrium, and failure of infection eradication. Moreover, severe cases generate richer dynamics and different outcomes with the same treatment. Calibration to different datasets can lead to diverse model predictions, but combining long- and short-term dynamics indicators allows the categorization of model predictions and determination of infection severity.

Pharmacometric Modeling of the Impact of Azelastine Nasal Spray on SARS-CoV-2 Viral Load and Related Symptoms in COVID-19 Patients

The histamine-1 receptor antagonist azelastine was recently found to impact SARS-CoV-2 viral kinetics in a Phase 2 clinical trial (CARVIN). Thus, we investigated the relationship between intranasal azelastine administrations and viral load, as well as symptom severity in COVID-19 patients and analyzed the impact of covariates using non-linear mixed-effects modeling. For this, we developed a pharmacokinetic (PK) model for the oral and intranasal administration of azelastine. A one-compartment model with parallel absorption after intranasal administration described the PK best, covering both the intranasal and the gastro-intestinal absorption pathways. For virus kinetic and symptoms modeling, viral load and symptom records were gathered from the CARVIN study that included data of 82 COVID-19 patients receiving placebo or intranasal azelastine. The effect of azelastine on viral load was described by a dose–effect model targeting the virus elimination rate. An extension of the model revealed a relationship between COVID-19 symptoms severity and the number of infected cells. The analysis revealed that the intranasal administration of azelastine led to a faster decline in viral load and symptoms severity compared to placebo. Moreover, older patients showed a slower decline in viral load compared to younger patients and male patients experienced higher peak viral loads than females.

Mathematical modeling of plus-strand RNA virus replication to identify broad-spectrum antiviral treatment strategies

Plus-strand RNA viruses are the largest group of viruses. Many are human pathogens that inflict a socio-economic burden. Interestingly, plus-strand RNA viruses share remarkable similarities in their replication. A hallmark of plus-strand RNA viruses is the remodeling of intracellular membranes to establish replication organelles (so-called "replication factories"), which provide a protected environment for the replicase complex, consisting of the viral genome and proteins necessary for viral RNA synthesis. In the current study, we investigate pan-viral similarities and virus-specific differences in the life cycle of this highly relevant group of viruses. We first measured the kinetics of viral RNA, viral protein, and infectious virus particle production of hepatitis C virus (HCV), dengue virus (DENV), and coxsackievirus B3 (CVB3) in the immuno-compromised Huh7 cell line and thus without perturbations by an intrinsic immune response. Based on these measurements, we developed a detailed mathematical model of the replication of HCV, DENV, and CVB3 and show that only small virus-specific changes in the model were necessary to describe the in vitro dynamics of the different viruses. Our model correctly predicted virus-specific mechanisms such as host cell translation shut off and different kinetics of replication organelles. Further, our model suggests that the ability to suppress or shut down host cell mRNA translation may be a key factor for in vitro replication efficiency which may determine acute self-limited or chronic infection. We further analyzed potential broad-spectrum antiviral treatment options in silico and found that targeting viral RNA translation, especially polyprotein cleavage, and viral RNA synthesis may be the most promising drug targets for all plus-strand RNA viruses. Moreover, we found that targeting only the formation of replicase complexes did not stop the viral replication in vitro early in infection, while inhibiting intracellular trafficking processes may even lead to amplified viral growth.

Author summary

Plus-strand RNA viruses comprise a large group of related and medically relevant viruses. The current global pandemic of COVID-19 caused by the SARS-coronavirus-2 as well as the constant spread of diseases such as dengue and chikungunya fever show the necessity of a comprehensive and precise analysis of plus-strand RNA virus infections. Plus-strand RNA viruses share similarities in their life cycle. To understand their within-host replication strategies, we developed a mathematical model that studies pan-viral similarities and virus-specific differences of three plus-strand RNA viruses, namely hepatitis C, dengue, and coxsackievirus. By fitting our model to in vitro data, we found that only small virus-specific variations in the model were required to describe the dynamics of all three viruses. Furthermore, our model predicted that ribosomes involved in viral RNA translation seem to be a key player in plus-strand RNA replication efficiency, which may determine acute or chronic infection outcome. Furthermore, our in-silico drug treatment analysis suggests that targeting viral proteases involved in polyprotein cleavage, in combination with viral RNA replication, may represent promising drug targets with broad-spectrum antiviral activity.

