Incorporating Intracellular Processes in Virus Dynamics Models.

In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus-host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.

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.

Mathematical Models of Early Hepatitis B Virus Dynamics in Humanized Mice.

Analyzing the impact of the adaptive immune response during acute hepatitis B virus (HBV) infection is essential for understanding disease progression and control. Here we developed mathematical models of HBV infection which either lack terms for adaptive immune responses, or assume adaptive immune responses in the form of cytolytic immune killing, non-cytolytic immune cure, or non-cytolytic-mediated block of viral production. We validated the model that does not include immune responses against temporal serum hepatitis B DNA (sHBV) and temporal serum hepatitis B surface-antigen (HBsAg) experimental data from mice engrafted with human hepatocytes (HEP). Moreover, we validated the immune models against sHBV and HBsAg experimental data from mice engrafted with HEP and human immune system (HEP/HIS). As expected, the model that does not include adaptive immune responses matches the observed high sHBV and HBsAg concentrations in all HEP mice. By contrast, while all immune response models predict reduction in sHBV and HBsAg concentrations in HEP/HIS mice, the Akaike Information Criterion cannot discriminate between non-cytolytic cure (resulting in a class of cells refractory to reinfection) and antiviral block functions (of up to 99 % viral production 1-3 weeks following peak viral load). We can, however, reject cytolytic killing, as it can only match the sHBV and HBsAg data when we predict unrealistic levels of hepatocyte loss.

The effect of model structure and data availability on Usutu virus dynamics at three biological scales.

Understanding the epidemiology of emerging pathogens, such as Usutu virus (USUV) infections, requires systems investigation at each scale involved in the host-virus transmission cycle, from individual bird infections, to bird-to-vector transmissions, and to USUV incidence in bird and vector populations. For new pathogens field data are sparse, and predictions can be aided by the use of laboratory-type inoculation and transmission experiments combined with dynamical mathematical modelling. In this study, we investigated the dynamics of two strains of USUV by constructing mathematical models for the within-host scale, bird-to-vector transmission scale and vector-borne epidemiological scale. We used individual within-host infectious virus data and per cent mosquito infection data to predict USUV incidence in birds and mosquitoes. We addressed the dependence of predictions on model structure, data uncertainty and experimental design. We found that uncertainty in predictions at one scale change predicted results at another scale. We proposed in silico experiments that showed that sampling every 12 hours ensures practical identifiability of the within-host scale model. At the same time, we showed that practical identifiability of the transmission scale functions can only be improved under unrealistically high sampling regimes. Instead, we proposed optimal experimental designs and suggested the types of experiments that can ensure identifiability at the transmission scale and, hence, induce robustness in predictions at the epidemiological scale.

Deficient Generation of Spike-Specific Long-Lived Plasma Cells in the Bone Marrow After Severe Acute Respiratory Syndrome Coronavirus 2 Infection.

Generation of a stable long-lived plasma cell (LLPC) population is the sine qua non of durable antibody responses after vaccination or infection. We studied 20 individuals with a prior coronavirus disease 2019 infection and characterized the antibody response using bone marrow aspiration and plasma samples. We noted deficient generation of spike-specific LLPCs in the bone marrow after severe acute respiratory syndrome coronavirus 2 infection. Furthermore, while the regression model explained 98% of the observed variance in anti-tetanus immunoglobulin G levels based on LLPC enzyme-linked immunospot assay, we were unable to fit the same model with anti-spike antibodies, again pointing to the lack of LLPC contribution to circulating anti-spike antibodies.

TCDD and CH223191 Alter T Cell Balance but Fail to Induce Anti-Inflammatory Response in Adult Lupus Mice.

