User:Jpeirce

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Hello! I'm a professor of mathematics at the University of Wisconsin-La Crosse with an interest in mathematical ecology and epidemiology.

Current Research

Temperature-driven Host-Parasite Model

Project Summary

In collaboration with Dr. Greg Sandland (UWL Biology Dept.), we study an annual model for waterfowl disease in the Upper Mississippi River. Transmission relies on stochastic water temperatures gleaned from empirical studies. As annual average temperatures rise, infected host populations initially increase. Infected host populations decay after temperatures exceed a certain threshold. Increasing temperatures in the region may have a negative effect on parasites.

Abstract

Bithynia tentaculata is an invasive snail that was discovered in the Upper Mississippi River (UMR) in 2002. In addition to being a threat to native benthos, the snail also harbors parasite associated with annual outbreaks of waterfowl mortality in the UMR. Trophic transmission of parasites between snails and birds occurs during seasonal waterfowl migrations, which can depend intimately on temperature. We developed an annual model for waterfowl disease in the UMR where transmission depends on water temperatures gleaned from empirical studies. By running simulations from annual temperature profiles selected randomly from a normal distribution, we quantified the association between the number of infected hosts and annual average temperatures. Model output demonstrated that as annual average temperatures rise, infected host populations initially increase and then decay after temperatures exceed a certain threshold. Results from this work suggest that increasing temperatures in the region may have a negative effect on parasites, decreasing their transmission and reducing infected host populations.

  • Peirce, J. P., G. J. Sandland, B. Bennie, and R. J. Haro. "Modeling and analysis of a temperature-driven outbreak of waterfowl disease in the Upper Mississippi River." Ecological Modelling 320 (2016): 71-78.
  • Sandland, Gregory J., et al. "Infection patterns in invasive and native snail hosts exposed to a parasite associated with waterfowl mortality in the Upper Mississippi River, USA." Journal of wildlife diseases 50.1 (2014): 125-129.

Background Papers

  • Altizer, Sonia, et al. "Seasonality and the dynamics of infectious diseases." Ecology letters 9.4 (2006): 467-484.
  • Grassly, Nicholas C., and Christophe Fraser. "Seasonal infectious disease epidemiology." Proceedings of the Royal Society of London B: Biological Sciences 273.1600 (2006): 2541-2550.
  • Liu, Luju, Xiao-Qiang Zhao, and Yicang Zhou. "A tuberculosis model with seasonality." Bulletin of mathematical biology 72.4 (2010): 931-952.
  • Wesley, Curtis L., and Linda JS Allen. "The basic reproduction number in epidemic models with periodic demographics." Journal of biological dynamics 3.2-3 (2009): 116-129.
  • Zhang, Juan, et al. "Modeling seasonal rabies epidemics in China." Bulletin of mathematical biology 74.5 (2012): 1226-1251.

Modeling the Influence of El Niño on Parasite Transmission in Sand Crab Populations and Shorebird Abundance Along the California Coast

Project Summary

Collaboration with Dr. Olcay Akman(Illinois State Univ.) and Abou Seck(Illinois State Univ.)

Abstract

Pacific mole crabs (Emerita analoga) are one of the most important and abundant invertebrates in sandy beach environments. Consequently, they are a common food source for shorebirds and sea otters. Since the mole crab serves as the primary intermediate host for acanthocephalans parasites, they have been linked to a number of mortality events. It is currently estimated that 13-16% of deaths in the threatened California sea otter population have been caused by infection. In addition, unusually high loads of acanthocephalan parasites have been linked to episodic deaths of thousands of surf scoters. Studies suggest that acanthocephalan development and transmission may be strongly effected by weather patterns. We have created a system of differential equations for parasite transmission between scoter, crab, and sea otter populations. Temperature-dependent parameters within the model allow us to examine the role climate oscillation in El Niño and La Niña years has on abundances of infected hosts.

Dynamic Energy Budgets

Project Summary

This is an investigate how an infection can alter a host's allocation of energy.

Abstract

Invading species and their parasitic hitchhikers are rapidly altering biological landscapes across North America and around the world. Interactions between invasive hosts and parasites can have significant consequences for the diversity of native communities, conservation policy, and ultimately, national and global economics. Bithynia tentaculata is an invasive aquatic snail that has recently spread to the Upper Mississippi River (UMR) from the Great Lakes region. This snail harbors 3 species of trematode (flatworm) parasites that have rippling effects throughout the ecosystem due to their detrimental impacts on thousands of migrating waterfowl every year. Unfortunately, even though these organisms are disrupting general ecosystem stability and economics in the upper Midwest, little is actually known about the factors responsible for successful snail colonization and subsequent parasite transmission. This 'informational void' severely limits our ability to predict the dynamics of both hosts and parasites in the future.

Our research group has developed an epidemiological (i.e. SIR-variate) model for the parasite’s transmission between homogeneous infection states. However, we have not done much work at the scale of an individual host. A dynamic energy budget (DEB) model of an individual organism describes the rates at which the organism assimilates and utilizes energy for maintenance, growth and reproduction, as a function of the state of the organism and of its environment. It is suspected that parasite infection may alter substantially a host’s energy allocation strategy. For example, empirical observations suggest that infected snails may be larger in size than uninfected. This may be related to parasitic castration of the host and consequently the under-utilization of energy towards reproduction. Integrating empirical data and results from recent publications, can we construct a DEB model for infected and uninfected Bithynia tentaculata?

