Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

Informing policy via dynamic models: Cholera in Haiti

Public health decisions must be made about when and how to implement interventions to control an infectious disease epidemic. These decisions should be informed by data on the epidemic as well as current understanding about the transmission dynamics. Such decisions can be posed as statistical questions about scientifically motivated dynamic models. Thus, we encounter the methodological task of building credible, data-informed decisions based on stochastic, partially observed, nonlinear dynamic models. This necessitates addressing the tradeoff between biological fidelity and model simplicity, and the reality of misspecification for models at all levels of complexity. We assess current methodological approaches to these issues via a case study of the 2010-2019 cholera epidemic in Haiti. We consider three dynamic models developed by expert teams to advise on vaccination policies. We evaluate previous methods used for fitting these models, and we demonstrate modified data analysis strategies leading to improved statistical fit. Specifically, we present approaches for diagnosing model misspecification and the consequent development of improved models. Additionally, we demonstrate the utility of recent advances in likelihood maximization for high-dimensional nonlinear dynamic models, enabling likelihood-based inference for spatiotemporal incidence data using this class of models. Our workflow is reproducible and extendable, facilitating future investigations of this disease system.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

Plants cope with fluctuating light by frequency-dependent nonphotochemical quenching and cyclic electron transport

In natural environments, plants are exposed to rapidly changing light. Maintaining photosynthetic efficiency while avoiding photodamage requires equally rapid regulation of photoprotective mechanisms. We asked what the operation frequency range of regulation is in which plants can efficiently respond to varying light. Chlorophyll fluorescence, P700, plastocyanin, and ferredoxin responses of wild-types Arabidopsis thaliana were measured in oscillating light of various frequencies. We also investigated the npq1 mutant lacking violaxanthin de-epoxidase, the npq4 mutant lacking PsbS protein, and the mutants crr2-2, and pgrl1ab impaired in different pathways of the cyclic electron transport. The fastest was the PsbS-regulation responding to oscillation periods longer than 10 s. Processes involving violaxanthin de-epoxidase dampened changes in chlorophyll fluorescence in oscillation periods of 2 min or longer. Knocking out the PGR5/PGRL1 pathway strongly reduced variations of all monitored parameters, probably due to congestion in the electron transport. Incapacitating the NDH-like pathway only slightly changed the photosynthetic dynamics. Our observations are consistent with the hypothesis that nonphotochemical quenching in slow light oscillations involves violaxanthin de-epoxidase to produce, presumably, a largely stationary level of zeaxanthin. We interpret the observed dynamics of photosystem I components as being formed in slow light oscillations partially by thylakoid remodeling that modulates the redox rates.

Mathematical Modeling to Guide Experimental Design: T Cell Clustering as a Case Study

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about [Formula: see text] parasites at 2, 4, and 8 h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.

Application of Mathematical Modeling and Computational Tools in the Modern Drug Design and Development Process

The conventional drug discovery approach is an expensive and time-consuming process, but its limitations have been overcome with the help of mathematical modeling and computational drug design approaches. Previously, finding a small molecular candidate as a drug against a disease was very costly and required a long time to screen a compound against a specific target. The development of novel targets and small molecular candidates against different diseases including emerging and reemerging diseases remains a major concern and necessitates the development of novel therapeutic targets as well as drug candidates as early as possible. In this regard, computational and mathematical modeling approaches for drug development are advantageous due to their fastest predictive ability and cost-effectiveness features. Computer-aided drug design (CADD) techniques utilize different computer programs as well as mathematics formulas to comprehend the interaction of a target and drugs. Traditional methods to determine small-molecule candidates as a drug have several limitations, but CADD utilizes novel methods that require little time and accurately predict a compound against a specific disease with minimal cost. Therefore, this review aims to provide a brief insight into the mathematical modeling and computational approaches for identifying a novel target and small molecular candidates for curing a specific disease. The comprehensive review mainly focuses on biological target prediction, structure-based and ligand-based drug design methods, molecular docking, virtual screening, pharmacophore modeling, quantitative structure-activity relationship (QSAR) models, molecular dynamics simulation, and MM-GBSA/MM-PBSA approaches along with valuable database resources and tools for identifying novel targets and therapeutics against a disease. This review will help researchers in a way that may open the road for the development of effective drugs and preventative measures against a disease in the future as early as possible.

