Seminar Series-2025

Pest management remains a critical challenge in both agriculture and ecology, requiring effective and sustainable strategies to regulate pest populations while minimizing environmental and economic impacts. A key approach in understanding and optimizing pest control measures is through mathematical modeling, which provides deep insights into the complex interactions between pests and their natural enemies—commonly referred to as prey-predator interactions. Such models help predict pest outbreaks, assess control measures, and design sustainable pest suppression techniques. In this talk, we will explore eco-epidemic models that integrate both continuous and impulsive control methods to regulate pest populations. We will begin by discussing continuous control strategies, which include biological control through predator-prey interactions, where natural enemies, such as parasitoids or predatory insects, help suppress pest outbreaks. We will then introduce impulsive control methods, which involve periodic interventions such as pesticide applications or the cyclical release of natural enemies to keep pest populations under control. These impulsive control strategies are modeled using impulsive differential equations, which account for sudden, discrete changes in population levels. To analyze the effectiveness of these control strategies, we will employ Floquet theory for studying the stability of periodic solutions and the comparison theorem for impulsive differential equations to examine system permanence. By leveraging a combination of biological and chemical control methods, we can gain valuable insights into the overall impact of these interventions on pest suppression and ecosystem stability. Additionally, we will extend our discussion to include the role of disease dynamics within pest populations, exploring how infections can serve as a natural regulatory mechanism and how they can be incorporated into pest control strategies. Using mathematical analysis and simulations, we will demonstrate how different control strategies influence long-term pest population dynamics, ultimately contributing to more efficient, sustainable, and environmentally friendly pest management practices.

We analyze the dynamics of epidemics in a community composed of both residents and short-stay visitors using a five-dimensional system of ordinary differential equations derived from the SIR and SIS models. By considering different perspectives on public health policies for disease control, we establish multiple basic reproduction numbers and examine their mathematical properties to clarify their implications for epidemic dynamics. Our analysis highlights the potential impact of short-stay visitors on disease transmission and progression within the community. Furthermore, we demonstrate the necessity of selecting an appropriate variant of the basic reproduction number to inform effective public health interventions. 

Catherine Morris and Harold Lecar introduced a foundational model of neuron dynamics in 1981, which has been the subject of extensive studies since then. In this talk, however, I will talk about a reduced two-dimensional denatured Morris-Lecar (dML) model, first discussed in the book by Schaeffer and Cain. I will start by talking about how codimension-one and -two bifurcation analyses reveal complex patterns in the system. We will observe saddle-node and Hopf bifurcations along with cusps and generalized Hopf. Next, I will discuss how the model dynamics can be perturbed with an external electromagnetic flux. Then, I will talk about a three-dimensional slow-fast system of the dML model that introduces bursting phenomena making the model more realistic. I will use various metrics and tools from nonlinear-dynamics literature to study various bifurcations and complex patterns that arise in the single-cell and a two-coupled slow-fast dML model. Finally, I will deviate a bit from the standard integer-order differential operators to study a system of Caputo-type fractional-order dML neurons, both single-cell and coupled. We will see how changing the fractional order, also known as memory index, induces Hopf bifurcations in the fractional model.

Diabetes is one of the most prevalent diseases worldwide, characterized by persistently high blood sugar levels, capable of damaging various internal organs and systems. Diabetes patients require routine check-ups, resulting in a time series of laboratory records, such as hemoglobin A1c, which reflects each patient's health behavior over time and informs their doctor's recommendations. Clustering patients into groups based on their entire time series data assists doctors in making recommendations and choosing treatments without the need to review all records. However, time series clustering of this type of dataset introduces some challenges; patients visit their doctors at different time points, making it difficult to capture and match trends, peaks, and patterns. Additionally, two aspects must be considered: differences in the levels of laboratory results and differences in trends and patterns. To address these challenges, we introduce a new clustering algorithm called Time and Trend Traveling Time Series Clustering (4TaStiC), using a base dissimilarity measure combined with  Euclidean and Pearson correlation metrics. We evaluated this algorithm on artificial datasets, comparing its performance with that of six existing methods. The results show that 4TaStiC outperformed the other methods on the targeted datasets. Finally, we applied 4TaStiC to cluster a cohort of 1,989 type 2 diabetes patients at Siriraj Hospital. Each group of patients exhibits clear characteristics that will benefit doctors in making efficient clinical decisions. Furthermore, the proposed algorithm can be applied to contexts outside the medical field.

The intricate dynamics of neural networks arise from both their underlying connectivity and the nature of interactions among neurons. This seminar explores emergent phenomena in neuronal systems, with a particular focus on first order (pairwise) and higher-order (multi-neuron) interactions modeled through FitzHugh–Nagumo (FHN) neurons in continuous, discrete, and memristive frameworks. We first examine spatially structured neuronal networks where coupling strength and distance-dependent interactions give rise to chimera states and self-induced switching behaviors (dynamics wherein neurons spontaneously transition between synchronized and unsynchronized states without external stimuli). Building on this, we delve into networks that include co-rotating and counter-rotating oscillators, revealing how rotation direction and higher-order connectivity critically influence network dynamics, including the suppression or facilitation of chimera states. Finally, the role of memristive coupling in discrete neuron models is analyzed, where nonlinear synchronization stability is assessed using Master Stability Functions (MSF). We identify critical coupling regimes and demonstrate how synchronization stability boundaries shift with memristor flux coefficients and higher-order interactions. Together, these studies underscore the rich interplay between topology, interaction order, and neuron dynamics, offering insights for brain-inspired computing and the design of robust neuromorphic systems.