Mechanistic Models of COVID-19: Insights into Disease Progression, Vaccines, and Therapeutics

The COVID-19 pandemic has severely impacted health systems and economies worldwide. Significant global efforts are therefore ongoing to improve vaccine efficacies, optimize vaccine deployment, and develop new antiviral therapies to combat the pandemic. Mechanistic viral dynamics and quantitative systems pharmacology models of SARS-CoV-2 infection, vaccines, immunomodulatory agents, and antiviral therapeutics have played a key role in advancing our understanding of SARS-CoV-2 pathogenesis and transmission, the interplay between innate and adaptive immunity to influence the outcomes of infection, effectiveness of treatments, mechanisms and performance of COVID-19 vaccines, and the impact of emerging SARS-CoV-2 variants. Here, we review some of the critical insights provided by these models and discuss the challenges ahead.

Immune response to SARS-CoV-2 in severe disease and long COVID-19

COVID-19 is mild to moderate in otherwise healthy individuals but may nonetheless cause life-threatening disease and/or a wide range of persistent symptoms. The general determinant of disease severity is age mainly because the immune response declines in aging patients. Here, we developed a mathematical model of the immune response to SARS-CoV-2 and revealed that typical age-related risk factors such as only a several 10% decrease in innate immune cell activity and inhibition of type-I interferon signaling by autoantibodies drastically increased the viral load. It was reported that the numbers of certain dendritic cell subsets remained less than half those in healthy donors even seven months after infection. Hence, the inflammatory response was ongoing. Our model predicted the persistent DC reduction and showed that certain patients with severe and even mild symptoms could not effectively eliminate the virus and could potentially develop long COVID.

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Systemic SARS-CoV-2 infection owing to ACE2 expression on a wide range of cell types

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Persistent viral infection can be ongoing within the host even if it is not severe

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Long-term dendritic cell deficiency is owing to viruses that cannot be removed by the host

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Ongoing persistent viral infection within the host potentially causes long COVID or PASC

Aerosol Transport Modeling: The Key Link Between Lung Infections of Individuals and Populations

The recent COVID-19 pandemic has propelled the field of aerosol science to the forefront, particularly the central role of virus-laden respiratory droplets and aerosols. The pandemic has also highlighted the critical need, and value for, an information bridge between epidemiological models (that inform policymakers to develop public health responses) and within-host models (that inform the public and health care providers how individuals develop respiratory infections). Here, we review existing data and models of generation of respiratory droplets and aerosols, their exhalation and inhalation, and the fate of infectious droplet transport and deposition throughout the respiratory tract. We then articulate how aerosol transport modeling can serve as a bridge between and guide calibration of within-host and epidemiological models, forming a comprehensive tool to formulate and test hypotheses about respiratory tract exposure and infection within and between individuals.

Modeling recapitulates the heterogeneous outcomes of SARS-CoV-2 infection and quantifies the differences in the innate immune and CD8 T-cell responses between patients experiencing mild and severe symptoms

SARS-CoV-2 infection results in highly heterogeneous outcomes, from cure without symptoms to acute respiratory distress and death. Empirical evidence points to the prominent roles of innate immune and CD8 T-cell responses in determining the outcomes. However, how these immune arms act in concert to elicit the outcomes remains unclear. Here, we developed a mathematical model of within-host SARS-CoV-2 infection that incorporates the essential features of the innate immune and CD8 T-cell responses. Remarkably, by varying the strengths and timings of the two immune arms, the model recapitulated the entire spectrum of outcomes realized. Furthermore, model predictions offered plausible explanations of several confounding clinical observations, including the occurrence of multiple peaks in viral load, viral recrudescence after symptom loss, and prolonged viral positivity. We applied the model to analyze published datasets of longitudinal viral load measurements from patients exhibiting diverse outcomes. The model provided excellent fits to the data. The best-fit parameter estimates indicated a nearly 80-fold stronger innate immune response and an over 200-fold more sensitive CD8 T-cell response in patients with mild compared to severe infection. These estimates provide quantitative insights into the likely origins of the dramatic inter-patient variability in the outcomes of SARS-CoV-2 infection. The insights have implications for interventions aimed at preventing severe disease and for understanding the differences between viral variants.

Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model’s solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model’s steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication.

In Silico Evaluation of Paxlovid's Pharmacometrics for SARS-CoV-2: A Multiscale Approach

Paxlovid is a promising, orally bioavailable novel drug for SARS-CoV-2 with excellent safety profiles. Our main goal here is to explore the pharmacometric features of this new antiviral. To provide a detailed assessment of Paxlovid, we propose a hybrid multiscale mathematical approach. We demonstrate that the results of the present in silico evaluation match the clinical expectations remarkably well: on the one hand, our computations successfully replicate the outcome of an actual in vitro experiment; on the other hand, we verify both the sufficiency and the necessity of Paxlovid's two main components (nirmatrelvir and ritonavir) for a simplified in vivo case. Moreover, in the simulated context of our computational framework, we visualize the importance of early interventions and identify the time window where a unit-length delay causes the highest level of tissue damage. Finally, the results' sensitivity to the diffusion coefficient of the virus is explored in detail.

Modeling insights into SARS-CoV-2 respiratory tract infections prior to immune protection

Mechanistic insights into human respiratory tract (RT) infections from SARS-CoV-2 can inform public awareness as well as guide medical prevention and treatment for COVID-19 disease. Yet the complexity of the RT and the inability to access diverse regions pose fundamental roadblocks to evaluation of potential mechanisms for the onset and progression of infection (and transmission). We present a model that incorporates detailed RT anatomy and physiology, including airway geometry, physical dimensions, thicknesses of airway surface liquids (ASLs), and mucus layer transport by cilia. The model further incorporates SARS-CoV-2 diffusivity in ASLs and best-known data for epithelial cell infection probabilities, and, once infected, duration of eclipse and replication phases, and replication rate of infectious virions. We apply this baseline model in the absence of immune protection to explore immediate, short-term outcomes from novel SARS-CoV-2 depositions onto the air-ASL interface. For each RT location, we compute probability to clear versus infect; per infected cell, we compute dynamics of viral load and cell infection. Results reveal that nasal infections are highly likely within 1-2 days from minimal exposure, and alveolar pneumonia occurs only if infectious virions are deposited directly into alveolar ducts and sacs, not via retrograde propagation to the deep lung. Furthermore, to infect just 1% of the 140 m2 of alveolar surface area within 1 week, either 103 boluses each with 106 infectious virions or 106 aerosols with one infectious virion, all physically separated, must be directly deposited. These results strongly suggest that COVID-19 disease occurs in stages: a nasal/upper RT infection, followed by self-transmission of infection to the deep lung. Two mechanisms of self-transmission are persistent aspiration of infected nasal boluses that drain to the deep lung and repeated rupture of nasal aerosols from infected mucosal membranes by speaking, singing, or cheering that are partially inhaled, exhaled, and re-inhaled, to the deep lung.

Daily longitudinal sampling of SARS-CoV-2 infection reveals substantial heterogeneity in infectiousness

The dynamics of SARS-CoV-2 replication and shedding in humans remain poorly understood. We captured the dynamics of infectious virus and viral RNA shedding during acute infection through daily longitudinal sampling of 60 individuals for up to 14 days. By fitting mechanistic models, we directly estimated viral expansion and clearance rates and overall infectiousness for each individual. Significant person-to-person variation in infectious virus shedding suggests that individual-level heterogeneity in viral dynamics contributes to 'superspreading'. Viral genome loads often peaked days earlier in saliva than in nasal swabs, indicating strong tissue compartmentalization and suggesting that saliva may serve as a superior sampling site for early detection of infection. Viral loads and clearance kinetics of Alpha (B.1.1.7) and previously circulating non-variant-of-concern viruses were mostly indistinguishable, indicating that the enhanced transmissibility of this variant cannot be explained simply by higher viral loads or delayed clearance. These results provide a high-resolution portrait of SARS-CoV-2 infection dynamics and implicate individual-level heterogeneity in infectiousness in superspreading.

