Influenza Virus Infection Model With Density Dependence Supports Biphasic Viral Decay

Identifiability investigation of within-host models of acute virus infection

Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we use four mathematical models of influenza A infection with increased degrees of biological realism. We test the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refine the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we present insight into the sources of uncertainty in parameter estimation and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.

How robust are estimates of key parameters in standard viral dynamic models?

Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.

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.

Modeling resistance to the broadly neutralizing antibody PGT121 in people living with HIV-1

PGT121 is a broadly neutralizing antibody in clinical development for the treatment and prevention of HIV-1 infection via passive administration. PGT121 targets the HIV-1 V3-glycan and demonstrated potent antiviral activity in a phase I clinical trial. Resistance to PGT121 monotherapy rapidly occurred in the majority of participants in this trial with the sampled rebound viruses being entirely resistant to PGT121 mediated neutralization. However, two individuals experienced long-term ART-free viral suppression following antibody infusion and retained sensitivity to PGT121 upon viral rebound. Here, we develop mathematical models of the HIV-1 dynamics during this phase I clinical trial. We utilize these models to understand the dynamics leading to PGT121 resistance and to identify the mechanisms driving the observed long-term viral control. Our modeling highlights the importance of the relative fitness difference between PGT121 sensitive and resistant subpopulations prior to treatment. Specifically, by fitting our models to data, we identify the treatment-induced competitive advantage of previously existing or newly generated resistant population as a primary driver of resistance. Finally, our modeling emphasizes the high neutralization ability of PGT121 in both participants who exhibited long-term viral control.

Differential lung gene expression changes in C57BL/6 and DBA/2 mice carrying an identical functional Mx1 gene reveals crucial differences in the host response

BACKGROUND

Influenza virus infections represent a major global health problem. The dynamin-like GTPase MX1 is an interferon-dependent antiviral host protein that confers resistance to influenza virus infections. Infection models in mice are an important experimental system to understand the host response and susceptibility to developing severe disease following influenza infections. However, almost all laboratory mouse strains carry a non-functional Mx1 gene whereas humans have a functional MX1 gene. Most studies in mice have been performed with strains carrying a non-functional Mx1 gene. It is therefore very important to investigate the host response in mouse strains with a functional Mx1 gene.

RESULTS

Here, we analyzed the host response to influenza virus infections in two congenic mouse strains carrying the functional Mx1 gene from the A2G strain. B6.A2G-Mx1r/r(B6-Mx1r/r) mice are highly resistant to influenza A virus (IAV) H1N1 infections. On the other hand, D2(B6).A2G-Mx1r/r(D2-Mx1r/r) mice, although carrying a functional Mx1 gene, were highly susceptible, exhibited rapid weight loss, and died. We performed gene expression analysis using RNAseq from infected lungs at days 3 and 5 post-infection (p.i.) of both mouse strains to identify genes and pathways that were differentially expressed between the two mouse strains. The susceptible D2-Mx1r/r mice showed a high viral replication already at day 3 p.i. and exhibited a much higher number of differentially expressed genes (DEGs) and many DEGs had elevated expression levels compared to B6-Mx1r/r mice. On the other hand, some DEGs were specifically up-regulated only in B6-Mx1r/r mice at day 3 p.i., many of which were related to host immune response functions.

CONCLUSIONS

From these results, we conclude that at early times of infection, D2-Mx1r/r mice showed a very high and rapid replication of the virus, which resulted in lung damage and a hyperinflammatory response leading to death. We hypothesize that the activation of certain immune response genes was missing and that others, especially Mx1, were expressed at a time in D2-Mx1r/r mice when the virus had already massively spread in the lung and were thus not able anymore to protect them from severe disease. Our study represents an important addition to previously published studies in mouse models and contributes to a better understanding of the molecular pathways and genes that protect against severe influenza disease.

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.

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.

Antiviral foods in the battle against viral infections: Understanding the molecular mechanism

Viruses produce a variety of illnesses, which may also cause acute respiratory syndrome. All viral infections, including COVID-19, are associated with the strength of the immune system. Till now, traditional medicine or vaccines for most viral diseases have not been effective. Antiviral and immune-boosting diets may provide defense against viral diseases by lowering the risk of infection and assisting rapid recovery. The purpose of this review was to gather, analyze, and present data based on scientific evidence in order to provide an overview of the mechanistic insights of antiviral bioactive metabolites. We have covered a wide range of food with antiviral properties in this review, along with their potential mechanism of action against viral infections. Additionally, the opportunities and challenges of using antiviral food have been critically reviewed. Bioactive plant compounds, not only help in maintaining the body's normal physiological mechanism and good health but are also essential for improving the body's immunity and therefore can be effective against viral diseases. These agents fight viral diseases either by incorporating the body's defense mechanism or by enhancing the cell's immune system. Regular intake of antiviral foods may prevent future pandemic and consumption of these antiviral agents with traditional medicine may reduce the severity of viral diseases. Therefore, the synergistic effect of antiviral foods and medication needs to be investigated.