Mathematical Modeling Suggests Cooperation of Plant-Infecting Viruses

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

Photosynthesis dynamics and regulation sensed in the frequency domain

Foundations of photosynthesis research have been established mainly by studying the response of plants to changing light, typically to sudden exposure to a constant light intensity after dark acclimation or light flashes. This approach remains valid and powerful, but can be limited by requiring dark acclimation before time-domain measurements and often assumes that rate constants determining the photosynthetic response do not change between dark and light acclimation. We show that these limits can be overcome by measuring plant responses to sinusoidally modulated light of varying frequency. By its nature, such frequency-domain characterization is performed in light-acclimated plants with no need for prior dark acclimation. Amplitudes, phase shifts, and upper harmonic modulation extracted from the data for a wide range of frequencies can target different kinetic domains and regulatory feedbacks. The occurrence of upper harmonic modulation reflects nonlinear phenomena, including photosynthetic regulation. To support these claims, we measured chlorophyll fluorescence emission of the green alga Chlorella sorokiniana in light that was sinusoidally modulated in the frequency range 1000-0.001 Hz. Based on these experimental data and numerical as well as analytical mathematical models, we propose that frequency-domain measurements can become a versatile tool in plant sensing.

A molecular theory of germinal center B cell selection and division

The selection of B cells (BCs) in germinal centers (GCs) is pivotal to the generation of high-affinity antibodies and memory BCs, but it lacks global understanding. Based on the idea of a single Tfh-cell signal that controls BC selection and division, experiments appear contradictory. Here, we use the current knowledge on the molecular pathways of GC BCs to develop a theory of GC BC selection and division based on the dynamics of molecular factors. This theory explains the seemingly contradictory experiments by the separation of signals for BC fate decision from signals controlling the number of BC divisions. Three model variants are proposed and experiments are predicted that allow one to distinguish those. Understanding information processing in molecular BC states is critical for targeted immune interventions, and the proposed theory implies that selection and division can be controlled independently in GC reactions.

Fusion and fission events regulate endosome maturation and viral escape

Endosomes are intracellular vesicles that mediate the communication of the cell with its extracellular environment. They are an essential part of the cell’s machinery regulating intracellular trafficking via the endocytic pathway. Many viruses, which in order to replicate require a host cell, attach themselves to the cellular membrane; an event which usually initiates uptake of a viral particle through the endocytic pathway. In this way viruses hijack endosomes for their journey towards intracellular sites of replication and avoid degradation without host detection by escaping the endosomal compartment. Recent experimental techniques have defined the role of endosomal maturation in the ability of enveloped viruses to release their genetic material into the cytoplasm. Endosome maturation depends on a family of small hydrolase enzymes (or GTPases) called Rab proteins, arranged on the cytoplasmic surface of its membrane. Here, we model endosomes as intracellular compartments described by two variables (its levels of active Rab5 and Rab7 proteins) and which can undergo coagulation (or fusion) and fragmentation (or fission). The key element in our approach is the “per-cell endosomal distribution” and its dynamical (Boltzmann) equation. The Boltzmann equation allows us to derive the dynamics of the total number of endosomes in a cell, as well as the mean and the standard deviation of its active Rab5 and Rab7 levels. We compare our mathematical results with experiments of Dengue viral escape from endosomes. The relationship between endosomal active Rab levels and pH suggests a mechanism that can account for the observed variability in viral escape times, which in turn regulate the viability of a viral intracellular infection.

