MS11: Mathematical methods in population biology and neuroscience
Organizers:
- Lucas Martins Stolerman, Oklahoma State University
- Pedro Maia, University of Texas at Arlington
Session A: Oct.2, 10:30am-11:50am, Classroom Building 121
MS11-A-1 |
Haridas K. Das, |
Network modeling and simulation of infectious diseases: new epidemic thresholds for the SIR-network model |
We study the SIR-network model proposed by Stolerman, Coombs, and Boatto in 2015 that established flux-driven epidemic control by analyzing epidemic thresholds for fully connected networks, where a single node has a different infection rate. Here we extend this result for a larger class of networks, establishing new epidemic thresholds using the basic reproduction number R0 obtained from the classic next-generation matrix. First, we look at star-shaped networks, where all nodes connect to the center with different transmission rates than the others and exhibit the same epidemic thresholds as the fully connected networks. Next, we find the same epidemic thresholds for star-background networks, in which all nodes except the center link with a different flux. Inspired by this preliminary result, we propose a class of networks headed by star-shaped networks that reveal the same epidemic threshold given by explicit formulas as fully connected networks. We also analyze cycle-shaped networks exhibit a different nature from such flux-driven epidemic control. Finally, we present numerical simulations showing a convergence of the epidemic threshold of cycle-shaped networks. We also numerically integrate our system to gain intuition where the theoretical estimates are challenging and explore the temporal epidemic dynamical behavior for the class of networks. |
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MS11-A-2 10:50am-11:10am (Oct 2) CLB 121 |
Chanaka Kottegoda, Oklahoma State University |
Complex dynamics of predator-prey systems with generalized Holling type IV functional response and Allee effects in prey |
This talk is devoted to high codimension bifurcations of a predator-prey system with generalized Holling type response function and Allee effects in prey. The system shows rich dynamics such as nilpotent cusp singularity of order 3, degenerate Hopf bifurcation of codimension 3 and Bogdanov-Takens bifurcation of order 3. Moreover, a new unfolding of nilpotent saddle of codimension 3 with a fixed invariant line is discovered and fully developed. Our work extends the existing results of predator-prey systems with Allee effects. The bifurcation analysis and diagram allow us to give biological interpretations. |
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MS11-A-3 11:10am-11:30am (Oct 2) CLB 121 |
Khitam Zuhair Bader Aqel, University of Texas at Arlington |
Data-driven Techniques for Dynamical System with Applications to Neuroscience |
The neuroscience community is keen to understand more about Local Field Potential(LFP) signal alterations in the murine brain's pain circuits in both the absence and presence of anesthesia. The purpose of the study was to compare the LFP signals' complexity in the anesthetized and awake rats using data-driven techniques. We use three data-driven methods: Eigensystem Realization Algorithm(ERA), Sparse Identification of Nonlinear Dynamics(SINDy), and Neural Networks(NNs), to extract coherent structures from the physiological time-series data. Data-driven approaches use the measured LFP signals to generate modal characteristics of the system. We apply these data-driven techniques to reconstruct signals recorded from four brain regions of two groups of rats: (i) freely moving and (ii) anesthetized. We will compare the reconstructions given by each method in different phases of the experiment and discuss their advantages and pitfalls. |
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MS11-A-4 11:30am-11:50am (Oct 2) CLB 121 |
Nethali Fernando, University of Texas Arlington |
Analysis of goal, feedback and rewards on sustained attention via machine learning |
Sustaining attention is a notoriously difficult task as shown in a recent experiment where reaction times (RTs) and pupillometry data were recorded from 350 subjects in a 30-minute vigilance task. Subjects were also presented with different types of goal, feedback, and reward. In this study, we revisit this experimental data and solve three families of machine learning problems: (i) RT-regression problems, to predict subjects' RTs using all available data, (ii) RT-classification problems, to classify responses more broadly as attentive, semi-attentive, and inattentive, and (iii) to predict the subjects' experimental conditions from physiological data. After establishing that regressing RTs is in general a difficult task, we achieve better results classifying them in broader categories. We also successfully disambiguate subjects who received goals and rewards from those who did not. Finally, we quantify changes in accuracy when coarser features (averaged throughout multiple trials) are used. Interestingly, the machine learning pipeline selects different features depending on their resolution, suggesting that predictive physiological features are also resolution specific. |