Reconciling contrasting effects of nitrogen on host immunity and pathogen transmission using stoichiometric models.

Hosts rely on the availability of nutrients for growth, and for defense against pathogens. At the same time, changes in host nutrition can alter the dynamics of pathogens that rely on their host for reproduction. For primary producer hosts, enhanced nutrient loads may increase host biomass or pathogen reproduction, promoting faster density-dependent pathogen transmission. However, the effect of elevated nutrients may be reduced if hosts allocate a growth-limiting nutrient to pathogen defense. In canonical disease models, transmission is not a function of nutrient availability. Yet, including nutrient availability is necessary to mechanistically understand the response of infection to changes in the environment. Here, we explore the implications of nutrient-mediated pathogen infectivity and host immunity on infection outcomes. We developed a stoichiometric disease model that explicitly integrates the contrasting dependencies of pathogen infectivity and host immunity on nitrogen (N) and parameterized it for an algal-host system. Our findings reveal dynamic shifts in host biomass build-up, pathogen prevalence, and the force of infection along N supply gradients with N-mediated host infectivity and immunity, compared with a model in which the transmission rate was fixed. We show contrasting responses in pathogen performance with increasing N supply between N-mediated infectivity and N-mediated immunity, revealing an optimum for pathogen transmission at intermediate N supply. This was caused by N limitation of the pathogen at a low N supply and by pathogen suppression via enhanced host immunity at a high N supply. By integrating both nutrient-mediated pathogen infectivity and host immunity into a stoichiometric model, we provide a theoretical framework that is a first step in reconciling the contrasting role nutrients can have on host-pathogen dynamics.

Data driven mixed effects modeling of the dual process framework of addiction among individuals with alcohol use disorder.

Alcohol use disorder (AUD) comprises a continuum of symptoms and associated problems that has led AUD to be a leading cause of morbidity and mortality across the globe. Given the heterogeneity of AUD from mild to severe, consideration is being given to providing a spectrum of interventions that offer goal choice to match this heterogeneity, including helping individuals with AUD to moderate or control their drinking at low-risk levels. Because so much remains unknown about the factors that contribute to successful moderated drinking, we use dynamical systems modeling to identify mechanisms of behavior change. Daily alcohol consumption and daily desire (i.e., craving) are modeled using a system of delayed difference equations. Employing a mixed effects implementation of this system allows us to garner information about these mechanisms at both the population and individual levels. Use of this mixed effects framework first requires a parameter set reduction via identifiability analysis. The model calibration is then performed using Bayesian parameter estimation techniques. Finally, we demonstrate how conducting a parameter sensitivity analysis can assist in identifying optimal targets of intervention at the patient-specific level. This proof-of-concept analysis provides a foundation for future modeling to describe mechanisms of behavior change and determine potential treatment strategies in patients with AUD.

A Comparison of Mathematical and Statistical Modeling with Longitudinal Data: An Application to Ecological Momentary Assessment of Behavior Change in Individuals with Alcohol Use Disorder.

Ecological momentary assessment (EMA) has been broadly used to collect real-time longitudinal data in behavioral research. Several analytic methods have been applied to EMA data to understand the changes of motivation, behavior, and emotions on a daily or within-day basis. One challenge when utilizing those methods on intensive datasets in the behavioral field is to understand when and why the methods are appropriate to investigate particular research questions. In this manuscript, we compared two widely used methods (generalized estimating equations and generalized linear mixed models) in behavioral research with three other less frequently used methods (Markov models, generalized linear mixed-effects Markov models, and differential equations) in behavioral research but widely used in other fields. The purpose of this manuscript is to illustrate the application of five distinct analytic methods to one dataset of intensive longitudinal data on drinking behavior, highlighting the utility of each method.

Elements of disease in a changing world: modelling feedbacks between infectious disease and ecosystems.

An overlooked effect of ecosystem eutrophication is the potential to alter disease dynamics in primary producers, inducing disease-mediated feedbacks that alter net primary productivity and elemental recycling. Models in disease ecology rarely track organisms past death, yet death from infection can alter important ecosystem processes including elemental recycling rates and nutrient supply to living hosts. In contrast, models in ecosystem ecology rarely track disease dynamics, yet elemental nutrient pools (e.g. nitrogen, phosphorus) can regulate important disease processes including pathogen reproduction and transmission. Thus, both disease and ecosystem ecology stand to grow as fields by exploring questions that arise at their intersection. However, we currently lack a framework explicitly linking these disciplines. We developed a stoichiometric model using elemental currencies to track primary producer biomass (carbon) in vegetation and soil pools, and to track prevalence and the basic reproduction number (R0 ) of a directly transmitted pathogen. This model, parameterised for a deciduous forest, demonstrates that anthropogenic nutrient supply can interact with disease to qualitatively alter both ecosystem and disease dynamics. Using this element-focused approach, we identify knowledge gaps and generate predictions about the impact of anthropogenic nutrient supply rates on infectious disease and feedbacks to ecosystem carbon and nutrient cycling.

