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Women Advancing Mathematical Biology: Understanding Complex Biological Systems with Mathematics Mathematical Biosciences Institute April 24-28, 2017 Organizers Rebecca Segal Ami Radunskaya Blerta Shtylla Leaders Linda Allen Jen-Mei Chang Nina Fefferman Co-leaders Angela Peace Kellie Archer Karamatou Djima Shelby Wilson Holly Gaff Laura Miller Helen Moore Gaby Hamerlinck Wanda Strychalski Nessy Tania Topic Stochastic modeling of infectious diseases Explaining Autism Spectrum Disorder with Placenta Ectoparasites and Allogrooming: Evolutionary Trade-offs in Animal Community Health Modeling Argasid Ticks Mechanics of super-fast nematocyst firing Disease and Combination Therapy Dynamics Stochastic modeling of infectious diseases: heterogeneity of hosts and pathogens Leader: Linda Allen, TTU Co-leader: Angela Peace, TTU Background: The severity of newly emerging infectious diseases depends on the ability of the pathogen to invade the host and to establish an infection and the ability of the infected host to transmit the pathogen to another individual. Pathogen virulence, host susceptibility and transmissibility, and population interactions are important considerations when developing models for intervention, prevention, and control of emerging diseases. Individual characteristics determine susceptibility and transmissibility such as history of exposure, genetic predisposition, and physical health. Population and environmental conditions determine spread to other individuals such as mixing patterns. The importance of host transmissibility in disease emergence has been demonstrated in historical and recent pandemics that involve superspreaders, infectious individuals able to transmit the infection to a large number of susceptible individuals, such as SARS in 2003 [2,4]. This phenomenon is referred to as the 20/80 rule of infection where 80% of infections are caused by 20% of the population [5]. Stochastic models and methods have captured some of the dynamics associated with heterogeneity through assumptions about variability in individual or population responses to pathogen infection [3,4,6]. Given a small number of infectious individuals introduced into a large susceptible population, application of multi-type branching process theory has been useful in estimating probability of disease emergence [1,3,4,6]. The basic reproduction number R0 and the underlying deterministic skeleton serve as a basis for constructing stochastic models and provide a source of comparison with the stochastic results [1,3]. Stochastic models with heterogeneity have been applied to specic diseases spread from human-to-human or animal-to-human (zoonotic diseases) and to theoretical investigations on the impact of specic groups or specic model parameters on disease emergence [1,3,4,6]. Objectives: The goals of this project are to review some stochastic modeling approaches and to develop new stochastic approaches to predict probability of disease emergence: (1) develop within-host or between-host models that characterize different sources of heterogeneity (e.g., pathogen virulence, host susceptibility, host transmissibility, duration of infection, mixing patterns, etc.), (2) to identify sources of heterogeneity relevant to specic environments or to specic types of diseases, (3) to make analytical or numerical predictions about probability of disease emergence, dependent on the source of heterogeneity, singly or in combination, and (4) to compare the mathematical results to data on specic disease outbreaks. References: [1] Allen LJS, van den Driessche P. 2013. Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models. Mathematical Biosciences 243: 99-108. [2] Galvani AP May RM. 2005. Dimensions of superspreading. Nature 438: 293-295. [3] Lloyd, AL, Zhang J, Morgan Root A. 2007. Stochasticity and heterogeneity in host-vector models. J. R. Soc. Interface 4: 851-853. [4] Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz GE. 2005. Superspreading and the effect of individual variance on disease emergence. Nature 438: 355-359. [5] Woolhouse MEJ, Dye C, Etard, JF, Smith T, Charlwood, JD, Garnet GP, Hagan, P. Hu, JLK, Ndhlovu PD, Quinnel RJ, Watts CH Chandiwana SK, Anderson RM. 1997. Heterogeneities in the transmission of infectious agents: Implications for the design of control programs. Proc. Natl. Acad. Sci 94: 338-342. [6] Yates A, Antia R, Regoes R. 2006. How do pathogen evolution and host heterogeneity interact in disease emergence? Proc. R. Soc. B. 273: 3075-3083. Explaining Autism Spectrum Disorder with Placenta Leader:Jen-Mei Chang, CSULB Co-leader: Kellie Archer, OSU Karamatou (Kara) Djima, Amherst College Background Recent medical research indicates