Impact of Oseltamivir Treatment on Influenza A and B Virus Dynamics in Human Volunteers

Influenza viruses infect millions of humans every year causing an estimated 400,000 deaths globally. Due to continuous virus evolution current vaccines provide only limited protection against the flu. Several antiviral drugs are available to treat influenza infection, and one of the most commonly used drugs is oseltamivir (Tamiflu). While the mechanism of action of oseltamivir as a neuraminidase inhibitor is well-understood, the impact of oseltamivir on influenza virus dynamics in humans has been controversial. Many clinical trials with oseltamivir have been done by pharmaceutical companies such as Roche but the results of these trials until recently have been provided as summary reports or papers. Typically, such reports included median virus shedding curves for placebo and drug-treated influenza virus infected volunteers often indicating high efficacy of the early treatment. However, median shedding curves may be not accurately representing drug impact in individual volunteers. Importantly, due to public pressure clinical trials data testing oseltamivir efficacy has been recently released in the form of redacted PDF documents. We digitized and re-analyzed experimental data on influenza virus shedding in human volunteers from three previously published trials: on influenza A (1 trial) or B viruses (2 trials). Given that not all volunteers exposed to influenza viruses actually start virus shedding we found that impact of oseltamivir on the virus shedding dynamics was dependent on (i) selection of volunteers that were infected with the virus, and (ii) the detection limit in the measurement assay; both of these details were not well-articulated in the published studies. By assuming that any non-zero viral measurement is above the limit of detection we could match previously published data on median influenza A virus (flu A study) shedding but not on influenza B virus shedding (flu B study B) in human volunteers. Additional analyses confirmed that oseltamivir had an impact on the duration of shedding and overall shedding (defined as area under the curve) but this result varied by the trial. Interestingly, treatment had no impact on the rates at which shedding increased or declined with time in individual volunteers. Additional analyses showed that oseltamivir impacted the kinetics of the end of viral shedding, and in about 20-40% of volunteers that shed the virus treatment had no impact on viral shedding duration. Our results suggest an unusual impact of oseltamivir on influenza viruses shedding kinetics and caution about the use of published median data or data from a few individuals for inferences. Furthermore, we call for the need to publish raw data from critical clinical trials that can be independently analyzed.

Cross-species/cross-modality physiologically based pharmacokinetics for biologics: 89Zr-labelled albumin-binding domain antibody GSK3128349 in humans

Two-pore physiologically-based pharmacokinetics (PBPK) for biologics describes the tissue distribution and elimination kinetics of soluble proteins as a function of their hydrodynamic radius and the physiological properties of the organs. Whilst many studies have been performed in rodents to parameterize the PBPK framework in terms of organ-specific lymph flow rates, similar validation in humans has been limited. This is mainly due to the paucity of the tissue distribution time course data for biologics that is not distorted by target-related binding. Here, we demonstrate that a PBPK model based on rodent data provided good to satisfactory extrapolation to the tissue distribution time course of ⁸⁹Zr-labeled albumin-binding domain antibody (AlbudAb™) GSK3128349 in healthy human volunteers, including correct prediction of albumin-like plasma half-life, volume of distribution, and extravasation half-life. The AlbudAb™ used only binds albumin, and hence it also provides information about the tissue distribution kinetics and turnover of that ubiquitous and multifunctional plasma protein.

Mathematical Biology: Expand, Expose, and Educate!

Mathematical biology has made significant contributions and advancements in the biological sciences. Recruitment efforts focus on encouraging students, especially those who are underrepresented and underserved, to pursue the field of mathematical biology, regardless of their undergraduate institution type, and raise awareness about the countless professional and academic possibilities provided by this specialized training. This article examines the need to expand, expose, and educate others about mathematical biology. To support field expansion, we give several recommendations of ways to integrate mathematics applied curricula to attract broader student interest. With this exposure-whether it is led by an individual, a department, a university, or researchers in mathematical biology-each can help to promote a base knowledge and appreciation of the field. In order to encourage the next generation of researchers to consider mathematical biology, we highlight current interdisciplinary programs, share popular mathematical tools, and present some thoughts on ways to support a thriving and inclusive mathematical biology community for years to come.

