Special Session 6: Modeling and Data Analysis for Complex Systems and Dynamics

Global stability analysis of a novel epidemic model with separate compartments for symptomatic and asymptomatic cases

Yerimbet Aitzhanov SDU university Kazakhstan Co-Author(s):    Shirali Kadyrov

Abstract: This talk presents a novel epidemic model that incorporates both reported and unreported cases, distinguishing between symptomatic and asymptomatic individuals. The global stability of the model is demonstrated using a Lyapunov function, emphasizing the significant impact of asymptomatic cases on disease dynamics and control measures. The results of elasticity analysis also explores, revealing how this division influences the fundamental reproduction number. Additionally, sensitivity analysis is performed using Partial Rank Correlation Coefficient (PRCC) and Sobol indices to assess the influence of various parameters on the model`s compartments ($E$, $I_r$, $I_u$, $R$). The results reveal the critical roles of transmission rate ($\beta$), recovery rates ($\lambda_r$, $\lambda_u$), and immunity loss rate ($\alpha$) in shaping model dynamics. These findings provide insights into the primary drivers of the model`s behavior and underscore the importance of considering both symptomatic and asymptomatic cases in developing effective epidemic models and control strategies.

Dynamics of prey-predator network model with application to virus and immune response evolution

Cameron Browne University of Louisiana at Lafayette USA Co-Author(s):

Abstract: Recent work has sought to understand assembly and coexistence of interacting species in ecosystem models. However, the overwhelming number of species combinations and connecting the models to evolution have challenged researchers, especially in higher dimensional systems. Here, we aim to address this gap by looking through an evolutionary genetics lens in a prey-predator model of virus-immune dynamics, where viral variants can be represented by binary sequences which encode their resistance to immune responses. First, persistence and stability of equilibria are studied using Lyapunov functions and invasion analysis. Then, bifurcations between distinct ecological network structures are linked to epistasis (non-additivity) in the viral fitness landscape. Results are discussed in the context of HIV escape of host immune responses and, more generally, finding simplifying rules for prey-predator network evolution.

Stock Exchange Critical States: Criticality Time Intervals and Avalanche-Like Dynamics

Andrey Dmitriev HSE Tikhonov Moscow Institute of Electronics and Mathematics, HSE University Russia Co-Author(s):    Nazar Yurakov, Vasily Kornilov

Abstract: Our study provides empirical, data-driven, and theoretical evidence that stock exchanges self-organize into a critical state with avalanche-like dynamics. We identified time intervals in the hourly stock volume series for 3,000 public company stocks for which the stock market is in a critical state. The time intervals were determined based on the behavior of the 100-hour moving average in the vicinity of the critical time. Next, we propose a model of self-organization of the stock exchange in a critical state, in which the control parameter is the measure of uncertainty of information about a public company`s share, and the order parameter is stock`s volume.

The seizure classification of focal epilepsy based on the network motif analysis

Denggui Fan University of Science and Technology Beijing Peoples Rep of China Co-Author(s):

Abstract: Due to the complexity of focal epilepsy and its risk for transiting to the generalized epilepsy, the development of reliable classification methods to accurately predict and classify focal and generalized seizures is critical for the clinical management of patients with epilepsy. In order to holistically understand the seizure propagation behavior of focal epilepsy, we propose a three-node motif reduced network by respectively simplifying the focal region, surrounding healthy region and their critical regions as the single node. Because three-node motif can richly characterize information evolutions, the motif analysis method could comprehensively investigate the seizure behavior of focal epilepsy. Firstly, we define a new seizure propagation marker value to capture the seizure onsets and intensity. Based on the three-node motif analysis, it is shown that the focal seizure and spreading can be categorized as inhibitory seizure, focal seizure, focal-critical seizure and generalized seizures, respectively. The four types of seizures correspond to specific modal types respectively, reflecting the strong correlation between seizure behavior and information flow evolution. In addition, it is found that the intensity difference of outflow and inflow information from the critical node (connection heterogeneity) and the excitability of the critical node significantly affected the distribution and transition of the four seizure types. In particular, the method of local linear stability analysis also verifies the effectiveness of four types of seizures classification. In sum, this paper computationally confirms the complex dynamic behavior of focal seizures, and the study of criticality is helpful to propose novel seizure control strategies.