Aryl hydrocarbon receptor (AhR) responds to endogenous and exogenous ligands as a cytosolic receptor, transcription factor, and E3 ubiquitin ligase. Several studies support an anti-inflammatory effect of AhR activation. However, exposure to the AhR agonist 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) during early stages of development results in an autoimmune phenotype and exacerbates lupus. The effects of TCDD on lupus in adults with pre-existing autoimmunity have not been described. We present novel evidence that AhR stimulation by TCDD alters T cell responses but fails to impact lupus-like disease using an adult mouse model. Interestingly, AhR antagonist CH223191 also changed T cell balance in our model. We next developed a conceptual framework for identifying cellular and molecular factors that contribute to physiological outcomes in lupus and created models that describe cytokine dynamics that were fed into a system of differential equations to predict the kinetics of T follicular helper (Tfh) and regulatory T (Treg) cell populations. The model predicted that Tfh cells expanded to larger values following TCDD exposure compared with vehicle and CH223191. Following the initial elevation, both Tfh and Treg cell populations continuously decayed over time. A function based on the ratio of predicted Treg/Tfh cells showed that Treg cells exceed Tfh cells in all groups, with TCDD and CH223191 showing lower Treg/Tfh cell ratios than the vehicle and that the ratio is relatively constant over time. We conclude that AhR ligands did not induce an anti-inflammatory response to attenuate autoimmunity in adult lupus mice. This study challenges the dogma that TCDD supports an immunosuppressive phenotype.

Prolonged viral shedding from noninfectious individuals confounds wastewater-based epidemiology.

Wastewater surveillance has been widely used to track and estimate SARS-CoV-2 incidence. While both infectious and recovered individuals shed virus into wastewater, epidemiological inferences using wastewater often only consider the viral contribution from the former group. Yet, the persistent shedding in the latter group could confound wastewater-based epidemiological inference, especially during the late stage of an outbreak when the recovered population outnumbers the infectious population. To determine the impact of recovered individuals' viral shedding on the utility of wastewater surveillance, we develop a quantitative framework that incorporates population-level viral shedding dynamics, measured viral RNA in wastewater, and an epidemic dynamic model. We find that the viral shedding from the recovered population can become higher than the infectious population after the transmission peak, which leads to a decrease in the correlation between wastewater viral RNA and case report data. Furthermore, the inclusion of recovered individuals' viral shedding into the model predicts earlier transmission dynamics and slower decreasing trends in wastewater viral RNA. The prolonged viral shedding also induces a potential delay in the detection of new variants due to the time needed to generate enough new cases for a significant viral signal in an environment dominated by virus shed by the recovered population. This effect is most prominent toward the end of an outbreak and is greatly affected by both the recovered individuals' shedding rate and shedding duration. Our results suggest that the inclusion of viral shedding from non-infectious recovered individuals into wastewater surveillance research is important for precision epidemiology.

Identifiability of parameters in mathematical models of SARS-CoV-2 infections in humans.

Determining accurate estimates for the characteristics of the severe acute respiratory syndrome coronavirus 2 in the upper and lower respiratory tracts, by fitting mathematical models to data, is made difficult by the lack of measurements early in the infection. To determine the sensitivity of the parameter estimates to the noise in the data, we developed a novel two-patch within-host mathematical model that considered the infection of both respiratory tracts and assumed that the viral load in the lower respiratory tract decays in a density dependent manner and investigated its ability to match population level data. We proposed several approaches that can improve practical identifiability of parameters, including an optimal experimental approach, and found that availability of viral data early in the infection is of essence for improving the accuracy of the estimates. Our findings can be useful for designing interventions.

Modeling within-host and aerosol dynamics of SARS-CoV-2: The relationship with infectiousness.

The relationship between transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the amount of virus present in the proximity of a susceptible host is not understood. Here, we developed a within-host and aerosol mathematical model and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions.

Modeling the Influence of Vaccine Administration on COVID-19 Testing Strategies.