Modeling how antibody responses may determine the efficacy of COVID-19 vaccines

Predicting the efficacy of COVID-19 vaccines would aid vaccine development and usage strategies, which is of importance given their limited supplies. Here we develop a multiscale mathematical model that proposes mechanistic links between COVID-19 vaccine efficacies and the neutralizing antibody (NAb) responses they elicit. We hypothesized that the collection of all NAbs would constitute a shape space and that responses of individuals are random samples from this space. We constructed the shape space by analyzing reported in vitro dose-response curves of ~80 NAbs. Sampling NAb subsets from the space, we recapitulated the responses of convalescent patients. We assumed that vaccination would elicit similar NAb responses. We developed a model of within-host SARS-CoV-2 dynamics, applied it to virtual patient populations and, invoking the NAb responses above, predicted vaccine efficacies. Our predictions quantitatively captured the efficacies from clinical trials. Our study thus suggests plausible mechanistic underpinnings of COVID-19 vaccines and generates testable hypotheses for establishing them.

An age-structured model of hepatitis B viral infection highlights the potential of different therapeutic strategies

Hepatitis B virus (HBV) is a global health threat, and its elimination by 2030 has been prioritised by the World Health Organisation. Here we present an age-structured model for the immune response to an HBV infection, which takes into account contributions from both cell-mediated and humoral immunity. The model has been validated using published patient data recorded during acute infection. It has been adapted to the scenarios of chronic infection, clearance of infection, and flare-ups via variation of the immune response parameters. The impacts of immune response exhaustion and non-infectious subviral particles on the immune response dynamics are analysed. A comparison of different treatment options in the context of this model reveals that drugs targeting aspects of the viral life cycle are more effective than exhaustion therapy, a form of therapy mitigating immune response exhaustion. Our results suggest that antiviral treatment is best started when viral load is declining rather than in a flare-up. The model suggests that a fast antibody production rate always leads to viral clearance, highlighting the promise of antibody therapies currently in clinical trials.

Effects of immunosuppressants on T-cell dynamics: Understanding from a generic coarse-grained immune network model

Long-term immunosuppressive therapy is a drug regimen often used to lower aggressive immune responses in various chronic inflammatory diseases. However, such long-term therapy leading to immune suppression may trigger other adverse reactions in the immune system. The rising concern regarding the optimal dose and duration of such treatment has motivated us to understand non-classical immunomodulatory responses induced by various immunosuppressive steroid and secosteroid drugs such as glucocorticoid and vitamin D supplements. The immunomodulatory actions of such immunosuppressants (that govern the adaptive immune response) are often mediated through their characteristic control over CD4+ T-cells involving pro- and antiinflammatory T-cells. Several early studies attempted to decode temporal and dose-dependent behaviors of such pro- and anti-inflammatory T-cells using the chemical dynamics approach. We first summarize these early works. Then, we develop a minimal coarse-grained kinetic network model to capture the commonality in their immunomodulatory functions. This generic model successfully reproduces the characteristic dynamical features, including the clinical latency period in long-term T-cell dynamics. The temporal behavior of T-cells is found to be sensitive to specific rate parameters and doses of immunosuppressants. The steady-state analysis reflects the transition from an early classified weakly regulated (autoimmune-prone) immune state to a strongly regulated state (immunocompromised state), separated by an intervening state of moderate/balanced regulation. An optimal dose and duration are essential in rescuing balanced immune regulation. This review elucidates how developing a simple generic coarse-grained immune network model may provide immense information that helps diagnose inefficacy in adaptive immune function before and after administering immunosuppressants such as glucocorticoid or vitamin D.