An explanation for SARS-CoV-2 rebound after Paxlovid treatment

In a fraction of SARS-CoV-2 infected individuals treated with the oral antiviral Paxlovid, the virus rebounds following treatment. The mechanism driving rebound is not understood. Here, we show that viral dynamic models based on the hypothesis that Paxlovid treatment near the time of symptom onset halts the depletion of target cells, but may not fully eliminate the virus, which can lead to viral rebound. We also show that the occurrence of viral rebound is sensitive to model parameters, and the time treatment is initiated, which may explain why only a fraction of individuals develop viral rebound. Finally, the models are used to test the therapeutic effects of two alternative treatment schemes. These findings also provide a possible explanation for rebounds following other antiviral treatments for SARS-CoV-2.

How Interactions during Viral-Viral Coinfection Can Shape Infection Kinetics

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

How Interactions During Viral-Viral Coinfection Can Shape Infection Kinetics

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

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.

The race to understand immunopathology in COVID-19: Perspectives on the impact of quantitative approaches to understand within-host interactions

The COVID-19 pandemic has revealed the need for the increased integration of modelling and data analysis to public health, experimental, and clinical studies. Throughout the first two years of the pandemic, there has been a concerted effort to improve our understanding of the within-host immune response to the SARS-CoV-2 virus to provide better predictions of COVID-19 severity, treatment and vaccine development questions, and insights into viral evolution and the impacts of variants on immunopathology. Here we provide perspectives on what has been accomplished using quantitative methods, including predictive modelling, population genetics, machine learning, and dimensionality reduction techniques, in the first 26 months of the COVID-19 pandemic approaches, and where we go from here to improve our responses to this and future pandemics.

Dissecting Phenotype from Genotype with Clinical Isolates of SARS-CoV-2 First Wave Variants

The emergence and availability of closely related clinical isolates of SARS-CoV-2 offers a unique opportunity to identify novel nonsynonymous mutations that may impact phenotype. Global sequencing efforts show that SARS-CoV-2 variants have emerged and then been replaced since the beginning of the pandemic, yet we have limited information regarding the breadth of variant-specific host responses. Using primary cell cultures and the K18-hACE2 mouse, we investigated the replication, innate immune response, and pathology of closely related, clinical variants circulating during the first wave of the pandemic. Mathematical modeling of the lung viral replication of four clinical isolates showed a dichotomy between two B.1. isolates with significantly faster and slower infected cell clearance rates, respectively. While isolates induced several common immune host responses to infection, one B.1 isolate was unique in the promotion of eosinophil-associated proteins IL-5 and CCL11. Moreover, its mortality rate was significantly slower. Lung microscopic histopathology suggested further phenotypic divergence among the five isolates showing three distinct sets of phenotypes: (i) consolidation, alveolar hemorrhage, and inflammation, (ii) interstitial inflammation/septal thickening and peribronchiolar/perivascular lymphoid cells, and (iii) consolidation, alveolar involvement, and endothelial hypertrophy/margination. Together these findings show divergence in the phenotypic outcomes of these clinical isolates and reveal the potential importance of nonsynonymous mutations in nsp2 and ORF8.

Increased virus dissemination leads to enhanced lung injury but not inflammation during influenza-associated secondary bacterial infection

Secondary bacterial infections increase influenza-related morbidity and mortality, particularly if acquired after 5-7 d from the viral onset. Synergistic host responses and direct pathogen-pathogen interactions are thought to lead to a state of hyperinflammation, but the kinetics of the lung pathology have not yet been detailed, and identifying the contribution of different mechanisms to disease is difficult because these may change over time. To address this gap, we examined host-pathogen and lung pathology dynamics following a secondary bacterial infection initiated at different time points after influenza within a murine model. We then used a mathematical approach to quantify the increased virus dissemination in the lung, coinfection time-dependent bacterial kinetics, and virus-mediated and postbacterial depletion of alveolar macrophages. The data showed that viral loads increase regardless of coinfection timing, which our mathematical model predicted and histomorphometry data confirmed was due to a robust increase in the number of infected cells. Bacterial loads were dependent on the time of coinfection and corresponded to the level of IAV-induced alveolar macrophage depletion. Our mathematical model suggested that the additional depletion of these cells following the bacterial invasion was mediated primarily by the virus. Contrary to current belief, inflammation was not enhanced and did not correlate with neutrophilia. The enhanced disease severity was correlated to inflammation, but this was due to a nonlinearity in this correlation. This study highlights the importance of dissecting nonlinearities during complex infections and demonstrated the increased dissemination of virus within the lung during bacterial coinfection and simultaneous modulation of immune responses during influenza-associated bacterial pneumonia.

Modelling the response to vaccine in non-human primates to define SARS-CoV-2 mechanistic correlates of protection

The definition of correlates of protection is critical for the development of next-generation SARS-CoV-2 vaccine platforms. Here, we propose a model-based approach for identifying mechanistic correlates of protection based on mathematical modelling of viral dynamics and data mining of immunological markers. The application to three different studies in non-human primates evaluating SARS-CoV-2 vaccines based on CD40-targeting, two-component spike nanoparticle and mRNA 1273 identifies and quantifies two main mechanisms that are a decrease of rate of cell infection and an increase in clearance of infected cells. Inhibition of RBD binding to ACE2 appears to be a robust mechanistic correlate of protection across the three vaccine platforms although not capturing the whole biological vaccine effect. The model shows that RBD/ACE2 binding inhibition represents a strong mechanism of protection which required significant reduction in blocking potency to effectively compromise the control of viral replication.