Vaccination is considered the best strategy for limiting and eliminating the COVID-19 pandemic. The success of this strategy relies on the rate of vaccine deployment and acceptance across the globe. As these efforts are being conducted, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is continuously mutating, which leads to the emergence of variants with increased transmissibility, virulence, and resistance to vaccines. One important question is whether surveillance testing is still needed in order to limit SARS-CoV-2 transmission in a vaccinated population. In this study, we developed a multi-scale mathematical model of SARS-CoV-2 transmission in a vaccinated population and used it to predict the role of testing in an outbreak with variants of increased transmissibility. We found that, for low transmissibility variants, testing was most effective when vaccination levels were low to moderate and its impact was diminished when vaccination levels were high. For high transmissibility variants, widespread vaccination was necessary in order for testing to have a significant impact on preventing outbreaks, with the impact of testing having maximum effects when focused on the non-vaccinated population.

Modeling the dynamics of Usutu virus infection in birds.

Usutu virus is an emerging zoonotic flavivirus causing high avian mortality rates and occasional severe neurological disorders in humans. Several virus strains are co-circulating and the differences in their characteristics and avian pathogenesis levels are still unknown. In this study, we use within-host mathematical models to characterize the mechanisms responsible for virus expansion and clearance in juvenile chickens challenged with four Usutu virus strains. We find heterogeneity between the virus strains, with the time between cell infection and viral production varying between 16 h and 23 h, the infected cell lifespan varying between 48 min and 9.5 h, and the basic reproductive number R0 varying between 12.05 and 19.49. The strains with high basic reproductive number have short infected cell lifespan, indicative of immune responses. The virus strains with low basic reproductive number have lower viral peaks and longer lasting viremia, due to lower infection rates and high infected cell lifespan. We discuss how the host and virus heterogeneities may differently impact the public health threat presented by these virus strains.

Quantification of the Tradeoff between Test Sensitivity and Test Frequency in a COVID-19 Epidemic-A Multi-Scale Modeling Approach.

Control strategies that employ real time polymerase chain reaction (RT-PCR) tests for the diagnosis and surveillance of COVID-19 epidemic are inefficient in fighting the epidemic due to high cost, delays in obtaining results, and the need of specialized personnel and equipment for laboratory processing. Cheaper and faster alternatives, such as antigen and paper-strip tests, have been proposed. They return results rapidly, but have lower sensitivity thresholds for detecting virus. To quantify the effects of the tradeoffs between sensitivity, cost, testing frequency, and delay in test return on the overall course of an outbreak, we built a multi-scale immuno-epidemiological model that connects the virus profile of infected individuals with transmission and testing at the population level. We investigated various randomized testing strategies and found that, for fixed testing capacity, lower sensitivity tests with shorter return delays slightly flatten the daily incidence curve and delay the time to the peak daily incidence. However, compared with RT-PCR testing, they do not always reduce the cumulative case count at half a year into the outbreak. When testing frequency is increased to account for the lower cost of less sensitive tests, we observe a large reduction in cumulative case counts, from 55.4% to as low as 1.22% half a year into the outbreak. The improvement is preserved even when the testing budget is reduced by one half or one third. Our results predict that surveillance testing that employs low-sensitivity tests at high frequency is an effective tool for epidemic control.

Pathogenesis and shedding of Usutu virus in juvenile chickens.

Usutu virus (USUV; family: Flaviviridae, genus: Flavivirus), is an emerging zoonotic arbovirus that causes severe neuroinvasive disease in humans and has been implicated in the loss of breeding bird populations in Europe. USUV is maintained in an enzootic cycle between ornithophilic mosquitos and wild birds. As a member of the Japanese encephalitis serocomplex, USUV is closely related to West Nile virus (WNV) and St. Louis encephalitis virus (SLEV), both neuroinvasive arboviruses endemic in wild bird populations in the United States. An avian model for USUV is essential to understanding zoonotic transmission. Here we describe the first avian models of USUV infection with the development of viremia. Juvenile commercial ISA Brown chickens were susceptible to infection by multiple USUV strains with evidence of cardiac lesions. Juvenile chickens from two chicken lines selected for high (HAS) or low (LAS) antibody production against sheep red blood cells showed markedly different responses to USUV infection. Morbidity and mortality were observed in the LAS chickens, but not HAS chickens. LAS chickens had significantly higher viral titers in blood and other tissues, as well as oral secretions, and significantly lower development of neutralizing antibody responses compared to HAS chickens. Mathematical modelling of virus-host interactions showed that the viral clearance rate is a stronger mitigating factor for USUV viremia than neutralizing antibody response in this avian model. These chicken models provide a tool for further understanding USUV pathogenesis in birds and evaluating transmission dynamics between avian hosts and mosquito vectors.