that the placenta may be the “crystal ball” for the health of the newborns since placenta is the source of nutrition, oxygen, and blood for the developing fetus; so problems with the placenta may manifest as developmental issues for the baby. An analysis of the placenta may help predict risks for certain diseases that develop in the womb such as diabetes, autism, and heart disease; in particular, the structure of the blood vessel network as well as the shape of the placenta may help to link the genetic and/or environmental factors to those diseases. A major feature of the whole placenta, the placental chorionic surface vascular network (PCSVN), has not been extensively studied due to the extreme difficulty in reliably extracting PCSVN features from digital images of the fetal surface [1]. We have hypothesized that variation in PCSVN structure, the template of the fetal organ positioned at the interface of the mother and the conceptus, may reflect both the overall effects of genetic and/or environmentally regulated variations in branching morphogenesis within the conceptus, and may also mirror vascular network alterations in the fetus' vital organs. For example, chorionic surface shapes and PCSVN features have been linked to immediate neonatal outcomes such as birth weight after adjustment for gestational length, and preliminary research results [2] suggested that there are significant differences in PCSVN features in children at increased risk for Autism Spectrum Disorders (ASD). If we assume that differences observed in placentas from the at-risk ASD cohort reflect differences that are relevant to ASD etiology, it seems most plausible that this would be related to some restricted ability to vary aspects of placental growth to compensate for changes in the maternal uterine environment. A range of obstetric complications are consistently documented as being associated with ASD, therefore it seems unlikely that pregnancies in the at-risk cohort would be less complicated, or have more uniform uterine environments throughout gestation, than the comparison population cohort. Recent findings indicate that there are gross morphological differences between population and high ASD risk placentas [3]. This work suggests that the ASD placenta might be less able to compensate for intrauterine variability. This could be merely a marker for vulnerability to risk factors or it could be mechanistically important in ASD etiology if reduced compensatory capacity leaves the fetus more vulnerable to other stressors. Objective In this project, we will explore whether differences in high-risk ASD placentas are confined to children actually diagnosed with ASD at 3 years of age, or whether high-risk families have global and basic differences in placental morphology. Familiarity with statistics and programming in MATLAB or another software such as SAS, R, C++, and Python is recommended. Related ongoing research questions 1. What discriminating PSCVN features are determined early in gestation, i.e., during the 1st trimester? 2. How much of the results established in 2-dimensional placental surface can be transferred to a 3-dimensional imaging environment? That is, what geometric signatures are measurable and capable of providing discriminating power in a 3-dimensional imaging environment? 3. What are the genetic causes for the group of PCSVN features responsible for explaining the differences between high- and low-risk ASD cohorts? Can we model this relationship mathematically using the structure and the function of placenta? Support Team We will have at our disposal an interdisciplinary research team who will be supporting us with data and answering any biology- and imaging-related problems associated with the project. References [1] R. Shah, C. Salafia, T. Girardi, L. Conrad, K. Keaty, A. Bartleotc, Shape matching algorithm to validate the tracing protocol of placental chorionic surface vessel networks, Placenta 36 (2015) 944—946. doi:10.1016/j.placenta.2015.05.004. [2] C. Salafia, Placental vascular tree as biomarker of autism/ASD risk, Annual report for U.S. Army Medical Research and Materiel Command at Fort Detrick, Maryland 21702-5012 W81XWH-10-1-0626, Research Foundation for Mental Hygiene, http://www.dtic.mil/dtic/tr/fulltext/u2/a575079.pdf (2014). [3] J.-M. Chang, H. Zeng, R. Han, Y.