Modeling the Viral Kinetics of Influenza A During Infection in Humans

This study explores the natural control system in the body for responding to exposure to the Influenza A virus. More specifically, it delves into the development of a model to simulate the responses of target uninfected cell counts, infected cell counts, and viral titers. There are two particular models of interest: a delayed model that incorporates the brief inactive period for newly infected cells, and a non-delayed model reflecting only infected cells without delay after initial infection. Both models are commonly used in the literature and the benefits of each model are studied and explained. We generate Simulink models for both the delayed and non-delayed sets of ordinary differential equations (ODEs) to simulate responses to different viral titer impulses. Additionally, this study aims to extrapolate these models to the case for a vaccinated individual. To do this, we modify the viral clearance rate and infected cell death rate of our initial model to account for the improved immune response generated by vaccines.

Modeling explains prolonged SARS-CoV-2 nasal shedding relative to lung shedding in remdesivir treated rhesus macaques

In clinical trials, remdesivir decreased recovery time in hospitalized patients with SARS- CoV-2 and prevented hospitalization when given early during infection, despite not reducing nasal viral loads. In rhesus macaques, early remdesivir prevented pneumonia and lowered lung viral loads, but viral loads increased in nasal passages after five days. We developed mathematical models to explain these results. Our model raises the hypotheses that: 1) in contrast to nasal passages viral load monotonically decreases in lungs during therapy because of infection-dependent generation of refractory cells, 2) slight reduction in lung viral loads with an imperfect agent may result in a substantial decrease in lung damage, and 3) increases in nasal viral load may occur due to a blunting of peak viral load which decreases the intensity of the innate immune response. We demonstrate that a higher potency drug could lower viral loads in nasal passages and lung.

Efficacy of the Sentinox Spray in Reducing Viral Load in Mild COVID-19 and Its Virucidal Activity against Other Respiratory Viruses: Results of a Randomized Controlled Trial and an In Vitro Study

Sentinox (STX) is an acid-oxidizing solution containing hypochlorous acid in spray whose virucidal activity against SARS-CoV-2 has been demonstrated. In this paper, results of a randomized controlled trial (RCT) on the efficacy of STX in reducing viral load in mild COVID-19 patients (NCT04909996) and a complementary in vitro study on its activity against different respiratory viruses are reported. In the RCT, 57 patients were randomized (1:1:1) to receive STX three (STX-3) or five (STX-5) times/day plus standard therapy or standard therapy only (controls). Compared with controls, the log₁₀ load reduction in groups STX-3 and STX-5 was 1.02 (p = 0.14) and 0.18 (p = 0.80), respectively. These results were likely driven by outliers with extreme baseline viral loads. When considering subjects with baseline cycle threshold values of 20–30, STX-3 showed a significant (p = 0.016) 2.01 log₁₀ reduction. The proportion of subjects that turned negative by the end of treatment (day 5) was significantly higher in the STX-3 group than in controls, suggesting a shorter virus clearance time. STX was safe and well-tolerated. In the in vitro study, ≥99.9% reduction in titers against common respiratory viruses was observed. STX is a safe device with large virucidal spectrum and may reduce viral loads in mild COVID-19 patients.

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.

Divergent COVID-19 Disease Trajectories Predicted by a DAMP-Centered Immune Network Model

COVID-19 presentations range from mild to moderate through severe disease but also manifest with persistent illness or viral recrudescence. We hypothesized that the spectrum of COVID-19 disease manifestations was a consequence of SARS-CoV-2-mediated delay in the pathogen-associated molecular pattern (PAMP) response, including dampened type I interferon signaling, thereby shifting the balance of the immune response to be dominated by damage-associated molecular pattern (DAMP) signaling. To test the hypothesis, we constructed a parsimonious mechanistic mathematical model. After calibration of the model for initial viral load and then by varying a few key parameters, we show that the core model generates four distinct viral load, immune response and associated disease trajectories termed “patient archetypes”, whose temporal dynamics are reflected in clinical data from hospitalized COVID-19 patients. The model also accounts for responses to corticosteroid therapy and predicts that vaccine-induced neutralizing antibodies and cellular memory will be protective, including from severe COVID-19 disease. This generalizable modeling framework could be used to analyze protective and pathogenic immune responses to diverse viral infections.

Personalized Virus Load Curves for Acute Viral Infections

We introduce an explicit function that describes virus-load curves on a patient-specific level. This function is based on simple and intuitive model parameters. It allows virus load analysis of acute viral infections without solving a full virus load dynamic model. We validate our model on data from mice influenza A, human rhinovirus data, human influenza A data, and monkey and human SARS-CoV-2 data. We find wide distributions for the model parameters, reflecting large variability in the disease outcomes between individuals. Further, we compare the virus load function to an established target model of virus dynamics, and we provide a new way to estimate the exponential growth rates of the corresponding infection phases. The virus load function, the target model, and the exponential approximations show excellent fits for the data considered. Our virus-load function offers a new way to analyze patient-specific virus load data, and it can be used as input for higher level models for the physiological effects of a virus infection, for models of tissue damage, and to estimate patient risks.

