Mathematical modeling provides kinetic details of the human immune response to vaccination

Appropriate sampling and long follow-up are required to rigorously evaluate longevity of humoral memory after Vaccination

One of the goals of vaccination is to induce long-term immunity against the infection and/or disease. However, evaluating the duration of protection following vaccination often requires long-term follow-ups that can conflict with the desire to rapidly publish results. Arunachalam et al. JCI 2023 followed individuals receiving third or fourth dose of mRNA COVID19 vaccines for up to 6 months and in finding that the levels of SARS-CoV2-specific antibodies (Abs) declined with similar rates for the two groups came to the conclusion that additional boosting is unnecessary to prolong immunity to SARS-CoV-2. However, this may be premature conclusion to make. Accordingly, we demonstrate that measuring Ab levels at 3 time points and only for a short (up to 6 month) duration does not allow to accurately and rigorously evaluate the long-term half-life of vaccine-induced Abs. By using the data from a cohort of blood donors followed for several years, we show that after re-vaccination with vaccinia virus (VV), VV-specific Abs decay bi-phasically and even the late decay rate exceeds the true slow loss rate of humoral memory observed years prior to the boosting. We argue that mathematical modeling should be used to better optimize sampling schedules to provide more reliable advice about the duration of humoral immunity after repeated vaccinations.

Estimating immunity with mathematical models for SARS-CoV-2 after COVID-19 vaccination

Tools that can be used to estimate antibody waning following COVID-19 vaccinations can facilitate an understanding of the current immune status of the population. In this study, a two-compartment-based mathematical model is formulated to describe the dynamics of the anti-SARS-CoV-2 antibody in healthy adults using serially measured waning antibody concentration data obtained in a prospective cohort study of 673 healthcare providers vaccinated with two doses of BNT162b2 vaccine. The datasets of 165 healthcare providers and 292 elderly patients with or without hemodialysis were used for external validation. Internal validation of the model demonstrated 97.0% accuracy, and external validation of the datasets of healthcare workers, hemodialysis patients, and nondialysis patients demonstrated 98.2%, 83.3%, and 83.8% accuracy, respectively. The internal and external validations demonstrated that this model also fits the data of various populations with or without underlying illnesses. Furthermore, using this model, we developed a smart device application that can rapidly calculate the timing of negative seroconversion.

Antibody Mediated Intercommunication of Germinal Centers

Antibody diversification and selection of B cells occur in dynamic structures called germinal centers (GCs). Passively administered soluble antibodies regulate the GC response by masking the antigen displayed on follicular dendritic cells (FDCs). This suggests that GCs might intercommunicate via naturally produced soluble antibodies, but the role of such GC-GC interactions is unknown. In this study, we performed in silico simulations of interacting GCs and predicted that intense interactions by soluble antibodies limit the magnitude and lifetime of GC responses. With asynchronous GC onset, we observed a higher inhibition of late formed GCs compared to early ones. We also predicted that GC-GC interactions can lead to a bias in the epitope recognition even in the presence of equally dominant epitopes due to differences in founder cell composition or initiation timing of GCs. We show that there exists an optimal range for GC-GC interaction strength that facilitates the affinity maturation towards an incoming antigenic variant during an ongoing GC reaction. These findings suggest that GC-GC interactions might be a contributing factor to the unexplained variability seen among individual GCs and a critical factor in the modulation of GC response to antigenic variants during viral infections.

Estimation of the in vivo neutralization potency of eCD4Ig and conditions for AAV-mediated production for SHIV long-term remission

The engineered protein eCD4Ig has emerged as a promising approach to achieve HIV remission in the absence of antiviral therapy. eCD4Ig neutralizes nearly all HIV-1 isolates and induces antibody-dependent cell-mediated cytotoxicity (ADCC) in vitro. To characterize the in vivo antiviral neutralization and possible ADCC effects of eCD4Ig, we fit mathematical models to eCD4Ig, anti–eCD4Ig-drug antibody (ADA), and viral load kinetics from healthy and simian-human immunodeficiency virus AD8 (SHIV-AD8) infected nonhuman primates that were treated with single or sequentially dosed eCD4Ig passive administrations. Our model predicts that eCD4Ig transiently decreases SHIV viral loads due to neutralization only with an in vivo IC₅₀ of ~25 μg/ml but with limited effect due to ADA. Simulations suggest that endogenous, continuous expression of eCD4Ig at levels greater than 10⁵ μg/day, as is possible with Adeno-associated virus (AAV) vector-based production, could overcome the diminishing effects of ADA and allow for long-term remission of SHIV viremia in nonhuman primates.