Strategies to minimize heterogeneity and optimize clinical trials in Acute Respiratory Distress Syndrome (ARDS): Insights from mathematical modelling

Background

Mathematical modelling may aid in understanding the complex interactions between injury and immune response in critical illness.

Methods

We utilize a system biology model of COVID-19 to analyze the effect of altering baseline patient characteristics on the outcome of immunomodulatory therapies. We create example parameter sets meant to mimic diverse patient types. For each patient type, we define the optimal treatment, identify biologic programs responsible for clinical responses, and predict biomarkers of those programs.

Findings

Model states representing older and hyperinflamed patients respond better to immunomodulation than those representing obese and diabetic patients. The disparate clinical responses are driven by distinct biologic programs. Optimal treatment initiation time is determined by neutrophil recruitment, systemic cytokine expression, systemic microthrombosis and the renin-angiotensin system (RAS) in older patients, and by RAS, systemic microthrombosis and trans IL6 signalling for hyperinflamed patients. For older and hyperinflamed patients, IL6 modulating therapy is predicted to be optimal when initiated very early (<4^th day of infection) and broad immunosuppression therapy (corticosteroids) is predicted to be optimally initiated later in the disease (7^th – 9^th day of infection). We show that markers of biologic programs identified by the model correspond to clinically identified markers of disease severity.

Interpretation

We demonstrate that modelling of COVID-19 pathobiology can suggest biomarkers that predict optimal response to a given immunomodulatory treatment. Mathematical modelling thus constitutes a novel adjunct to predictive enrichment and may aid in the reduction of heterogeneity in critical care trials.

Funding

C.V. received a Marie Skłodowska Curie Actions Individual Fellowship (MSCA-IF-GF-2020-101028945). R.K.J.'s research is supported by R01-CA208205, and U01-CA 224348, R35-CA197743 and grants from the National Foundation for Cancer Research, Jane's Trust Foundation, Advanced Medical Research Foundation and Harvard Ludwig Cancer Center. No funder had a role in production or approval of this manuscript.

Impairment of T cells' antiviral and anti-inflammation immunities may be critical to death from COVID-19

Clarifying dominant factors determining the immune heterogeneity from non-survivors to survivors is crucial for developing therapeutics and vaccines against COVID-19. The main difficulty is quantitatively analysing the multi-level clinical data, including viral dynamics, immune response and tissue damages. Here, we adopt a top-down modelling approach to quantify key functional aspects and their dynamical interplay in the battle between the virus and the immune system, yielding an accurate description of real-time clinical data involving hundreds of patients for the first time. The quantification of antiviral responses gives that, compared to antibodies, T cells play a more dominant role in virus clearance, especially for mild patients (96.5%). Moreover, the anti-inflammatory responses, namely the cytokine inhibition and tissue repair rates, also positively correlate with T cell number and are significantly suppressed in non-survivors. Simulations show that the lack of T cells can lead to more significant inflammation, proposing an explanation for the monotonic increase of COVID-19 mortality with age and higher mortality for males. We propose that T cells play a crucial role in the immunity against COVID-19, which provides a new direction-improvement of T cell number for advancing current prevention and treatment.

Intracellular Life Cycle Kinetics of SARS-CoV-2 Predicted Using Mathematical Modelling

SARS-CoV-2 infection represents a global threat to human health. Various approaches were employed to reveal the pathogenetic mechanisms of COVID-19. Mathematical and computational modelling is a powerful tool to describe and analyze the infection dynamics in relation to a plethora of processes contributing to the observed disease phenotypes. In our study here, we formulate and calibrate a deterministic model of the SARS-CoV-2 life cycle. It provides a kinetic description of the major replication stages of SARS-CoV-2. Sensitivity analysis of the net viral progeny with respect to model parameters enables the identification of the life cycle stages that have the strongest impact on viral replication. These three most influential parameters are (i) degradation rate of positive sense vRNAs in cytoplasm (negative effect), (ii) threshold number of non-structural proteins enhancing vRNA transcription (negative effect), and (iii) translation rate of non-structural proteins (positive effect). The results of our analysis could be used for guiding the search for antiviral drug targets to combat SARS-CoV-2 infection.