Modelling the dynamics of tuberculosis lesions in a virtual lung: Role of the bronchial tree in endogenous reinfection

Tuberculosis (TB) is an infectious disease that still causes more than 1.5 million deaths annually. The World Health Organization estimates that around 30% of the world's population is latently infected. However, the mechanisms responsible for 10% of this reserve (i.e., of the latently infected population) developing an active disease are not fully understood, yet. The dynamic hypothesis suggests that endogenous reinfection has an important role in maintaining latent infection. In order to examine this hypothesis for falsifiability, an agent-based model of growth, merging, and proliferation of TB lesions was implemented in a computational bronchial tree, built with an iterative algorithm for the generation of bronchial bifurcations and tubes applied inside a virtual 3D pulmonary surface. The computational model was fed and parameterized with computed tomography (CT) experimental data from 5 latently infected minipigs. First, we used CT images to reconstruct the virtual pulmonary surfaces where bronchial trees are built. Then, CT data about TB lesion' size and location to each minipig were used in the parameterization process. The model's outcome provides spatial and size distributions of TB lesions that successfully reproduced experimental data, thus reinforcing the role of the bronchial tree as the spatial structure triggering endogenous reinfection. A sensitivity analysis of the model shows that the final number of lesions is strongly related with the endogenous reinfection frequency and maximum growth rate of the lesions, while their mean diameter mainly depends on the spatial spreading of new lesions and the maximum radius. Finally, the model was used as an in silico experimental platform to explore the transition from latent infection to active disease, identifying two main triggering factors: a high inflammatory response and the combination of a moderate inflammatory response with a small breathing amplitude.

Model Averaging in Viral Dynamic Models

The paucity of experimental data makes both inference and prediction particularly challenging in viral dynamic models. In the presence of several candidate models, a common strategy is model selection (MS), in which models are fitted to the data but only results obtained with the "best model" are presented. However, this approach ignores model uncertainty, which may lead to inaccurate predictions. When several models provide a good fit to the data, another approach is model averaging (MA) that weights the predictions of each model according to its consistency to the data. Here, we evaluated by simulations in a nonlinear mixed-effect model framework the performances of MS and MA in two realistic cases of acute viral infection, i.e., (1) inference in the presence of poorly identifiable parameters, namely, initial viral inoculum and eclipse phase duration, (2) uncertainty on the mechanisms of action of the immune response. MS was associated in some scenarios with a large rate of false selection. This led to a coverage rate lower than the nominal coverage rate of 0.95 in the majority of cases and below 0.50 in some scenarios. In contrast, MA provided better estimation of parameter uncertainty, with coverage rates ranging from 0.72 to 0.98 and mostly comprised within the nominal coverage rate. Finally, MA provided similar predictions than those obtained with MS. In conclusion, parameter estimates obtained with MS should be taken with caution, especially when several models well describe the data. In this situation, MA has better performances and could be performed to account for model uncertainty.

Clustering of Activated CD8 T Cells Around Malaria-Infected Hepatocytes Is Rapid and Is Driven by Antigen-Specific Cells