Background Papers

Start Here
  • Peirce, J. P., G. J. Sandland, B. Bennie, and R. J. Haro. "Modeling and analysis of a temperature-driven outbreak of waterfowl disease in the Upper Mississippi River." Ecological Modelling 320 (2016): 71-78.
  • Nisbet, R. M., E. B. Muller, K. Lika, and S. A. L. M. Kooijman. "From molecules to ecosystems through dynamic energy budget models." Journal of animal ecology 69, no. 6 (2000): 913-926.
  • Ledder, Glenn, J. David Logan, and Anthony Joern. "Dynamic energy budget models with size-dependent hazard rates." Journal of mathematical biology 48, no. 6 (2004): 605-622.
Other Sources
  • Hall, Spencer R., Claes Becker, and Carla E. Cáceres. "Parasitic castration: a perspective from a model of dynamic energy budgets." Integrative and comparative biology 47, no. 2 (2007): 295-309.
  • Kooijman, Sebastiaan Adriaan Louis Maria. Dynamic energy and mass budgets in biological systems. Cambridge university press, 2000.
  • Ledder, Glenn. "The Basic Dynamic Energy Budget Model and Some Implications." Letters in Biomathematics 1, no. 2 (2014): 221-233.
  • van der Meer, Jaap. "An introduction to Dynamic Energy Budget (DEB) models with special emphasis on parameter estimation." Journal of Sea Research 56, no. 2 (2006): 85-102.

Biomath Curriculum

In 2009, I created a course, Mathematical Models in Biology, for students with only a Calculus I background. The course introduces students (early!) to the mathematical modeling process as it applied to the biological and chemical sciences. Students are provided an introduction to discrete- and continuous-time dynamical systems and inferential statistics. They are repeatedly expected to: develop a conceptual models, formulate a mathematical models from the conceptual model, analyze the model using mathematics or computer programming (in this class, we use R), and validate the model by comparing results to their initial assumptions. My colleague, Eric Eager, recently flipped the course so that the lecture content was watched outside of class and students worked on case studies during class. A summary of the course and the flipped format can be found in the paper referenced below.

  • E Alan Eager, J Peirce, P Barlow. "Math Bio or Biomath? Flipping the mathematical biology classroom." Letters in Biomathematics 1 (2), 139-155.

Previous Projects

UBM-Collaborations on Riverine Ecology

2010-2013 - Our interdisciplinary team received a National Science Foundation grant, “UBM-CORE: Collaborations on Riverine Ecology“ (PI: J. Peirce, Co-PIs: G. Sandland, R. Haro, and B. Bennie), to investigate various aspects of species invasion and disease transmission. The CORE project supported the research of four undergraduate students from UWL per year for three years. The mathematics and biology students supported by the grant worked in interdisciplinary pairs to address ecologically relevant questions empirically with laboratory experiments and/or field observations and theoretically with mathematical and/or statistical models.

CORE Students have made over 40 oral or poster presentations at local, regional, and national levels. Venues of dissemination include JMM, the National Conference on Undergraduate Research, and the National Institute for Mathematical and Biological Synthesis. A noteworthy impact of the CORE program was the development of research skills and experience for the 12 participating undergraduate mathematics and biology students. Through their participation in CORE, the students have developed a strong understanding of disease dynamics and developing models around such systems. In addition, students have had the opportunity to put their theoretical questions into practice by designing empirical experiments that not only test their hypotheses, but also elucidate parameters for their theoretical models. To date, all 12 students have finished their undergraduate degrees, five have gone on to graduate school in STEM fields, and one specifically in Mathematical Biology. Two other students are employed in a capacity that supports research at the interface between math and biology.

Example of projects:

  • A model for optimal energy allocation for a snail host exposed to parasite infection (2013).
  • Modeling the effects of multiple host species on disease transmission in the Upper Mississippi River (2012).
  • Investigating the role of host competition in the transmission of waterfowl disease in the upper Mississippi River (2011).

UWL Dean's Distinguished Summer Fellowship

  • Investigating the dependence of transmission rate to water temperature in a host-parasite system (2014-2015)
  • Predicting and Understanding Waterfowl Die-offs (2010)

How Infectious was #Deflategate

In mid-Janurary 2015 the National Football League (NFL) started an investigation into whether the New England Patriots deliberately deflated the footballs used during their AFC Championship win. Like an infectious disease, the initial discussion regarding Deflategate grew rapidly on social media sites in the days after the release of the story, only to slowly dissipate as interest in the NFL waned following the completion of its season. Working with my colleague, Eric Eager, and a student we apply a simple epidemic model for the infectiousness of the Deflategate news story. We find that the infectiousness of Deflategate rivals that of many of the infectious diseases that we have seen historically, and is actually more infectious than recent news stories of seemingly greater cultural importance.

  • Eberle, Megan, Eric A. Eager, and James Peirce. "How Infectious Was #Deflategate?." Spora: A Journal of Biomathematics 1.1 (2016): 5.

Contact Information

Mathematica Workshop

For the IBA Conference 2016, I provided an introduction to the mathematical software Mathematica and a few of its uses in Biomathematics. The Mathematica notebooks linked below contain

1) An introduction to Mathematica (notational nuances, plotting, using the manipulate command)
2) Numerical approximations of differential equations (DEs) (Euler's Method and built-in solvers)
3) Analysis of nonlinear systems of DEs (finding equilibrium, plotting phase portrait and nullclines, computing Jacobian matrix)
4) Fitting nonlinear functions to data.  

with applications to population and disease models.

https://about.illinoisstate.edu/iba/Pages/Workshops.aspx