CTW: From Within Host Dynamics to the Epidemiology of Infectious Disease
As part of the Malaria Host-Pathogen Interaction Center, our goal is to study and model the response of both host and pathogen to the course of malarial infection, treatment, and recurrence or recrudescence, using multiple levels of "omic" data. Detailed mathematical models are a desired ultimate product of our study of malaria, and while there are certainly some intuitive candidate systems for such modeling, it is not necessarily clear a priori which other systems should be modeled, nor which variables are important to include in those models. Our goal is to exploit the multiple levels of systems-scale datasets being generated in our center to identify such candidates for detailed models and follow-up experiments.
The main task in achieving this goal is discovery of novel, unknown interactions between our measured variables. This can be accomplished via a number of classes of approaches, including statistical analyses and machine learning. Here, we will focus on our machine learning approaches to identifying subnetworks of interesting interactions, specifically using probabilistic graphical models to construct interaction networks. Within this domain, two of the biggest obstacles to accomplishing our goal are 1) computational tractability given the high dimensional variable space, and 2) integrating multiple disparate data types, each with potentially different scales of variable space dimensionality (tens of measurements vs. tens of thousands of measurements) and different time scales, such that no data type dominates or is dwarfed in importance. We will present our algorithmic work addressing these problems, along with applications to the malaria data that has been generated by our center to date.
The blood stage of a malaria infection is the final step of the dual-host multi-stage disease. It is at this stage that most symptoms manifest and where the outcome is critical for the future disease trajectory toward either chronic infection or death. The blood stage is marked by the interplay between malarial merozoites, the erythropoietic system, and the immune system. Failure to properly up-regulate erythropoiesis results in anemia, while an improper immune response may lead to chronic infection that is characterized by recrudescence or relapse.
The production of red blood cells (RBCs) by the erythropoietic system takes about 5 days in our model organism, Macaca mulatta, and the RBCs normally remain in the blood stream for about 100 days. During this life cycle, only RBCs of the early age-classes are prone to merozoite invasion. Upon invasion, growth of the tropozoites into schizonts and the subsequent release of about 14 to 20 new merozoites take about 48 hours for the infecting parasite, Plasmodium cynomolgi. A computational systems analysis of the processes involved in the dynamics of RBCs in malaria demonstrated that the blood stage events are strongly dependent on different time delays and the structure of age-classes among the RBCs.
In this workshop presentation, we will discuss the advantages and disadvantages of using: ordinary differential equation (ODE) models with and without age-classes; delay differential equations (DDE); or discrete recursive models with age-classes. DDEs and ODEs with age-classes are well suited for the generation of delays, but lack the required flexibility to properly address issues associated with the constantly changing differentiation time of RBC precursors. By contrast, discrete recursive models allow the proper movement of all cells through their life cycle, while also allowing variables to be associated with dynamically changing delays, amplification ratios, and different types of injuries or infections, including malaria.
Insights into Plasmodium vivax from spatial maps of human gene polymorphisms: Duffy blood group and G6PD deficiency.Rosalind Howes
Over a third of the worldâ€™s population lives at risk of potentially life-threatening Plasmodium vivax malaria infections. Unique aspects of this parasiteâ€™s biology and interactions with its human host make it harder to control and eliminate than the better studied Plasmodium falciparum parasite. The spatial epidemiology of two human genetic systems associated with these traits has been investigated in a multi-scale, model-based framework to generate estimates of populations of risk of P. vivax infection, and assessments of associated therapeutic risks.
First, the two key SNPs determining expression of the Duffy blood group were modelled to map the prevalence of Duffy phenotypes globally. The Duffy antigen is the only known erythrocyte receptor for P. vivax infection, and was used as a proxy indicator of population susceptibility to infection. The maps are discussed in light of reports of apparent Duffy-independent transmission.
Second, the global epidemiology of G6PD enzyme deficiency â€“ both its phenotypic prevalence and genetic heterogeneity â€“ is mapped. A geostatistical framework structured around the geneâ€™s X-linked inheritance generated global estimates of G6PD deficiency prevalence, and estimates of affected population numbers. Poorly quantified risks from this spatially heterogeneous enzyme deficiency currently hinder widespread use of primaquine, a drug necessary for progress towards malaria elimination, particularly against the relapsing P. vivax life-stages.
These examples illustrate the positive contribution that integrating spatial epidemiological human genetic data can make in supporting the evidence-base for strategic planning for control of an infectious disease, thereby attempting to bridge the gap between basic biological research and the health sciences.
The modern era of Amazon frontier expansion in Brazil witnessed the introduction of large-scale colonization projects focused on agriculture and wide-ranging human settlement, as well as the construction of infrastructure, such as roads and dams. These initiatives led to massive human migration, substantial environmental transformation, and severe malaria transmission. Interactions between development efforts, agricultural colonization, environment and health, at given levels of socioeconomic conditions, are very complex and demand a multidisciplinary analysis to serve as the basis for rational and successful policies. The talk will focus on a specific settlement project, and present a spatially explicit methodological approach that combined spatial analysis, geostatistical tools, and fuzzy sets, in a multidisciplinary way, in order to identify the most important factors impacting transmission. Results revealed that during the early stages of frontier settlement transmission was mainly driven by environmental risks, consequential to ecosystem transformations that promote larval habitats of Anopheles darlingi. With the advance of forest clearance and the establishment of agriculture, ranching, and urban development, malaria transmission was substantially reduced, and risks of new infection were largely driven by human behavioral factors.