Multiple Treatment Cycles of Neural Stem Cell Delivered Oncolytic Adenovirus for the Treatment of Glioblastoma

Tumor tropic neural stem cells (NSCs) can improve the anti-tumor efficacy of oncovirotherapy agents by protecting them from rapid clearance by the immune system and delivering them to multiple distant tumor sites. We recently completed a first-in-human trial assessing the safety of a single intracerebral dose of NSC-delivered CRAd-Survivin-pk7 (NSC.CRAd-S-pk7) combined with radiation and chemotherapy in newly diagnosed high-grade glioma patients. The maximum feasible dose was determined to be 150 million NSC.CRAd-Sp-k7 (1.875 × 1011 viral particles). Higher doses were not assessed due to volume limitations for intracerebral administration and the inability to further concentrate the study agent. It is possible that therapeutic efficacy could be maximized by administering even higher doses. Here, we report IND-enabling studies in which an improvement in treatment efficacy is achieved in immunocompetent mice by administering multiple treatment cycles intracerebrally. The results imply that pre-existing immunity does not preclude therapeutic benefits attainable by administering multiple rounds of an oncolytic adenovirus directly into the brain.

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.

Predictive Markers of Immunogenicity and Efficacy for Human Vaccines

Vaccines represent one of the major advances of modern medicine. Despite the many successes of vaccination, continuous efforts to design new vaccines are needed to fight "old" pandemics, such as tuberculosis and malaria, as well as emerging pathogens, such as Zika virus and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Vaccination aims at reaching sterilizing immunity, however assessing vaccine efficacy is still challenging and underscores the need for a better understanding of immune protective responses. Identifying reliable predictive markers of immunogenicity can help to select and develop promising vaccine candidates during early preclinical studies and can lead to improved, personalized, vaccination strategies. A systems biology approach is increasingly being adopted to address these major challenges using multiple high-dimensional technologies combined with in silico models. Although the goal is to develop predictive models of vaccine efficacy in humans, applying this approach to animal models empowers basic and translational vaccine research. In this review, we provide an overview of vaccine immune signatures in preclinical models, as well as in target human populations. We also discuss high-throughput technologies used to probe vaccine-induced responses, along with data analysis and computational methodologies applied to the predictive modeling of vaccine efficacy.

Validation of a yellow fever vaccine model using data from primary vaccination in children and adults, re-vaccination and dose-response in adults and studies with immunocompromised individuals

BACKGROUND

An effective yellow fever (YF) vaccine has been available since 1937. Nevertheless, questions regarding its use remain poorly understood, such as the ideal dose to confer immunity against the disease, the need for a booster dose, the optimal immunisation schedule for immunocompetent, immunosuppressed, and pediatric populations, among other issues. This work aims to demonstrate that computational tools can be used to simulate different scenarios regarding YF vaccination and the immune response of individuals to this vaccine, thus assisting the response of some of these open questions.

RESULTS

This work presents the computational results obtained by a mathematical model of the human immune response to vaccination against YF. Five scenarios were simulated: primovaccination in adults and children, booster dose in adult individuals, vaccination of individuals with autoimmune diseases under immunomodulatory therapy, and the immune response to different vaccine doses. Where data were available, the model was able to quantitatively replicate the levels of antibodies obtained experimentally. In addition, for those scenarios where data were not available, it was possible to qualitatively reproduce the immune response behaviours described in the literature.

CONCLUSIONS

Our simulations show that the minimum dose to confer immunity against YF is half of the reference dose. The results also suggest that immunological immaturity in children limits the induction and persistence of long-lived plasma cells are related to the antibody decay observed experimentally. Finally, the decay observed in the antibody level after ten years suggests that a booster dose is necessary to keep immunity against YF.

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.