Quantifying dose-, strain-, and tissue-specific kinetics of parainfluenza virus infection

Human parainfluenza viruses (HPIVs) are a leading cause of acute respiratory infection hospitalization in children, yet little is known about how dose, strain, tissue tropism, and individual heterogeneity affects the processes driving growth and clearance kinetics. Longitudinal measurements are possible by using reporter Sendai viruses, the murine counterpart of HPIV 1, that express luciferase, where the insertion location yields a wild-type (rSeV-luc(M-F*)) or attenuated (rSeV-luc(P-M)) phenotype. Bioluminescence from individual animals suggests that there is a rapid increase in expression followed by a peak, biphasic clearance, and resolution. However, these kinetics vary between individuals and with dose, strain, and whether the infection was initiated in the upper and/or lower respiratory tract. To quantify the differences, we translated the bioluminescence measurements from the nasopharynx, trachea, and lung into viral loads and used a mathematical model together a nonlinear mixed effects approach to define the mechanisms distinguishing each scenario. The results confirmed a higher rate of virus production with the rSeV-luc(M-F*) virus compared to its attenuated counterpart, and suggested that low doses result in disproportionately fewer infected cells. The analyses indicated faster infectivity and infected cell clearance rates in the lung and that higher viral doses, and concomitantly higher infected cell numbers, resulted in more rapid clearance. This parameter was also highly variable amongst individuals, which was particularly evident during infection in the lung. These critical differences provide important insight into distinct HPIV dynamics, and show how bioluminescence data can be combined with quantitative analyses to dissect host-, virus-, and dose-dependent effects.

Human parainfluenza viruses (HPIVs) cause acute respiratory infections and can lead to the hospitalization of children. HPIV infection severity may vary due to dose, strain, patient, and whether the infection initiates within the upper or lower respiratory tract. There is a need to determine how the rates of virus spread and clearance change in different infection scenarios in order to better understand varying clinical manifestations. The significance of our research is in identifying the dominant mechanisms driving strain-, dose-, and tissue-specific HPIV infection kinetics, and in pairing bioluminescence data with quantitative analyses to determine how the same virus can yield patient-specific outcomes. This work enhances our understanding of HPIV infection and broadens our knowledge viral dynamics in the upper and lower respiratory tracts.

A multi-approach and multi-scale platform to model CD4+ T cells responding to infections

Immune responses rely on a complex adaptive system in which the body and infections interact at multiple scales and in different compartments. We developed a modular model of CD4+ T cells, which uses four modeling approaches to integrate processes at three spatial scales in different tissues. In each cell, signal transduction and gene regulation are described by a logical model, metabolism by constraint-based models. Cell population dynamics are described by an agent-based model and systemic cytokine concentrations by ordinary differential equations. A Monte Carlo simulation algorithm allows information to flow efficiently between the four modules by separating the time scales. Such modularity improves computational performance and versatility and facilitates data integration. We validated our technology by reproducing known experimental results, including differentiation patterns of CD4+ T cells triggered by different combinations of cytokines, metabolic regulation by IL2 in these cells, and their response to influenza infection. In doing so, we added multi-scale insights to single-scale studies and demonstrated its predictive power by discovering switch-like and oscillatory behaviors of CD4+ T cells that arise from nonlinear dynamics interwoven across three scales. We identified the inflamed lymph node’s ability to retain naive CD4+ T cells as a key mechanism in generating these emergent behaviors. We envision our model and the generic framework encompassing it to serve as a tool for understanding cellular and molecular immunological problems through the lens of systems immunology.

CD4+ T cells are a key part of the adaptive immune system. They differentiate into different phenotypes to carry out different functions. They do so by secreting molecules called cytokines to regulate other immune cells. Multi-scale modeling can potentially explain their emergent behaviors by integrating biological phenomena occurring at different spatial (intracellular, cellular, and systemic), temporal, and organizational scales (signal transduction, gene regulation, metabolism, cellular behaviors, and cytokine transport). We built a computational platform by combining disparate modeling frameworks (compartmental ordinary differential equations, agent-based modeling, Boolean network modeling, and constraint-based modeling). We validated the platform’s ability to predict CD4+ T cells’ emergent behaviors by reproducing their differentiation patterns, metabolic regulation, and population dynamics in response to influenza infection. We then used it to predict and explain novel switch-like and oscillatory behaviors for CD4+ T cells. On the basis of these results, we believe that our multi-approach and multi-scale platform will be a valuable addition to the systems immunology toolkit. In addition to its immediate relevance to CD4+ T cells, it also has the potential to become the foundation of a virtual immune system.

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.

COVID-19 virtual patient cohort suggests immune mechanisms driving disease outcomes

To understand the diversity of immune responses to SARS-CoV-2 and distinguish features that predispose individuals to severe COVID-19, we developed a mechanistic, within-host mathematical model and virtual patient cohort. Our results suggest that virtual patients with low production rates of infected cell derived IFN subsequently experienced highly inflammatory disease phenotypes, compared to those with early and robust IFN responses. In these in silico patients, the maximum concentration of IL-6 was also a major predictor of CD8+ T cell depletion. Our analyses predicted that individuals with severe COVID-19 also have accelerated monocyte-to-macrophage differentiation mediated by increased IL-6 and reduced type I IFN signalling. Together, these findings suggest biomarkers driving the development of severe COVID-19 and support early interventions aimed at reducing inflammation.