Bistable Mathematical Model of Neutrophil Migratory Patterns After LPS-Induced Epigenetic Reprogramming.

The highly controlled migration of neutrophils toward the site of an infection can be altered when they are trained with lipopolysaccharides (LPS), with high dose LPS enhancing neutrophil migratory pattern toward the bacterial derived source signal and super-low dose LPS inducing either migration toward an intermediary signal or dysregulation and oscillatory movement. Empirical studies that use microfluidic chemotaxis-chip devices with two opposing chemoattractants showed differential neutrophil migration after challenge with different LPS doses. The epigenetic alterations responsible for changes in neutrophil migratory behavior are unknown. We developed two mathematical models that evaluate the mechanistic interactions responsible for neutrophil migratory decision-making when exposed to competing chemoattractants and challenged with LPS. The first model, which considers the interactions between the receptor densities of two competing chemoattractants, their kinases, and LPS, displayed bistability between high and low ratios of primary to intermediary chemoattractant receptor densities. In particular, at equilibrium, we observe equal receptor densities for low LPS (< 15ng/mL); and dominance of receptors for the primary chemoattractant for high LPS (> 15ng/mL). The second model, which included additional interactions with an extracellular signal-regulated kinase in both phosphorylated and non-phosphorylated forms, has an additional dynamic outcome, oscillatory dynamics for both receptors, as seen in the data. In particular, it found equal receptor densities in the absence of oscillation for super-low and high LPS challenge (< 0.4 and 1.1 376 ng/mL). Predicting the mechanisms and the type of external LPS challenge responsible for neutrophils migration toward pro-inflammatory chemoattractants, migration toward pro-tolerant chemoattractants, or oscillatory movement is necessary knowledge in designing interventions against immune diseases, such as sepsis.

Early events in hepatitis B infection: the role of inoculum dose.

The relationship between the inoculum dose and the ability of the pathogen to invade the host is poorly understood. Experimental studies in non-human primates infected with different inoculum doses of hepatitis B virus have shown a non-monotonic relationship between dose magnitude and infection outcome, with high and low doses leading to 100% liver infection and intermediate doses leading to less than 0.1% liver infection, corresponding to CD4 T-cell priming. Since hepatitis B clearance is CD8 T-cell mediated, the question of whether the inoculum dose influences CD8 T-cell dynamics arises. To help answer this question, we developed a mathematical model of virus-host interaction following hepatitis B virus infection. Our model explains the experimental data well, and predicts that the inoculum dose affects both the timing of the CD8 T-cell expansion and the quality of its response, especially the non-cytotoxic function. We find that a low-dose challenge leads to slow CD8 T-cell expansion, weak non-cytotoxic functions, and virus persistence; high- and medium-dose challenges lead to fast CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance; while a super-low-dose challenge leads to delayed CD8 T-cell expansion, strong cytotoxic and non-cytotoxic function, and virus clearance. These results are useful for designing immune cell-based interventions.

Understanding the antiviral effects of RNAi-based therapy in HBeAg-positive chronic hepatitis B infection.