Malaria, a disease caused by parasites of the Plasmodium genus, begins when Plasmodium-infected mosquitoes inject malaria sporozoites while searching for blood. Sporozoites migrate from the skin via blood to the liver, infect hepatocytes, and form liver stages which in mice 48 h later escape into blood and cause clinical malaria. Vaccine-induced activated or memory CD8 T cells are capable of locating and eliminating all liver stages in 48 h, thus preventing the blood-stage disease. However, the rules of how CD8 T cells are able to locate all liver stages within a relatively short time period remains poorly understood. We recently reported formation of clusters consisting of variable numbers of activated CD8 T cells around Plasmodium yoelii (Py)-infected hepatocytes. Using a combination of experimental data and mathematical models we now provide additional insights into mechanisms of formation of these clusters. First, we show that a model in which cluster formation is driven exclusively by T-cell-extrinsic factors, such as variability in "attractiveness" of different liver stages, cannot explain distribution of cluster sizes in different experimental conditions. In contrast, the model in which cluster formation is driven by the positive feedback loop (i.e., larger clusters attract more CD8 T cells) can accurately explain the available data. Second, while both Py-specific CD8 T cells and T cells of irrelevant specificity (non-specific CD8 T cells) are attracted to the clusters, we found no evidence that non-specific CD8 T cells play a role in cluster formation. Third and finally, mathematical modeling suggested that formation of clusters occurs rapidly, within few hours after adoptive transfer of CD8 T cells, thus illustrating high efficiency of CD8 T cells in locating their targets in complex peripheral organs, such as the liver. Taken together, our analysis provides novel insights into and attempts to discriminate between alternative mechanisms driving the formation of clusters of antigen-specific CD8 T cells in the liver.

Immune network for viral hepatitis B: Topological representation

The liver is a well-known immunotolerogenic environment, which provides the adequate setting for liver infectious pathogens persistence such as the hepatitis B virus (HBV). Consequently, HBV infection can derive in the development of chronic disease in a proportion of the patients. If this situation persists in time, chronic hepatitis B (CHB) would end in cirrhosis, hepatocellular carcinoma and eventually, the death of the patient. It is thought that this immunotolerogenic environment is the result of complex interactions between different elements of the immune system and the viral biology. Therefore, the purpose of this work is to unravel the mechanisms implied in the development of CHB and to design a tool able to help in the study of adequate therapies. Firstly, a conceptual framework with the main components of the immune system and viral dynamics was constructed providing an overall insight on the pathways and interactions implied in this disease. Secondly, a review of the literature was performed in a modular fashion: (i) viral dynamics, (ii) innate immune response, (iii) humoral and (iv) cellular adaptive immune responses and (v) tolerogenic aspects. Finally, the information collected was integrated into a single topological representation that could serve as the plan for the systems pharmacology model architecture. This representation can be considered as the previous unavoidable step to the construction of a quantitative model that could assist in biomarker and target identification, drug design and development, dosing optimization and disease progression analysis.

Combining Mathematical Models With Experimentation to Drive Novel Mechanistic Insights Into Macrophage Function

This perspective outlines an approach to improve mechanistic understanding of macrophages in inflammation and tissue homeostasis, with a focus on human inflammatory bowel disease (IBD). The approach integrates wet-lab and in-silico experimentation, driven by mechanistic mathematical models of relevant biological processes. Although wet-lab experimentation with genetically modified mouse models and primary human cells and tissues have provided important insights, the role of macrophages in human IBD remains poorly understood. Key open questions include: (1) To what degree hyperinflammatory processes (e.g., gain of cytokine production) and immunodeficiency (e.g., loss of bacterial killing) intersect to drive IBD pathophysiology? and (2) What are the roles of macrophage heterogeneity in IBD onset and progression? Mathematical modeling offers a synergistic approach that can be used to address such questions. Mechanistic models are useful for informing wet-lab experimental designs and provide a knowledge constrained framework for quantitative analysis and interpretation of resulting experimental data. The majority of published mathematical models of macrophage function are based either on animal models, or immortalized human cell lines. These experimental models do not recapitulate important features of human gastrointestinal pathophysiology, and, therefore are limited in the extent to which they can fully inform understanding of human IBD. Thus, we envision a future where mechanistic mathematical models are based on features relevant to human disease and parametrized by richer human datasets, including biopsy tissues taken from IBD patients, human organ-on-a-chip systems and other high-throughput clinical data derived from experimental medicine studies and/or clinical trials on IBD patients.