A model for establishment, maintenance and reactivation of the immune response after vaccination against Ebola virus

The 2014-2016 Ebola outbreak in West Africa has triggered accelerated development of several preventive vaccines against Ebola virus. Under the EBOVAC1 consortium, three phase I studies were carried out to assess safety and immunogenicity of a two-dose heterologous vaccination regimen developed by Janssen Vaccines and Prevention in collaboration with Bavarian Nordic. To describe the immune response induced by the two-dose heterologous vaccine regimen, we propose a mechanistic ODE based model, which takes into account the role of immunological memory. We perform identifiability and sensitivity analysis of the proposed model to establish which kind of biological data are ideally needed in order to accurately estimate parameters, and additionally, which of those are non-identifiable based on the available data. Antibody concentrations data from phase I studies have been used to calibrate the model and show its ability in reproducing the observed antibody dynamics. Together with other factors, the establishment of an effective and reactive immunological memory is of pivotal importance for several prophylactic vaccines. We show that introducing a memory compartment in our calibrated model allows to evaluate the magnitude of the immune response induced by a booster dose and its long-term persistence afterwards.

Dynamics of the Humoral Immune Response to a Prime-Boost Ebola Vaccine: Quantification and Sources of Variation

The Ebola vaccine based on Ad26.ZEBOV/MVA-BN-Filo prime-boost regimens is being evaluated in multiple clinical trials. The long-term immune response to the vaccine is unknown, including factors associated with the response and variability around the response. We analyzed data from three phase 1 trials performed by the EBOVAC1 Consortium in four countries: the United Kingdom, Kenya, Tanzania, and Uganda. Participants were randomized into four groups based on the interval between prime and boost immunizations (28 or 56 days) and the sequence in which Ad26.ZEBOV and MVA-BN-Filo were administered. Consecutive enzyme-linked immunosorbent assay (ELISA) measurements of the IgG binding antibody concentrations against the Kikwit glycoprotein (GP) were available for 177 participants to assess the humoral immune response up to 1 year postprime. Using a mathematical model for the dynamics of the humoral response, from 7 days after the boost immunization up to 1 year after the prime immunization, we estimated the durability of the antibody response and the influence of different factors on the dynamics of the humoral response. Ordinary differential equations (ODEs) described the dynamics of antibody response and two populations of antibody-secreting cells (ASCs), short-lived (SL) and long-lived (LL). Parameters of the ODEs were estimated using a population approach. We estimated that half of the LL ASCs could persist for at least 5 years. The vaccine regimen significantly affected the SL ASCs and the antibody peak but not the long-term response. The LL ASC compartment dynamics differed significantly by geographic regions analyzed, with a higher long-term antibody persistence in European subjects. These differences could not be explained by the observed differences in cellular immune response.IMPORTANCE With no available licensed vaccines or therapies, the West African Ebola virus disease epidemic of 2014 to 2016 caused 11,310 deaths. Following this outbreak, the development of vaccines has been accelerated. Combining different vector-based vaccines as heterologous regimens could induce a durable immune response, assessed through antibody concentrations. Based on data from phase 1 trials in East Africa and Europe, the dynamics of the humoral immune response from 7 days after the boost immunization onwards were modeled to estimate the durability of the response and understand its variability. Antibody production is maintained by a population of long-lived cells. Estimation suggests that half of these cells can persist for at least 5 years in humans. Differences in prime-boost vaccine regimens affect only the short-term immune response. Geographical differences in long-lived cell dynamics were inferred, with higher long-term antibody concentrations induced in European participants.

Characterising antibody kinetics from multiple influenza infection and vaccination events in ferrets

The strength and breadth of an individual's antibody repertoire is an important predictor of their response to influenza infection or vaccination. Although progress has been made in understanding qualitatively how repeated exposures shape the antibody mediated immune response, quantitative understanding remains limited. We developed a set of mathematical models describing short-term antibody kinetics following influenza infection or vaccination and fit them to haemagglutination inhibition (HI) titres from 5 groups of ferrets which were exposed to different combinations of trivalent inactivated influenza vaccine (TIV with or without adjuvant), A/H3N2 priming inoculation and post-vaccination A/H1N1 inoculation. We fit models with various immunological mechanisms that have been empirically observed but have not previously been included in mathematical models of antibody landscapes, including: titre ceiling effects, antigenic seniority and exposure-type specific cross reactivity. Based on the parameter estimates of the best supported models, we describe a number of key immunological features. We found quantifiable differences in the degree of homologous and cross-reactive antibody boosting elicited by different exposure types. Infection and adjuvanted vaccination generally resulted in strong, broadly reactive responses whereas unadjuvanted vaccination resulted in a weak, narrow response. We found that the order of exposure mattered: priming with A/H3N2 improved subsequent vaccine response, and the second dose of adjuvanted vaccination resulted in substantially greater antibody boosting than the first. Either antigenic seniority or a titre ceiling effect were included in the two best fitting models, suggesting a role for a mechanism describing diminishing antibody boosting with repeated exposures. Although there was considerable uncertainty in our estimates of antibody waning parameters, our results suggest that both short and long term waning were present and would be identifiable with a larger set of experiments. These results highlight the potential use of repeat exposure animal models in revealing short-term, strain-specific immune dynamics of influenza.