A tutorial review of mathematical techniques for quantifying tumor heterogeneity.

Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https://github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.

Disease-mediated ecosystem services: Pathogens, plants, and people.

Despite the ubiquity of pathogens in ecological systems, their roles in influencing ecosystem services are often overlooked. Pathogens that infect primary producers (i.e., plants, algae, cyanobacteria) can have particularly strong effects because autotrophs are responsible for a wide range of provisioning, regulating, and cultural services. We review the roles of pathogens in mediating ecosystem services provided by autotrophs and outline scenarios in which infection may lead to unexpected outcomes in response to global change. Our synthesis highlights a deficit of information on this topic, and we outline a vision for future research that includes integrative theory and cross-system empirical studies. Ultimately, knowledge about the mediating roles of pathogens on ecosystem services should inform environmental policy and practice.

Agent-based and continuous models of hopper bands for the Australian plague locust: How resource consumption mediates pulse formation and geometry.

Locusts are significant agricultural pests. Under favorable environmental conditions flightless juveniles may aggregate into coherent, aligned swarms referred to as hopper bands. These bands are often observed as a propagating wave having a dense front with rapidly decreasing density in the wake. A tantalizing and common observation is that these fronts slow and steepen in the presence of green vegetation. This suggests the collective motion of the band is mediated by resource consumption. Our goal is to model and quantify this effect. We focus on the Australian plague locust, for which excellent field and experimental data is available. Exploiting the alignment of locusts in hopper bands, we concentrate solely on the density variation perpendicular to the front. We develop two models in tandem; an agent-based model that tracks the position of individuals and a partial differential equation model that describes locust density. In both these models, locust are either stationary (and feeding) or moving. Resources decrease with feeding. The rate at which locusts transition between moving and stationary (and vice versa) is enhanced (diminished) by resource abundance. This effect proves essential to the formation, shape, and speed of locust hopper bands in our models. From the biological literature we estimate ranges for the ten input parameters of our models. Sobol sensitivity analysis yields insight into how the band's collective characteristics vary with changes in the input parameters. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations. We thus demonstrate that resource-dependent behavior can explain the density distribution observed in locust hopper bands. This work suggests that feeding behaviors should be an intrinsic part of future modeling efforts.

Computational modeling of interventions and protective thresholds to prevent disease transmission in deploying populations.

Military personnel are deployed abroad for missions ranging from humanitarian relief efforts to combat actions; delay or interruption in these activities due to disease transmission can cause operational disruptions, significant economic loss, and stressed or exceeded military medical resources. Deployed troops function in environments favorable to the rapid and efficient transmission of many viruses particularly when levels of protection are suboptimal. When immunity among deployed military populations is low, the risk of vaccine-preventable disease outbreaks increases, impacting troop readiness and achievement of mission objectives. However, targeted vaccination and the optimization of preexisting immunity among deployed populations can decrease the threat of outbreaks among deployed troops. Here we describe methods for the computational modeling of disease transmission to explore how preexisting immunity compares with vaccination at the time of deployment as a means of preventing outbreaks and protecting troops and mission objectives during extended military deployment actions. These methods are illustrated with five modeling case studies for separate diseases common in many parts of the world, to show different approaches required in varying epidemiological settings.

Mechanisms of resistance to intermittent androgen deprivation in patients with prostate cancer identified by a novel computational method.

For progressive prostate cancer, intermittent androgen deprivation (IAD) is one of the most common and effective treatments. Although this treatment is usually initially effective at regressing tumors, most patients eventually develop castration-resistant prostate cancer (CRPC), for which there is no effective treatment and is generally fatal. Although several biologic mechanisms leading to CRPC development and their relative frequencies have been identified, it is difficult to determine which mechanisms of resistance are developing in a given patient. Personalized therapy that identifies and targets specific mechanisms of resistance developing in individual patients is likely one of the most promising methods of future cancer therapy. Prostate-specific antigen (PSA) is a biomarker for monitoring tumor progression. We incorporated a cell death rate (CDR) function into a previous dynamical PSA model that was highly accurate at fitting clinical PSA data for 7 patients. The mechanism of action of IAD is largely induction of apoptosis, and each mechanism of resistance varies in its CDR dynamics. Thus, we analyze the CDR levels and their time-dependent oscillations to identify mechanisms of resistance to IAD developing in individual patients.