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.

Treatment timing shifts the benefits of short and long antibiotic treatment over infection

Antibiotics are the major tool for treating bacterial infections. Rising antibiotic resistance, however, calls for a better use of antibiotics. While classical recommendations favor long and aggressive treatments, more recent clinical trials advocate for moderate regimens. In this debate, two axes of 'aggression' have typically been conflated: treatment intensity (dose) and treatment duration. The third dimension of treatment timing along each individual's infection course has rarely been addressed. By using a generic mathematical model of bacterial infection controlled by immune response, we examine how the relative effectiveness of antibiotic treatment varies with its timing, duration and antibiotic kill rate. We show that short or long treatments may both be beneficial depending on treatment onset, the target criterion for success and on antibiotic efficacy. This results from the dynamic trade-off between immune response build-up and resistance risk in acute, self-limiting infections, and uncertainty relating symptoms to infection variables. We show that in our model early optimal treatments tend to be 'short and strong', while late optimal treatments tend to be 'mild and long'. This suggests a shift in the aggression axis depending on the timing of treatment. We find that any specific optimal treatment schedule may perform more poorly if evaluated by other criteria, or under different host-specific conditions. Our results suggest that major advances in antibiotic stewardship must come from a deeper empirical understanding of bacterial infection processes in individual hosts. To guide rational therapy, mathematical models need to be constrained by data, including a better quantification of personal disease trajectory in humans. Lay summary: Bacterial infections are becoming more difficult to treat worldwide because bacteria are becoming resistant to the antibiotics used. Addressing this problem requires a better understanding of how treatment along with other host factors impact antibiotic resistance. Until recently, most theoretical research has focused on the importance of antibiotic dosing on antibiotic resistance, however, duration and timing of treatment remain less explored. Here, we use a mathematical model of a generic bacterial infection to study three aspects of treatment: treatment dose/efficacy (defined by the antibiotic kill rate), duration, and timing, and their impact on several infection endpoints. We show that short and long treatment success strongly depends on when treatment begins (defined by the symptom threshold), the target criterion to optimize, and on antibiotic efficacy. We find that if administered early in an infection, "strong and short" therapy performs better, while if treatment begins at higher bacterial densities, a "mild and long" course of antibiotics is favored. In the model host immune defenses are key in preventing relapses, controlling antibiotic resistant bacteria and increasing the effectiveness of moderate intervention. In order to improve rational treatments of human infections, we call for a better quantification of individual disease trajectories in bacteria-immunity space.

Potency and timing of antiviral therapy as determinants of duration of SARS-CoV-2 shedding and intensity of inflammatory response

To affect the COVID-19 pandemic, lifesaving antiviral therapies must be identified. The number of clinical trials that can be performed is limited. We developed mathematical models to project multiple therapeutic approaches. Our models recapitulate off-treatment viral dynamics and predict a three-phase immune response. Simulated treatment with remdesivir, selinexor, neutralizing antibodies, or cellular immunotherapy demonstrates that rapid viral elimination is possible if in vivo potency is sufficiently high. Therapies dosed soon after peak viral load when symptoms develop may decrease shedding duration and immune response intensity but have little effect on viral area under the curve (AUC), which is driven by high early viral loads. Potent therapy dosed before viral peak during presymptomatic infection could lower AUC. Drug resistance may emerge with a moderately potent agent dosed before viral peak. Our results support early treatment for COVID-19 if shedding duration, not AUC, is most predictive of clinical severity.

Potency and timing of antiviral therapy as determinants of duration of SARS-CoV-2 shedding and intensity of inflammatory response

To affect the COVID-19 pandemic, lifesaving antiviral therapies must be identified. The number of clinical trials that can be performed is limited. We developed mathematical models to project multiple therapeutic approaches. Our models recapitulate off-treatment viral dynamics and predict a three-phase immune response. Simulated treatment with remdesivir, selinexor, neutralizing antibodies, or cellular immunotherapy demonstrates that rapid viral elimination is possible if in vivo potency is sufficiently high. Therapies dosed soon after peak viral load when symptoms develop may decrease shedding duration and immune response intensity but have little effect on viral area under the curve (AUC), which is driven by high early viral loads. Potent therapy dosed before viral peak during presymptomatic infection could lower AUC. Drug resistance may emerge with a moderately potent agent dosed before viral peak. Our results support early treatment for COVID-19 if shedding duration, not AUC, is most predictive of clinical severity.

Modeling Competitive Mixtures With the Lotka-Volterra Framework for More Complex Fitness Assessment Between Strains

With increasing resolution of microbial diversity at the genomic level, experimental and modeling frameworks that translate such diversity into phenotypes are highly needed. This is particularly important when comparing drug-resistant with drug-sensitive pathogen strains, when anticipating epidemiological implications of microbial diversity, and when designing control measures. Classical approaches quantify differences between microbial strains using the exponential growth model, and typically report a selection coefficient for the relative fitness differential between two strains. The apparent simplicity of such approaches comes with the costs of limiting the range of biological scenarios that can be captured, and biases strain fitness estimates to polarized extremes of competitive exclusion. Here, we propose a mathematical and statistical framework based on the Lotka-Volterra model, that can capture frequency-dependent competition between microbial strains within-host and upon transmission. As a proof-of-concept, the model is applied to a previously-published dataset from in-vivo competitive mixture experiments with influenza strains in ferrets (McCaw et al., 2011). We show that for the same data, our model predicts a scenario of coexistence between strains, and supports a higher bottleneck size in the range of 35–145 virions transmitted from donor to recipient host. Thanks to its simplicity and generality, such framework could be applied to other ecological scenarios of microbial competition, enabling a more complex and nuanced view of possible outcomes between two strains, beyond competitive exclusion.