The RNA interference (RNAi) drug ARC-520 was shown to be effective in reducing serum hepatitis B virus (HBV) DNA, hepatitis B e antigen (HBeAg) and hepatitis B surface antigen (HBsAg) in HBeAg-positive patients treated with a single dose of ARC-520 and daily nucleosidic analogue (entecavir). To provide insights into HBV dynamics under ARC-520 treatment and its efficacy in blocking HBV DNA, HBsAg, and HBeAg production we developed a multi-compartmental pharmacokinetic-pharamacodynamic model and calibrated it with frequent measured HBV kinetic data. We showed that the time-dependent single dose ARC-520 efficacies in blocking HBsAg and HBeAg are more than 96% effective around day 1, and slowly wane to 50% in 1-4 months. The combined single dose ARC-520 and entecavir effect on HBV DNA was constant over time, with efficacy of more than 99.8%. The observed continuous HBV DNA decline is entecavir mediated, the strong but transient HBsAg and HBeAg decays are ARC-520 mediated. The modeling framework may help assess ongoing RNAi drug development for hepatitis B virus infection.

Mathematical model of broadly reactive plasma cell production.

Strain-specific plasma cells are capable of producing neutralizing antibodies that are essential for clearance of challenging pathogens. These neutralizing antibodies also function as a main defense against disease establishment in a host. However, when a rapidly mutating pathogen infects a host, successful control of the invasion requires shifting the production of plasma cells from strain-specific to broadly reactive. In this study, we develop a mathematical model of germinal center dynamics and use it to predict the events that lead to improved breadth of the plasma cell response. We examine scenarios that lead to germinal centers that are composed of B-cells that come from a single strain-specific clone, a single broadly reactive clone or both clones. We find that the initial B-cell clonal composition, T-follicular helper cell signaling, increased rounds of productive somatic hypermutation, and B-cell selection strength are among the mechanisms differentiating between strain-specific and broadly reactive plasma cell production during infections. Understanding the contribution of these factors to emergence of breadth may assist in boosting broadly reactive plasma cells production.

Mathematical investigation of HBeAg seroclearance.

Spontaneous or drug-induced loss of hepatitis B e antigen is considered a beneficial event in the disease progression of chronic hepatitis B virus infections. Mathematical models of within-host interactions are proposed; which provide insight into hepatitis B e antibody formation, its influence on hepatitis B e antigen seroclearance, and reversion of anergic cytotoxic immune responses. They predict that antibody expansion causes immune activation and hepatitis B e antigen seroclearance. Quantification of the time between antibody expansion and hepatitis B e antigen seroclearance in the presence and absence of treatment shows that potent short-term treatment speeds up the time between antibody expansion and hepatitis B e antigen seroclearance. The monthly hepatocyte turnover during this time can be increased or decreased by treatment depending on the amount of core promoter or precore mutated virus produced. The results can inform human interventions.

Modeling the Bistable Dynamics of the Innate Immune System.

The size of primary challenge with lipopolysaccharide induces changes in the innate immune cells phenotype between pro-inflammatory and pro-tolerant states when facing a secondary lipopolysaccharide challenge. To determine the molecular mechanisms governing this differential response, we propose a mathematical model for the interaction between three proteins involved in the immune cell decision making: IRAK-1, PI3K, and RelB. The mutual inhibition of IRAK-1 and PI3K in the model leads to bistable dynamics. By using the levels of RelB as indicative of strength of the immune responses, we connect the size of different primary lipopolysaccharide doses to the differential phenotypical outcomes following a secondary challenge. We further predict under what circumstances the primary LPS dose does not influence the response to a secondary challenge. Our results can be used to guide treatments for patients with either autoimmune disease or compromised immune system.

Modeling the dynamics of hepatitis B infection, immunity, and drug therapy.

Hepatitis B virus infection is the cause of liver diseases such as cirrhosis and liver cancer. Understanding the host-virus mechanisms that mediate virus pathogenesis can help design better preventive measures for disease control. Mathematical models have been used alongside experimental data to provide insight into the role of immune responses during the acute and chronic hepatitis B infections as well as virus dynamics following administration of combined drug therapy. In this paper, we review several modeling studies on virus-host interactions during acute infection, the virus-host characteristics responsible for transition to chronic disease, and the efficacy and optimal control measures of drug therapy. We conclude by presenting our opinion on the future directions of the field.