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Mathematics & Statistics

College of Arts & Sciences

Spatial Epidemics of Cassava Mosaic Virus Disease

Cassava (Manihot esculenta Crantz) is the crop with largest weight production in Africa, and may be considered as a viable solution for the hindering food crisis in this continent. More than 400 million people in Africa rely on cassava crops as a means of food security. Both roots and leaves are used as food consumption. Currently, plant virus pandemic is being driven by overly abundant whitefly (Bemisia tabaci) vectors. This project will employ datasets on vector abundance, virus disease incidence, and fresh root yield collected in Uganda and Tanzania, by the International Institute of Tropical Agriculture. Weekly longitudinal observations within a year will be used to validate vector-host dynamic models of disease. Compartmental ODE models will be proposed for this study. Computer simulations would account for virus-vector interactions, population dynamics, vector-natural enemy interactions and biological control.  Additionally, spatial data, from a 2 degree by 2 degree quadrant in north-western Tanzania, will be incorporated to assess the spread of the cassava mosaic virus disease pandemic in arrays of interconnected fields.  Hypothesis testing yielding extended knowledge and better understanding of this plant virus pandemic is a key to effective management.  External collaborator: James Legg is a plant virologist at IITA, with more than 20 years experience of working on plant viruses and their insect vectors.  His research portfolio includes: virus-vector interactions; development and deployment of host plant resistance; and vector population dynamics/bionomics.


Diabetes in Specific Demographics

We consider racial or ethnic minority populations in the United States (US) to include American Indians, Alaska Natives, Black or African Americans, Hispanics or Latinos, Asian Americans, Pacific Islanders. The project addresses disease prevalence among minority populations. Specifically, type 2 diabetes prevalence in the US is significantly higher in the African American population. Yet, the physiological reasons contributing to this health disparity have not been fully elucidated. Diabetes is a disease influenced by interdependent genetic factors with the potential of environmental triggers in new borns. Clearly, there is a need to determine what is driving the racial differences in diabetes prevalence. A review article by Staiano, et al., [1], synthesizes and evaluates the potential genetic mechanisms that may contribute to the higher susceptibility of African Americans to type 2 diabetes. The paper highlights the clinical significance of findings and limitations of the recent literature. Our student research group will note the limitations cited and discuss possible research avenues to address, in some part at least, these limitations.

We propose to investigate type 2 diabetes prevalence with mathematical modeling from two fronts: network analysis and system dynamics.  The endgame will be to address the question: How do our findings in this program contribute to our understanding of
the disparity of type 2 diabetes in minority populations?

Network Analysis.  Protein-protein interactions regulate nearly every living process and are best modeled by protein-protein interaction networks (PPIN). It is known that PPIN's are often perturbed by disease and the study of these PPIN has become a major focus in biomedical research in the realm of systems biology.

It is well known that increased rates of inflammatory diseases are highly associated with type 2 diabetes. Availability of high-throughput data has enabled the construction of numerous PPIN for both healthy and diseased states. In [1], the authors present a systems biology
approach to develop gene interaction network models, comprised of high throughput genomic and PPI data for type 2 diabetes. The genes that are differentially regulated by patients with type 2 diabetes were studied to get a more complete understanding of the overall gene network topology and their role in disease progression. They present a highly regulated gene-disease integrated network model that provides functional linkages among groups of genes. Based on the investigations around the 'hubs', a hypothetical co-regulation
disease mechanism model is proposed. Their findings provide an approach for understanding the relation of type 2 diabetes to other inflammatory diseases by combining the power of pathway analysis with gene regulatory network evaluation.

Other research articles such as [2,3,4] that employ network science to investigate type 2 diabetes will be utilized for student reserch projects. Although most people with type 2 diabetes are obese, most obese people never develop diabetes. They are able to compensate for the insulin resistance that usually accompanies obesity by producing more insulin. The authors of [3] studied
gene expression relative to gene variation and used these data to generate network models, which incorporate gene loci, mRNA abundance, and other phenotypes.

System Dynamics.  The system dynamics methodology assumes the interplay of feedback loops, stocks and flows, and delays gives rise to complexity. Model-building takes center stage while representing dynamic complexity of aggregate phenomena, such as: predatory-prey temporal relationships, reaction kinetics, or pharmacokinetic dynamics. Simulation of proposed models often facilitates evaluation of temporal patterns, together with comparison against hypothesized system behaviors. Nonlinear systems of ordinary differential equations will be implemented within the context of pharmacokinetic-pharmacodynamic modeling. The compartmental modeling methodology formulated by Sun, et al. [5], will employed as a central guideline. Here state variables are conceptually equivalent to physiological compartments in a typical human body (e.g., brain, heart, lungs, liver, gut, kidney, etc).  The differential equations in this type of approach preserve well-known mass balance laws.

Student participants will estimate model parameters from previously published longitudinal datasets via least squares methods. Upon model calibration, treatment schedules will be formulated as optimal control problems. Assessment of various pharmacological agents will be explored by numerical experiments.

Another venue of exploration with differential equation modeling is pathways of gene expression.  A well-understood result is that gene networks act as a switch. The so-called genetic toggle switch models [6,7] bring together compartmental methodology and gene-protein connectivity, by realizing these type of systems resemble electrical circuits. We will review the work by Hasty, et al. [6], pertaining to
engineered gene circuits, where this resemblance is formally mathematized while laying the foundations
for synthetic gene networks: the backbone of synthetic biology [7].

[1] Staiano, A.E., et al., Uncovering physiological mechanisms for health disparities in type 2 diabetes, Ethn Dis. 2015 Winter, 25 (1): 31–37.

[2] Attie, A.D., and Keller, M.P., Gene co-expression modules and type 2 diabetes, Results Probl Cell Differ. 2010;52:47-56.

[3] Keller, M.P., et al., A gene expression network model of type 2 diabetes links cell
cycle regulation in islets with diabetes susceptibility, Genone Res. 2008, 18:706?716.

[4] Topfa, F. , et al., .The Human Diabetes Proteome Project (HDPP): From
network biology to targets for therapies and prevention, Transl. Proteomics, 2013; 1(1):3--11.

[5] Sun, L., et al., Pharmacokinetic-Pharmacodynamic
modeling of metformin for the treatment of type 2 diabetes mellitus,
Open Biomed Eng J, 2011, 5, 1--7.

[6] Hasty, J., McMillen, D., Collins, J.J., Engineered gene circuits,
Nature, 2002, 420, 224--230.

[7] Khalil, A.S., and Collins, J.J., Synthetic biology: applications come of age,
Nature Rev. Genetics, 2010, 11, 367--379.

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