Chemical kinetics of the development of coronaviral infection in the human body: Critical conditions, toxicity mechanisms, "thermoheliox", and "thermovaccination"

Kinetic modeling of the behavior of complex chemical and biochemical systems is an effective approach to study of the mechanisms of the process. A kinetic model of coronaviral infection development with a description of the dynamic behavior of the main variables, including the concentration of viral particles, affected cells, and pathogenic microflora, is proposed. Changes in the concentration of hydrogen ions in the lungs and the pH -dependence of carbonic anhydrase activity (a key breathing enzyme) are critical. A significant result is the demonstration of an acute bifurcation transition that determines life or system collapse. This transition is connected with exponential growth of concentrations of the process participants and with functioning of the key enzyme carbonic anhydrase in development of toxic effects. Physical and chemical interpretations of the therapeutic effects of the body temperature rise and the potential therapeutic effect of “thermoheliox” (respiration with a thermolized mixture of helium and oxygen) are given. The phenomenon of “thermovaccination” is predicted, which involves stimulation of the immune response by “thermoheliox”.

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The proposed kinetic model describes the dynamics of coronaviral infection development.

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Acidification and pH dependence of key enzymes is discussed as a basis of viral toxicity.

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An acute bifurcation transition of the system to collapse is demonstrated.

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The theory and experimental facts of “thermoheliox” therapy are discussed.

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“Thermovaccination” by “thermoheliox” is predicted.

Reliability of self-sampling for accurate assessment of respiratory virus viral and immunologic kinetics

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic demonstrates the need for accurate and convenient approaches to diagnose and therapeutically monitor respiratory viral infections. We demonstrated that self-sampling with mid-nasal foam swabs is well-tolerated and provides quantitative viral output concordant with flocked swabs. Using longitudinal home-based self-sampling, we demonstrate that nasal cytokine levels correlate and cluster according to immune cell of origin. Periods of stable viral loads are followed by rapid elimination, which could be coupled with cytokine expansion and contraction. Nasal foam swab self-sampling at home provides a precise, mechanistic readout of respiratory virus shedding and local immune responses.

Impaired Geotaxis as a Novel Phenotype of Nora Virus Infection of Drosophila melanogaster

Nora virus (NV) is a picorna-like virus that contains a positive-sense, single-stranded RNA genome. The virus infects Drosophila melanogaster with no known characterized phenotype. In this study, geotaxis assays and longevity analyses were used to determine if Nora virus infection affects D. melanogaster's locomotor ability. In addition, Drosophila C virus (DCV), a well-characterized D. melanogaster virus, was used as a positive control, as it has previously shown a locomotor defect in infected flies. Stocks infected with NV (NV+) and DCV (DCV+) and virus-free (NV-/DCV-) stocks were established. Over a 3-year period, approximately 2,500 virgin female flies were tested for geotaxis and longevity using Kaplan-Meier analyses, as well as the Cox Proportional Hazards regression for survivorship. There was a significant decrease in the geotaxis when the D. melanogaster flies were infected with Nora virus compared to uninfected controls, but no difference was found between DCV+ and NV+ trials. There were not significant differences in longevity between the three groups. This is the first time that a phenotype has been recorded in association with Nora virus infection. Overall, the data demonstrate that geotaxis dysfunction may be a phenotypic hallmark of Nora virus infection.

Safety, tolerability, pharmacokinetics, and antimalarial efficacy of a novel Plasmodium falciparum ATP4 inhibitor SJ733: a first-in-human and induced blood-stage malaria phase 1a/b trial

BACKGROUND

(+)-SJ000557733 (SJ733) is a novel, orally bioavailable inhibitor of Plasmodium falciparum ATP4. In this first-in-human and induced blood-stage malaria phase 1a/b trial, we investigated the safety, tolerability, pharmacokinetics, and antimalarial activity of SJ733 in humans.