Experimental malaria infections in non-human primates (NHPs) are a prime setting to assess the changing biological conditions associated with disease, notably with regards to the host immune system. While much attention has been focused on T-cell and B-cell dependent ("adaptive") responses that are key to vaccine development and long-term protection in malaria, relatively little is known of the involvement of the innate immune system. Here, we will highlight a novel approach that addresses this gap in knowledge, and will show early data obtained as part of the Malaria Host Pathogen Interaction Center (MaHPIC) consortium at Emory University, Georgia Tech and University of Georgia (PI: Mary Galinski, Co-PIs: Alberto Moreno, Jessica Kissinger). By tracking functional responses mounted by the innate immune system in malaria-infected NHPs, we show that this arm of the immune system is mobilized to a major extent during the course of infection. This data is the first of its kind and will be discussed in relation to integration with other omics technologies and use in building mathematical models that include both adaptive and innate host immunity.
Chet Joyner, Mary Galinski, Rabindra Tirouvanziam, Emory University
Host movements can have a profound impact on the transmission of vector-borne diseases because they can increase or reduce he rate of contact between hosts and vectors. It is clear that host movement can introduce pathogens to new environments, but models suggest that it can also increase or decrease the basic reproduction number (R0) within an environment by influencing the contact rates between hosts and infected vectors or between vectors and infected hosts. There are two distinct types of movement that are relevant in this context. They can be characterized as commuting and migration. The distinction is that migration envisions hosts changing the location of their primary residence, while commuting envisions that each host maintains a particular location of residence but visits other locations in the course of routine activities. These two types of movement require different models and may have different effects. This talk will review some models and results for the effects of host movement in vector-borne disease systems.
It has recently been suggested that for avian influenza viruses, prolonged persistence in the environment plays an important role in the transmission between birds. In such situations, influenza virus strains may face a trade-off: They need to persist well in the environment at low temperatures, but they also need to do well inside an infected bird at higher temperatures. Here, we report an analysis of fitness for avian influenza A viruses across scales, focusing on the phenotype of viral persistence. Taking advantage of a unique dataset that not only reports environmental virus persistence, but also strain-specific viral kinetics from duck challenge experiments, we show that the environmental persistence phenotype of a strain does not impact within-host infection dynamics and virus load. We thereby establish that for this phenotype, the scales of within-host infection dynamics and between-host environmental persistence do not interact: the virus can optimize fitness on each scale without cross-scale trade-offs. Instead, we confirm the existence of a temperature-dependent persistence trade-off on a single scale, with some strains optimizing environmental persistence in water at low temperatures while others reduce sensitivity to increasing temperatures.
In this talk I will outline the impact that parasitic sea lice have on the ecology of pacific salmon and the role that parasite spill over and spill back with aquaculture has taken in modifying the ecology of pacific salmon. These modifications are far reaching, and include changes in salmon returns, establishment of nonlinear population thresholds such as Allee effects, and shifts in predator prey dynamics. My talk will involve a mixture of modelling and data, based on over a decade of intensive field work.
With this presentation I will try to set the stage for the modeling efforts to be discussed in the workshop. As the title â€œFrom Within Host Dynamics to the Epidemiology of Infectious Diseaseâ€? directly suggests, infectious diseases involve many scales, with respect to time, space, and organization, with the latter spanning the range from molecules to global effects. While a hallmark goal of systems biology is the integration of heterogeneous information across multiple scales and levels, our computational modeling capabilities are clearly not quite ready to cover all aspects of infectious diseases. Thus, the workshop is hoped to address three fundamental questions, namely:
1. How can modeling help us bridge the gaps between scales or levels of organization?
2. How can we make optimal use of very diverse data (from traditional biology and biochemistry, high-throughput â€“omics methods, physiology, clinical observations, host-parasite interactions, disease spread, interventions) in order to deepen our understanding of disease dynamics and adaptation, by both hosts and parasites, and to devise treatment options that are generic or even personalized, and executable at a global scale?
3. What can modelers of different sub-disciplines within the span between within-host-dynamics and epidemiology learn from each other?
In addition to these research questions, the workshop is hoped to discuss means of â€œbidirectionalâ€? education between the often separate groups of clinicians and experimentalists on one side and computational analysts on the other. This education should give clinicians and experimentalists a feel for what is achievable with modern modeling tools and help modelers frame specific and relevant biological questions for analyses that offer genuine added value.
As this meeting of expert minds is a workshop rather than a conference, polished answers are not necessarily the goal. Instead, the workshop will be a success if the participants collectively take account of where we are, what we can do with todayâ€™s methods, where we want to be in N years, and what we need to do to get there.