Mathematical modelling of contact dermatitis from nickel and chromium

Dermal exposure to metal allergens can lead to irritant and allergic contact dermatitis (ACD). In this paper we present a mathematical model of the absorption of metal ions, hexavalent chromium and nickel, into the viable epidermis and compare the localised irritant and T-lymphocyte (T-cell) mediated immune responses. The model accounts for the spatial-temporal variation of skin health, extra and intracellular allergen concentrations, innate immune cells, T-cells, cytokine signalling and lymph node activity up to about 6 days after contact with these metals; repair processes associated with withdrawal of exposure to both metals is not considered in the current model, being assumed secondary during the initial phases of exposure. Simulations of the resulting system of PDEs are studied in one-dimension, i.e. across skin depth, and three-dimensional scenarios with the aim of comparing the responses to the two ions in the cases of first contact (no T-cells initially present) and second contact (T-cells initially present). The results show that on continuous contact, chromium ions elicit stronger skin inflammation, but for nickel, subsequent re-exposure stimulates stronger responses due to an accumulation of cytotoxic T-cell mediated responses which characterise ACD. Furthermore, the surface area of contact to these metals has little effect on the speed of response, whilst sensitivity is predicted to increase with the thickness of skin. The modelling approach is generic and should be applicable to describe contact dermatitis from a wide range of allergens.

Defining Kinetic Properties of HIV-Specific CD8⁺ T-Cell Responses in Acute Infection

Multiple lines of evidence indicate that CD8 + T cells are important in the control of HIV-1 (HIV) replication. However, CD8 + T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8 + T-cell responses induced during HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8 + T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8 + T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8 + T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8 + T cells in the chronic infection. The breadth of HIV-specific CD8 + T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8 + T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8 + T-cell responses and the presence of intra- and interclonal competition between multiple CD8 + T-cell responses; such competition may limit the magnitude of CD8 + T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8 + T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.

Using vaccine Immunostimulation/Immunodynamic modelling methods to inform vaccine dose decision-making

Unlike drug dose optimisation, mathematical modelling has not been applied to vaccine dose finding. We applied a novel Immunostimulation/Immunodynamic mathematical modelling framework to translate multi-dose TB vaccine immune responses from mice, to predict most immunogenic dose in humans. Data were previously collected on IFN-γ secreting CD4+ T cells over time for novel TB vaccines H56 and H1 adjuvanted with IC31 in mice (1 dose groups (0.1-1.5 and 15 μg H56 + IC31), 45 mice) and humans (1 dose (50 μg H56/H1 + IC31), 18 humans). A two-compartment mathematical model, describing the dynamics of the post-vaccination IFN-γ T cell response, was fitted to mouse and human data, separately, using nonlinear mixed effects methods. We used these fitted models and a vaccine dose allometric scaling assumption, to predict the most immunogenic human dose. Based on the changes in model parameters by mouse H56 + IC31 dose and by varying the H56 dose allometric scaling factor between mouse and humans, we established that, at a late time point (224 days) doses of 0.8-8 μg H56 + IC31 in humans may be the most immunogenic. A 0.8-8 μg of H-series TB vaccines in humans, may be as, or more, immunogenic, as larger doses. The Immunostimulation/Immunodynamic mathematical modelling framework is a novel, and potentially revolutionary tool, to predict most immunogenic vaccine doses, and accelerate vaccine development.