METHODS

The phase 1a was a single-centre, dose-escalation, first-in-human study of SJ733 allowing modifications to dose increments and dose-cohort size on the basis of safety and pharmacokinetic results. The phase 1a took place at St Jude Children's Research Hospital and at the University of Tennessee Clinical Research Center (Memphis, TN, USA). Enrolment in more than one non-consecutive dose cohort was allowed with at least 14 days required between doses. Participants were fasted in seven dose cohorts and fed in one 600 mg dose cohort. Single ascending doses of SJ733 (75, 150, 300, 600, 900, or 1200 mg) were administered to participants, who were followed up for 14 days after SJ733 dosing. Phase 1a primary endpoints were safety, tolerability, and pharmacokinetics of SJ733, and identification of an SJ733 dose to test in the induced blood-stage malaria model. The phase 1b was a single-centre, open-label, volunteer infection study using the induced blood-stage malaria model in which fasted participants were intravenously infected with blood-stage P falciparum and subsequently treated with a single dose of SJ733. Phase 1b took place at Q-Pharm (Herston, QLD, Australia) and was initiated only after phase 1a showed that exposure exceeding the threshold minimum exposure could be safely achieved in humans. Participants were inoculated on day 0 with P falciparum-infected human erythrocytes (around 2800 parasites in the 150 mg dose cohort and around 2300 parasites in the 600 mg dose cohort), and parasitaemia was monitored before malaria inoculation, after inoculation, immediately before SJ733 dosing, and then post-dose. Participants were treated with SJ733 within 24 h of reaching 5000 parasites per mL or at a clinical score higher than 6. Phase 1b primary endpoints were calculation of a parasite reduction ratio (PRR₄₈) and parasite clearance half-life, and safety and tolerability of SJ733 (incidence, severity, and drug-relatedness of adverse events). In both phases of the trial, SJ733 hydrochloride salt was formulated as a powder blend in capsules containing 75 mg or 300 mg for oral administration. Healthy men and women (of non-childbearing potential) aged 18-55 years were eligible for both studies. Both studies are registered with ClinicalTrials.gov (NCT02661373 for the phase 1a and NCT02867059 for the phase 1b).

FINDINGS

In the phase 1a, 23 healthy participants were enrolled and received one to three non-consecutive doses of SJ733 between March 14 and Dec 7, 2016. SJ733 was safe and well tolerated at all doses and in fasted and fed conditions. 119 adverse events were recorded: 54 (45%) were unrelated, 63 (53%) unlikely to be related, and two (2%) possibly related to SJ733. In the phase 1b, 17 malaria-naive, healthy participants were enrolled. Seven participants in the 150 mg dose cohort were inoculated and dosed with SJ733. Eight participants in the 600 mg dose cohort were inoculated, but two participants could not be dosed with SJ733. Two additional participants were subsequently inoculated and dosed with SJ733. SJ733 exposure increased proportional to the dose through to the 600 mg dose, then was saturable at higher doses. Fasted participants receiving 600 mg exceeded the target area under the concentration curve extrapolated to infinity (AUC_0-∞) of 13 000 μg × h/L (median AUC_0-∞ 24 283 [IQR 16 135-31 311] μg × h/L, median terminal half-life 17·4 h [IQR 16·1-24·0], and median timepoint at which peak plasma concentration is reached 1·0 h [0·6-1·3]), and this dose was tested in the phase 1b. All 15 participants dosed with SJ733 had at least one adverse event. Of the 172 adverse events recorded, 128 (74%) were mild. The only adverse event attributed to SJ733 was mild bilateral foot paraesthesia that lasted 3·75 h and resolved spontaneously. The most common adverse events were related to malaria. Based on parasite clearance half-life, the derived log₁₀PRR₄₈ and corresponding parasite clearance half-lives were 2·2 (95% CI 2·0-2·5) and 6·47 h (95% CI 5·88-7·18) for 150 mg, and 4·1 (3·7-4·4) and 3·56 h (3·29-3·88) for 600 mg.

INTERPRETATION

The favourable pharmacokinetic, tolerability, and safety profile of SJ733, and rapid antiparasitic effect support its development as a fast-acting component of combination antimalarial therapy.

FUNDING

Global Health Innovative Technology Fund, Medicines for Malaria Venture, and the American Lebanese Syrian Associated Charities.

Reliability of self-sampling for accurate assessment of respiratory virus viral and immunologic kinetics

The SARS-CoV-2 pandemic demonstrates the need for accurate and convenient approaches to diagnose and therapeutically monitor respiratory viral infections. We demonstrated that self-sampling with foam swabs at home is well-tolerated and provides quantitative viral output concordant with flocked swabs. Nasal cytokine levels correlate and cluster according to immune cell of origin. Periods of stable viral loads are followed by rapid elimination, which could be coupled with cytokine expansion and contraction using mathematical models. Nasal foam swab self-sampling at home provides a precise, mechanistic readout of respiratory virus shedding and local immune responses.

Varying Inoculum Dose to Assess the Roles of the Immune Response and Target Cell Depletion by the Pathogen in Control of Acute Viral Infections

It is difficult to determine whether an immune response or target cell depletion by the infectious agent is most responsible for the control of acute primary infection. Both mechanisms can explain the basic dynamics of an acute infection-exponential growth of the pathogen followed by control and clearance-and can also be represented by many different differential equation models. Consequently, traditional model comparison techniques using time series data can be ambiguous or inconclusive. We propose that varying the inoculum dose and measuring the subsequent infectious load can rule out target cell depletion by the pathogen as the main control mechanism. Infectious load can be any measure that is proportional to the number of infected cells, such as viraemia. We show that a twofold or greater change in infectious load is unlikely when target cell depletion controls infection, regardless of the model details. Analyzing previously published data from mice infected with influenza, we find the proportion of lung epithelial cells infected was 21-fold greater (95% confidence interval 14-32) in the highest dose group than in the lowest. This provides evidence in favor of an alternative to target cell depletion, such as innate immunity, in controlling influenza infections in this experimental system. Data from other experimental animal models of acute primary infection have a similar pattern.

