Speaker: Kevin Flores

Title: A mathematical model to correlate the importance of gene specific mutations and tumor development

Affiliation: Department of Mathematics and Statistics, Arizona State University

Abstract: Understanding the correlation of gene specific mutations and tumor development has important implications in cancer therapy. Recent empirical data have elucidated the candidate cancer genes responsible for carcinogenesis through mutation and expression analysis. This work has revealed the heterogeneities in genotype that encode cancers of the same malignancy grade, providing evidence for the existence of multiple mutational paths that a population of cancer cells can take to manifest itself as a disease. The cell genotypes that are present in a tumor affect the malignancy grade through their effect on the phenotypes of individual cells that the tumor is comprised of.
  We use a graph theoretical approach to connect the gene expression and mutation data to cell phenotype. We have constructed a gene regulatory network from the KEGG pathway database. This network includes most accurately and completely the relevant pathways that contain the known cancer genes, which in turn encode distinct cell phenotypes. We are analyzing the network to predict the sensitivity of cell signaling pathways that control cell growth and death to alterations caused by gene mutations. The prevalence of gene mutations show no correlation to the betweenness- centrality of their respective nodes in the network and a low correlation with the number of paths that affect proteins whose expression are known to cause different cell phenotypes. Because of the lack of necessary reaction rate data to model any of the interactions, we turn to a network boolean dynamics model. With synchronous updating we find that the phenotypic output resulting from the deterministic network dynamics are insensitive to the candidate gene mutations. With asynchronous updating we find that the state space of the dynamics becomes too large to sample using random initial conditions. We employ the Wang-Landau monte carlo algorithm with the network states in which the expression of specific phenotype proteins determine the energies of the initial conditions. We consider 4 energies that correspond to distinct cell phenotypes: Proliferation, Apoptosis, Survival, and None of the above. With this type of sampling we can determine whether changes in the network caused by mutations lead to altered proportions of states whose asynchronous progression will end in the phenotypes that are represented by the predefined energies.

Speaker: Carlos Torre

Title: Spatial transmission dynamics of dengue fever in Peru

Affiliation: Department of Mathematics and Statistics, Arizona State University

Abstract: According to the NIH, 50 to 100 million cases of dengue infection occur each year. This includes 100 to 200 cases in the United States, mostly in people who have recently traveled abroad. Dengue cases range from asymptomatic, clinically non-specific flu like symptoms, dengue fever, dengue hemorrhagic fever, and dengue shock syndrome. We developed a spatial mathematical model that incorporates the epidemiology of dengue fever to study the patterns of transmissibility of dengue in Peru. We used data of the number of weekly dengue cases in Peru at the level of Provinces and departments for the years 1994-2006. We assessed the correlations of transmissibility and final epidemic size with climatological, demographic, and geographic variables. We also studied the distribution of the final epidemic size and the distribution of epidemic duration. We are currently evaluating different ways of coupling 195 provinces to study the global spread of dengue in Peru.

Speaker: Chad Gonzales

Title: Estimating the Impact of Seasonal Influenza on a Subtropical City

Affiliation: Department of Mathematics and Statistics, Arizona State University

Abstract: Influenza is a common illness and is a major cause of acute respiratory diseases. It infects millions of people annually and it is one whose complications, usually secondary infection with pneumonia, cause an estimated one million deaths worldwide. Estimating the burden of influenza is difficult due to the transmission mechanism and is an important public health problem.
   We have constructed a compartmental model of the transmission dynamics of influenza followed by secondary infection with bacterial pneumonia. The model coupled with data from pneumonia hospitalization cases in Guadalajara, Mexico have allowed us to estimate the annual burden of influenza.
  We also estimated the transmissibility of the influenza seasons as measured by the reproduction number (R), defined as the number of secondary cases caused by an infectious individual in a partially immune population. If R is greater than 1 an epidemic can occur. If R is less than 1, the epidemic cannot be sustained. We estimated the reproduction number for each of the years of data and found estimates that range from 1.6 to 1.9, which is in agreement with the estimates obtained using data from France, Australia and the United States.