-M. Chang, R. Shah, C. Salafia, C. Newschaffer, R. K. Miller, P. J. Katzman, J. Moye, M. Fallin, C. K. Walker, Lisa Croen, Discriminating placentas of increased risk for autism with chorionic surface vascular network features, submitted (2016). Ectoparasites and Allogrooming - Evolutionary Trade-offs in Animal Community Health Leader: Nina Fefferman, University of Tennessee, Knoxville Co-leader: Shelby Wilson, Morehouse College Project Summary: This project will use a combination of differential equations, network models, and agent based simulations to consider trade-offs between exposure to parasitic infection and expected health benefits from social support. We will work to characterize co-evolutionary trajectories governed by interactions of demographic vital rates of hosts and parasites, the epidemiology of ectoparasitic infections, and the social/hygienic behavior of the hosts. If time and expertise permits, we will attempt to explain observed patterns in wildlife populations. Modeling Argasid Ticks Leader: Holly Gaff, ODU Co-Leader: Gaby Hamerlinck, Bioquest Background Argasid or soft-bodied ticks are known vectors of many human and animal pathogens worldwide. These animals are poorly understood and incompletely studied because of their complex life histories. Unlike hard-bodied ticks, soft ticks have variable life histories with the multiple instars in each life stage and variable time between life stages depending on host density. While soft ticks can live up to 20 years, the generation time is generally closer to five years. There is currently no published mathematical model looking at the dynamics of this family of ticks. Our goal is to use published models for hard ticks, mosquitos, and other arthropods to create an initial soft tick model. Objectives 1. Develop a simple life history model for soft ticks with constant host density. 2. Add variable host types to assess impact on tick dynamics. 3. Add a pathogen to explore disease dynamics. Suggested reading Anderson, J.F. and Magnarelli, L.A., 2008. Biology of ticks. Infectious disease clinics of North America, 22(2), pp.195-215. Dworkin, M.S., Shoemaker, P.C., Fritz, C.L., Dowell, M.E. and Anderson, D.E., 2002. The epidemiology of tick-borne relapsing fever in the United States. The American journal of tropical medicine and hygiene, 66(6), pp.753-758. Gaff, H.D. and Gross, L.J., 2007. Modeling tick-borne disease: a metapopulation model. Bulletin of mathematical biology, 69(1), pp.265-288. Sánchez-Vizcaíno, J.M., Mur, L. and Martínez-López, B., 2012. African swine fever: an epidemiological update. Transboundary and emerging diseases,59(s1), pp.27-35. Mechanics of super-fast nematocyst firing Leader: Laura Miller, UNC Co-leader: Wanda Strychalski, Case Western University Nematocysts are the specialized cells of jellyfish and other Cnidarians that sting. They contain a barbed, venomous thread that accelerates faster than almost anything else in the animal kingdom. In this project, we will simulate the fluid-structure interaction of the barbed thread accelerating through water to puncture its prey using the immersed boundary method. Both twoand three-dimensional simulations will be performed using an adaptive and parallelized software library that is freely available (IBAMR). We will use ultra-fast high speed video to parameterize the model. One aspect of this project that is particularly interesting is that the micron-sized barbed thread reaches Reynolds numbers above one, where inertial effects become important. At this scale, even small changes in speed and shape can have dramatic changes on the local flow field. This suggests that the large variety of sizes and shapes of nematocyst may have important fluid dynamic consequences. References: Timm Nüchter, Martin Benoit, Ulrike Engel, Suat Özbek and Thomas W. Holstein (2006). Nanosecond- scale kinetics of nematocyst discharge. Current Biology, 16(9): R316. C. S. Peskin (2002). The immersed boundary method. Acta Numerica, 11: 479-517. Disease and Combination Therapy Dynamics Leader: Helen Moore, BMS Co-leader: Nessy Tania, MBI Selecting doses for a new therapy combines modeling and experimental testing and validation. When multiple therapies are combined, it can be more challenging to determine optimal regimens, due to the number of variables and limited amount of experimental testing possible. In this project, we will analyze a system of ordinary differential equations representing a disease and multiple therapies. The goal is to understand and describe the behavior of the model from a dynamical systems point of view, as this will aid the search for the best regimens. Typically, we might perform identifiability, bifurcation, and sensitivity analyses, as well as literature searches to find parameter estimates and related information and to restrict the parameter space. We will decide as a team how best to approach this problem. This work is part of a larger program to determine combination regimens that are most efficacious for particular diseases. Suggested Reading: Moore, H. and Li. "A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction.” J Theor Bio (2004) 227:513-523.