PARAMETER AND UNCERTAINTY ESTIMATION FOR DYNAMICAL SYSTEMS USING SURROGATE STOCHASTIC PROCESSES

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical theory with empirical measurements in a statistically coherent way is critical and challenges abound, e.g., ill-posedness of the parameter estimation problem, proper regularization and incorporation of prior knowledge, and computational limitations. To address these issues, we propose a new method for learning parameterized dynamical systems from data. We first customize and fit a surrogate stochastic process directly to observational data, front-loading with statistical learning to respect prior knowledge (e.g., smoothness), cope with challenging data features like heteroskedasticity, heavy tails, and censoring. Then, samples of the stochastic process are used as "surrogate data" and point estimates are computed via ordinary point estimation methods in a modular fashion. Attractive features of this two-step approach include modularity and trivial parallelizability. We demonstrate its advantages on a predator-prey simulation study and on a real-world application involving within-host influenza virus infection data paired with a viral kinetic model, with comparisons to a more conventional Markov chain Monte Carlo (MCMC) based Bayesian approach.

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.

Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis

Influenza A virus is recognized today as one of the most challenging viruses that threatens both human and animal health worldwide. Understanding the control mechanisms of influenza infection and dynamics is crucial and could result in effective future treatment strategies. Many kinetic models based on differential equations have been developed in recent decades to capture viral dynamics within a host. These models differ in their complexity in terms of number of species elements and number of reactions. Here, we present a new approach to understanding the overall structure of twelve influenza A virus infection models and their relationship to each other. To this end, we apply chemical organization theory to obtain a hierarchical decomposition of the models into chemical organizations. The decomposition is based on the model structure (reaction rules) but is independent of kinetic details such as rate constants. We found different types of model structures ranging from two to eight organizations. Furthermore, the model's organizations imply a partial order among models entailing a hierarchy of model, revealing a high model diversity with respect to their long-term behavior. Our methods and results can be helpful in model development and model integration, also beyond the influenza area.

Causes and Consequences of Spatial Within-Host Viral Spread

The spread of viral pathogens both between and within hosts is inherently a spatial process. While the spatial aspects of viral spread at the epidemiological level have been increasingly well characterized, the spatial aspects of viral spread within infected hosts are still understudied. Here, with a focus on influenza A viruses (IAVs), we first review experimental studies that have shed light on the mechanisms and spatial dynamics of viral spread within hosts. These studies provide strong empirical evidence for highly localized IAV spread within hosts. Since mathematical and computational within-host models have been increasingly used to gain a quantitative understanding of observed viral dynamic patterns, we then review the (relatively few) computational modeling studies that have shed light on possible factors that structure the dynamics of spatial within-host IAV spread. These factors include the dispersal distance of virions, the localization of the immune response, and heterogeneity in host cell phenotypes across the respiratory tract. While informative, we find in these studies a striking absence of theoretical expectations of how spatial dynamics may impact the dynamics of viral populations. To mitigate this, we turn to the extensive ecological and evolutionary literature on range expansions to provide informed theoretical expectations. We find that factors such as the type of density dependence, the frequency of long-distance dispersal, specific life history characteristics, and the extent of spatial heterogeneity are critical factors affecting the speed of population spread and the genetic composition of spatially expanding populations. For each factor that we identified in the theoretical literature, we draw parallels to its analog in viral populations. We end by discussing current knowledge gaps related to the spatial component of within-host IAV spread and the potential for within-host spatial considerations to inform the development of disease control strategies.

Validated Models of Immune Response to Virus Infection

Viruses are a main cause of disease worldwide and many are without effective therapeutics or vaccines. A lack of understanding about how host responses work to control viral spread is one factor limiting effective management. How different immune components regulate infection dynamics is beginning to be better understood with the help of mathematical models. These models have been key in discriminating between hypotheses and in identifying rates of virus growth and clearance, dynamical control by different host factors and antivirals, and synergistic interactions during multi-pathogen infections. A recent focus in evaluating model predictions in the laboratory and clinic has illuminate the accuracy of models for a variety of viruses and highlighted the critical nature of theoretical approaches in virology. Here, I discuss recent model-driven exploration of host-pathogen interactions that have illustrated the importance of model validation in establishing the model's predictive capability and in defining new biology.

Host-pathogen kinetics during influenza infection and coinfection: insights from predictive modeling

Influenza virus infections are a leading cause of morbidity and mortality worldwide. This is due in part to the continual emergence of new viral variants and to synergistic interactions with other viruses and bacteria. There is a lack of understanding about how host responses work to control the infection and how other pathogens capitalize on the altered immune state. The complexity of multi-pathogen infections makes dissecting contributing mechanisms, which may be non-linear and occur on different time scales, challenging. Fortunately, mathematical models have been able to uncover infection control mechanisms, establish regulatory feedbacks, connect mechanisms across time scales, and determine the processes that dictate different disease outcomes. These models have tested existing hypotheses and generated new hypotheses, some of which have been subsequently tested and validated in the laboratory. They have been particularly a key in studying influenza-bacteria coinfections and will be undoubtedly be useful in examining the interplay between influenza virus and other viruses. Here, I review recent advances in modeling influenza-related infections, the novel biological insight that has been gained through modeling, the importance of model-driven experimental design, and future directions of the field.