Influenza Virus Infection Model With Density Dependence Supports Biphasic Viral Decay

Mathematical models that describe infection kinetics help elucidate the time scales, effectiveness, and mechanisms underlying viral growth and infection resolution. For influenza A virus (IAV) infections, the standard viral kinetic model has been used to investigate the effect of different IAV proteins, immune mechanisms, antiviral actions, and bacterial coinfection, among others. We sought to further define the kinetics of IAV infections by infecting mice with influenza A/PR8 and measuring viral loads with high frequency and precision over the course of infection. The data highlighted dynamics that were not previously noted, including viral titers that remain elevated for several days during mid-infection and a sharp 4–5 log₁₀ decline in virus within 1 day as the infection resolves. The standard viral kinetic model, which has been widely used within the field, could not capture these dynamics. Thus, we developed a new model that could simultaneously quantify the different phases of viral growth and decay with high accuracy. The model suggests that the slow and fast phases of virus decay are due to the infected cell clearance rate changing as the density of infected cells changes. To characterize this model, we fit the model to the viral load data, examined the parameter behavior, and connected the results and parameters to linear regression estimates. The resulting parameters and model dynamics revealed that the rate of viral clearance during resolution occurs 25 times faster than the clearance during mid-infection and that small decreases to this rate can significantly prolong the infection. This likely reflects the high efficiency of the adaptive immune response. The new model provides a well-characterized representation of IAV infection dynamics, is useful for analyzing and interpreting viral load dynamics in the absence of immunological data, and gives further insight into the regulation of viral control.

A qualitatively validated mathematical-computational model of the immune response to the yellow fever vaccine

Background

Although a safe and effective yellow fever vaccine was developed more than 80 years ago, several issues regarding its use remain unclear. For example, what is the minimum dose that can provide immunity against the disease? A useful tool that can help researchers answer this and other related questions is a computational simulator that implements a mathematical model describing the human immune response to vaccination against yellow fever.

Methods

This work uses a system of ten ordinary differential equations to represent a few important populations in the response process generated by the body after vaccination. The main populations include viruses, APCs, CD8+ T cells, short-lived and long-lived plasma cells, B cells and antibodies.

Results

In order to qualitatively validate our model, four experiments were carried out, and their computational results were compared to experimental data obtained from the literature. The four experiments were: a) simulation of a scenario in which an individual was vaccinated against yellow fever for the first time; b) simulation of a booster dose ten years after the first dose; c) simulation of the immune response to the yellow fever vaccine in individuals with different levels of naïve CD8+ T cells; and d) simulation of the immune response to distinct doses of the yellow fever vaccine.

Conclusions

This work shows that the simulator was able to qualitatively reproduce some of the experimental results reported in the literature, such as the amount of antibodies and viremia throughout time, as well as to reproduce other behaviors of the immune response reported in the literature, such as those that occur after a booster dose of the vaccine.

Quantification of plasma cell dynamics using mathematical modelling

Plasma cells (PCs) are the main antibody-producing cells in humans. They are long-lived so that specific antibodies against either pathogens or vaccines are produced for decades. PC longevity is attributed to specific areas within the bone marrow micro-environment, the so-called 'niche', providing the cells with required growth and survival factors. With antigen encounters, e.g. infection or vaccination, new PCs are generated and home to the bone marrow where they compete with resident PCs for the niche. We propose a parametrized mathematical model describing healthy PC dynamics in the bone marrow. The model accounts for competition for the niche between newly produced PCs owing to vaccination and resident PCs. Mathematical analysis and numerical simulations of the model allow explanation of the recovery of PC homoeostasis after a vaccine-induced perturbation, and the fraction of vaccine-specific PCs inside the niche. The model enables quantification of the niche-related dynamics of PCs, i.e. the duration of PC transition into the niche and the impact of different rates for PC transitions into and out of the niche on the observed cell dynamics. Ultimately, it provides a potential basis for further investigations in health and disease.

What Controls the Acute Viral Infection Following Yellow Fever Vaccination?

Does target cell depletion, innate immunity, or adaptive immunity play the dominant role in controlling primary acute viral infections? Why do some individuals have higher peak virus titers than others? Answering these questions is a basic problem in immunology and can be particularly difficult in humans due to limited data, heterogeneity in responses in different individuals, and limited ability for experimental manipulation. We address these questions for infections following vaccination with the live attenuated yellow fever virus (YFV-17D) by analyzing viral load data from 80 volunteers. Using a mixed effects modeling approach, we find that target cell depletion models do not fit the data as well as innate or adaptive immunity models. Examination of the fits of the innate and adaptive immunity models to the data allows us to select a minimal model that gives improved fits by widely used model selection criteria (AICc and BIC) and explains why it is hard to distinguish between the innate and adaptive immunity models. We then ask why some individuals have over 1000-fold higher virus titers than others and find that most of the variation arises from differences in the initial/maximum growth rate of the virus in different individuals.