The Rate of CD4 T Cell Entry into the Lungs during Mycobacterium tuberculosis Infection Is Determined by Partial and Opposing Effects of Multiple Chemokine Receptors

The specific chemokine receptors utilized by Th1 cells to migrate into the lung during Mycobacterium tuberculosis infection are unknown. We previously showed in mice that CXCR3⁺ Th1 cells enter the lung parenchyma and suppress M. tuberculosis growth, while CX3CR1⁺ KLRG1⁺ Th1 cells accumulate in the lung vasculature and are nonprotective. Here we quantify the contributions of these chemokine receptors to the migration and entry rate of Th1 cells into M. tuberculosis-infected lungs using competitive adoptive transfer migration assays and mathematical modeling. We found that in 8.6 h half of M. tuberculosis-specific CD4 T cells migrate from the blood to the lung parenchyma. CXCR3 deficiency decreases the average rate of Th1 cell entry into the lung parenchyma by half, while CX3CR1 deficiency doubles it. KLRG1 blockade has no effect on Th1 cell lung migration. CCR2, CXCR5, and, to a lesser degree, CCR5 and CXCR6 also promote the entry of Th1 cells into the lungs of infected mice. Moreover, blockade of G-protein-coupled receptors with pertussis toxin treatment prior to transfer only partially inhibits T cell migration into the lungs. Thus, the fraction of Th1 cell input into the lungs during M. tuberculosis infection that is regulated by chemokine receptors likely reflects the cumulative effects of multiple chemokine receptors that mostly promote but that can also inhibit entry into the parenchyma.

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.

Noise Is Not Error: Detecting Parametric Heterogeneity Between Epidemiologic Time Series

Mathematical models play a central role in epidemiology. For example, models unify heterogeneous data into a single framework, suggest experimental designs, and generate hypotheses. Traditional methods based on deterministic assumptions, such as ordinary differential equations (ODE), have been successful in those scenarios. However, noise caused by random variations rather than true differences is an intrinsic feature of the cellular/molecular/social world. Time series data from patients (in the case of clinical science) or number of infections (in the case of epidemics) can vary due to both intrinsic differences or incidental fluctuations. The use of traditional fitting methods for ODEs applied to noisy problems implies that deviation from some trend can only be due to error or parametric heterogeneity, that is noise can be wrongly classified as parametric heterogeneity. This leads to unstable predictions and potentially misguided policies or research programs. In this paper, we quantify the ability of ODEs under different hypotheses (fixed or random effects) to capture individual differences in the underlying data. We explore a simple (exactly solvable) example displaying an initial exponential growth by comparing state-of-the-art stochastic fitting and traditional least squares approximations. We also provide a potential approach for determining the limitations and risks of traditional fitting methodologies. Finally, we discuss the implications of our results for the interpretation of data from the 2014-2015 Ebola epidemic in Africa.

Persistent infections in immunocompromised hosts are rarely sources of new pathogen variants

Many viruses, including human norovirus and influenza, cause self-limiting diseases of short duration. However, infection by the same viruses in an immunocompromised host can result in prolonged illness in the absence of effective treatment. Such persistent infections are often characterized by increased genetic diversity with potentially elevated rates of evolution compared to acute infections, leading to suggestions that immunocompromised hosts represent an important reservoir for the emergence of novel viral variants. Here, we develop a mathematical model that combines epidemiological dynamics with within-host evolution to quantify the relative contribution of immunocompromised hosts to the overall rate of pathogen evolution. Using human norovirus as a case study we show that the majority of evolutionary substitutions are expected to occur in acute infections of immunocompetent hosts. Hence, despite their potential to generate a high level of diversity, infections of immunocompromised hosts likely contribute less to the evolution and emergence of new genetic variants at the epidemiological scale because such hosts are rare and tend to be isolated. This result is robust to variation in key parameters, including the proportion of the population immunocompromised, and provides a means to understand the adaptive significance of mutations that arise during chronic infections in immunocompromised hosts.