Juan B. Gutierrez
Traditional epidemiological models consists of compartmentalizing hosts into susceptible, exposed, infected, recovered (SEIR), and variations of this paradigm (e.g. SIR, SIR/SI, etc.). These models are challenged when the within-host dynamics of disease is taken into account with aspects such as: (i) Simultaneous Infection: Simultaneous presence of several distinct pathogen genomes, from the same or multiple species, thus causing individual to belong to multiple compartments simultaneously. (ii) Antigenic diversity and variation: Antigenic variation, defined as the ability of a pathogen to change antigens presented to the immune system during an infection, and antigenic diversity, defined as antigenic differences between pathogens in a population, are central to the pathogen's ability to 1) infect previously exposed hosts, and 2) maintain a long-term infection in the face of the immune response. Immune evasion facilitated by this variability is a critical factor in the dynamics of pathogen growth, and therefore, transmission. This talk explores an alternate mechanistic formulation of epidemiological dynamics based upon studying the influence of within-host dynamics in environmental transmission. A basic propagation number is calculated that could guide public health policy.
In this talk, I will review the basic features of deterministic models of within-host viral dynamics. I will discuss the global asymptotic behavior of such models, and extensions of the stability results to models including multi-strain competition, antiviral treatment, and immune response.
Within host dynamics in diseases is essentially the same as dynamics within metapopulations in an ecological context. I will review results from metapopulation models, and draw parallels to disease dynamics. I will emphasize both similarities and differences. The goal will be to see how various assumptions about within host (equivalently within patch) dynamics reduce the complexity of the model and study and lead to models which can be studied analytically.
Optimal control can be used to design intervention strategies for the management of infectious diseases, and has been applied in immunological and epidemiological models separately. We formulate an immuno-epidemiological model of coupled within-host model of ODEs and between-host model of ODE and PDE. Existence and uniqueness of solution to the between-host model is established, and an explicit expression for the basic reproduction number of the between-host model is derived. Stability of disease-free and endemic equilibria of the between-host model is investigated. An optimal control problem with drug-treatment control on the within-host system is formulated and analyzed. Numerical simulations based on the forward-backward sweep method are obtained.
Thresholds for Extinction in Stochastic Models of Infectious Diseases: Importance of Time and LocationLinda Allen
Relations between Markov chain models and differential equation models for infectious diseases near the infection-free state are derived. Approximation of the Markov chain model by a multitype branching process leads to an estimate of the probability of disease extinction. We summarize some extinction results for multi-patch, multi-group, and multi-stage models of infectious diseases for epidemics and within-host models. The successful invasion of a pathogen often depends on the conditions of the environment at a specific time and location.
Consider a set of communities (patches), connected to one another by a network. When can disease invade this network? Intuitively, this should depend upon both the properties of the communities, as well as on the network structure. Here we make this dependence explicit for a broad class of disease models with environmental pathogen movement. In particular, the rooted spanning trees of the network and a generalization of the group inverse of the graph Laplacian play fundamental roles in determining the ability of disease to invade. This is joint work with Z. Shuai, M. Eisenberg, and P. van den Driessche.
Disease processes often involve interacting factors at multiple scales, which can affect both how we build models of these systems and the data sets needed to estimate model parameters. In this talk I will discuss some examples of disease transmission models that depend on processes at scales ranging from cellular to environmental, including cholera and human papillomavirus (HPV).
The pathogenic bacterium Mycoplasma gallisepticum jumped from poultry into North American House Finch populations during the early 1990s, and has since proven to be an accessible system in which to study the many faces of emerging infectious diseases in vertebrates. In this talk I'll begin by introducing the system, then I'll discuss some sources of individual-level variation in this system (and likely many others) including some results obtained by "scaling up" from the individual level. Then, I'll discuss the use of models to address questions at the population level including evolutionary dynamics and the importance of a novel virulence trade-off present in this system which is likely a factor driving evolutionary dynamics of other parasites with mobile host species.
The incidence of tick-borne rickettsial disease in the southeastern United States has been rising steadily through the past decade, and the range expansions of tick species and tick-borne infectious agents, new and old, has resulted in an unprecedented mix of vectors and pathogens. The results of an ongoing 5-year surveillance project describe the relative abundance of questing tick populations in southeastern Virginia. Since 2009, more than 100,000 questing ticks of a variety of species have been collected from vegetation in a variety of habitats, with Amblyomma americanum constituting over 95% of ticks collected. We found that 26.9â€“54.9% of A. americanum ticks tested were positive for Rickettsia amblyommii, a non-pathogenic symbiont of this tick species. Rickettsia parkeri was found in 41.8â€“55.7% of Amblyomma maculatum ticks. The rate of R. parkeri in A. maculatum ticks is among the highest in the literature and has increased in the 2 years since R. parkeri and A. maculatum were first reported in southeastern Virginia. Additionally, R. parkeri is started to be found in A. americanum ticks throughout the region. While this is at extremely low prevalence, the sheer abundance of these ticks may increase the encounters with rickettsial agents with the potential for increased risk to human health.