On the Role of CD8+ T Cells in Determining Recovery Time from Influenza Virus Infection

Myriad experiments have identified an important role for CD8⁺ T cell response mechanisms in determining recovery from influenza A virus infection. Animal models of influenza infection further implicate multiple elements of the immune response in defining the dynamical characteristics of viral infection. To date, influenza virus models, while capturing particular aspects of the natural infection history, have been unable to reproduce the full gamut of observed viral kinetic behavior in a single coherent framework. Here, we introduce a mathematical model of influenza viral dynamics incorporating innate, humoral, and cellular immune components and explore its properties with a particular emphasis on the role of cellular immunity. Calibrated against a range of murine data, our model is capable of recapitulating observed viral kinetics from a multitude of experiments. Importantly, the model predicts a robust exponential relationship between the level of effector CD8⁺ T cells and recovery time, whereby recovery time rapidly decreases to a fixed minimum recovery time with an increasing level of effector CD8⁺ T cells. We find support for this relationship in recent clinical data from influenza A (H7N9) hospitalized patients. The exponential relationship implies that people with a lower level of naive CD8⁺ T cells may receive significantly more benefit from induction of additional effector CD8⁺ T cells arising from immunological memory, itself established through either previous viral infection or T cell-based vaccines.

Broad CTL Response in Early HIV Infection Drives Multiple Concurrent CTL Escapes

Recent studies have highlighted the ability of HIV to escape from cytotoxic T lymphocyte (CTL) responses that concurrently target multiple viral epitopes. Yet, the viral dynamics involved in such escape are incompletely understood. Previous analyses have made several strong assumptions regarding HIV escape from CTL responses such as independent or non-concurrent escape from individual CTL responses. Using experimental data from evolution of HIV half genomes in four patients we observe concurrent viral escape from multiple CTL responses during early infection (first 100 days of infection), providing confirmation of a recent result found in a study of one HIV-infected patient. We show that current methods of estimating CTL escape rates, based on the assumption of independent escapes, are biased and perform poorly when CTL escape proceeds concurrently at multiple epitopes. We propose a new method for analyzing longitudinal sequence data to estimate the rate of CTL escape across multiple epitopes; this method involves few parameters and performs well in simulation studies. By applying our novel method to experimental data, we find that concurrent multiple escapes occur at rates between 0.03 and 0.4 day⁻¹, a relatively broad range that reflects uncertainty due to sparse sampling and wide ranges of parameter values. However, we show that concurrent escape at rates 0.1–0.2 day⁻¹ across multiple epitopes is consistent with our patient datasets.

Since the early 1990s, cytotoxic T lymphocytes (CTLs) have been known to play an important role in HIV infection with CTLs targeting HIV epitopes and, in turn, HIV escapes arising through mutations in the targeted epitopes. Over the past decade, studies have shown that CTL responses concurrently target multiple HIV epitopes, yet the effect of concurrent responses on HIV dynamics and evolution is not well understood. Through an analysis of patient datasets and a novel statistical method, we show that during early HIV infection concurrent CTL responses drive concurrent HIV escapes at multiple epitopes with significant pressure, suggesting a complex picture in which HIV simultaneously explores multiple mutational pathways to escape from broad and potent CTL response.

Modeling Influenza Virus Infection: A Roadmap for Influenza Research

Influenza A virus (IAV) infection represents a global threat causing seasonal outbreaks and pandemics. Additionally, secondary bacterial infections, caused mainly by Streptococcus pneumoniae, are one of the main complications and responsible for the enhanced morbidity and mortality associated with IAV infections. In spite of the significant advances in our knowledge of IAV infections, holistic comprehension of the interplay between IAV and the host immune response (IR) remains largely fragmented. During the last decade, mathematical modeling has been instrumental to explain and quantify IAV dynamics. In this paper, we review not only the state of the art of mathematical models of IAV infection but also the methodologies exploited for parameter estimation. We focus on the adaptive IR control of IAV infection and the possible mechanisms that could promote a secondary bacterial coinfection. To exemplify IAV dynamics and identifiability issues, a mathematical model to explain the interactions between adaptive IR and IAV infection is considered. Furthermore, in this paper we propose a roadmap for future influenza research. The development of a mathematical modeling framework with a secondary bacterial coinfection, immunosenescence, host genetic factors and responsiveness to vaccination will be pivotal to advance IAV infection understanding and treatment optimization.