Advancing therapies for viral infections using mechanistic computational models of the dynamic interplay between the virus and host immune response

The COVID-19 pandemic has highlighted a need for improved frameworks for drug discovery, repurposing, clinical trial design and therapy optimization and personalization. Mechanistic computational models can play an important role in developing these frameworks. We discuss how mechanistic models, which consider viral entry, replication in target cells, viral spread in the body, immune response, and the complex factors involved in tissue and organ damage and recovery, can clarify the mechanisms of humoral and cellular immune responses to the virus, viral distribution and replication in tissues, the origins of pathogenesis and patient-to-patient heterogeneity in responses. These models are already improving our understanding of the mechanisms of action of antivirals and immune modulators. We discuss how closer collaboration between the experimentalists, clinicians and modelers could result in more predictive models which may guide therapies for viral infections, improving survival and leading to faster and more complete recovery.

Viral Load Kinetics of Severe Acute Respiratory Syndrome Coronavirus 2 in Hospitalized Individuals With Coronavirus Disease 2019

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) kinetics remain understudied, including the impact of remdesivir. In hospitalized individuals, peak sputum viral load occurred in week 2 of symptoms, whereas viremia peaked within 1 week of symptom-onset, suggesting early systemic seeding of SARS-CoV-2. Remdesivir treatment was associated with faster viral decay.

Modeling Within-Host Dynamics of SARS-CoV-2 Infection: A Case Study in Ferrets

The pre-clinical development of antiviral agents involves experimental trials in animals and ferrets as an animal model for the study of SARS-CoV-2. Here, we used mathematical models and experimental data to characterize the within-host infection dynamics of SARS-CoV-2 in ferrets. We also performed a global sensitivity analysis of model parameters impacting the characteristics of the viral infection. We provide estimates of the viral dynamic parameters in ferrets, such as the infection rate, the virus production rate, the infectious virus proportion, the infected cell death rate, the virus clearance rate, as well as other related characteristics, including the basic reproduction number, pre-peak infectious viral growth rate, post-peak infectious viral decay rate, pre-peak infectious viral doubling time, post-peak infectious virus half-life, and the target cell loss in the respiratory tract. These parameters and indices are not significantly different between animals infected with viral strains isolated from the environment and isolated from human hosts, indicating a potential for transmission from fomites. While the infection period in ferrets is relatively short, the similarity observed between our results and previous results in humans supports that ferrets can be an appropriate animal model for SARS-CoV-2 dynamics-related studies, and our estimates provide helpful information for such studies.

Comparing antiviral strategies against COVID-19 via multiscale within-host modelling

Within-host models of COVID-19 infection dynamics enable the merits of different forms of antiviral therapy to be assessed in individual patients. A stochastic agent-based model of COVID-19 intracellular dynamics is introduced here, that incorporates essential steps of the viral life cycle targeted by treatment options. Integration of model predictions with an intercellular ODE model of within-host infection dynamics, fitted to patient data, generates a generic profile of disease progression in patients that have recovered in the absence of treatment. This is contrasted with the profiles obtained after variation of model parameters pertinent to the immune response, such as effector cell and antibody proliferation rates, mimicking disease progression in immunocompromised patients. These profiles are then compared with disease progression in the presence of antiviral and convalescent plasma therapy against COVID-19 infections. The model reveals that using both therapies in combination can be very effective in reducing the length of infection, but these synergistic effects decline with a delayed treatment start. Conversely, early treatment with either therapy alone can actually increase the duration of infection, with infectious virions still present after the decline of other markers of infection. This suggests that usage of these treatments should remain carefully controlled in a clinical environment.