Bistability in a Model of Hepatitis B Virus Dynamics

Hayriye Gulbudak University of Louisiana at Lafayette USA Co-Author(s):

Abstract: Understanding the mechanisms responsible for different clinical outcomes following hepatitis B infection requires a systems investigation of dynamical interactions between the virus and the immune system. To help elucidate mechanisms of protection, we developed a deterministic mathematical model of hepatitis B infection that accounts for cytotoxic immune responses resulting in infected cell death, non- cytotoxic immune responses resulting in infected cell cure and protective immunity from reinfection, and cell proliferation. We analyzed the model and presented outcomes based on three important disease markers: the basic reproduction number R0, the infected cells death rate (describing the effect of cytotoxic immune responses), and the liver carrying capacity K (describing the liver susceptibility to infection). Using asymptotic and bifurcation analysis techniques, we determined regions where virus is cleared, virus persists, and where clearance-persistence is determined by the size of viral inoculum. These results can guide the development of personalized intervention.

Data Fitting in Fuzzy Epidemic Models Using Genetic Algorithms

Shirali Kadyrov New Uzbekistan University Uzbekistan Co-Author(s):    Yerimbet Aitzhanov, Nurdaulet Shynarbek

Abstract: The need for advanced modeling techniques in epidemiology has become increasingly evident. This presentation explores the integration of fuzzy set theory and genetic algorithms to enhance data fitting in fuzzy epidemic models. We focus on fuzzy epidemic models that accommodate uncertainties and population heterogeneity by treating epidemiological parameters as fuzzy variables. Our approach employs genetic algorithms for parameter estimation, enabling effective fitting of real-world epidemic data while addressing the complexities of disease transmission dynamics. The presentation highlights how genetic algorithms can refine model parameters and improve alignment between theoretical models and observed data.

Forecasting the Long-Term Trends of Tuberculosis Using the Time-series Analysis and Susceptible-Infectious-Recovered (SIR) Model

Aigerim Kalizhanova Nazarbayev University Kazakhstan Co-Author(s):    Sauran Yerdessov, Yesbolat Sakko, Aigul Tursynbayeva, Shirali Kadyrov, Abduzhappar Gaipov, Ardak Kashkynbayev

Abstract: Tuberculosis (TB) is a highly contagious disease that remains a global concern affecting numerous countries. Kazakhstan has been facing considerable challenges in TB control for decades. This talk explains TB dynamics by developing and comparing statistical and deterministic models: Seasonal Autoregressive Integrated Moving Average (SARIMA) and the basic Susceptible-Infected-Recovered (SIR). TB data from 2014 to 2019 were collected from the Unified National Electronic Health System (UNEHS) using retrospective quantitative analysis. SARIMA models were able to capture seasonal variations, with Model 2 exhibiting superior predictive accuracy. Both models showed declining TB incidence and revealed a notable predictive performance evaluated by statistical metrics. In addition, the SIR model calculated the basic reproduction number ($R_0$) below 1, indicating a receding epidemic. Models proved the capability of each to accurately capture trends (SARIMA) and provide mathematical insights (SIR) into TB dynamics. This talk contributes to the general knowledge of TB dynamics in Kazakhstan thus laying the foundation for more comprehensive studies on TB and control strategies.

Complex Systems on the Edge of Chaos: Temporal Precursors vs. Spatiotemporal Precursors

Vasily Kornilov Graduate School of Business, HSE University Russia Co-Author(s):    Vasily Kornilov, Dmitry Mosharov, Andrey Dmitriev

Abstract: Most complex systems, both natural and artificial, are capable of self-organization to the edge of a phase transition known as the edge of chaos. Examples of such systems include stock markets, online social networks, epidemic spread networks, and many others. The irreversible presence of a complex system on the edge of chaos is characterized by its avalanche-like behavior, which often leads to catastrophic consequences for the system. Therefore, early warning is very important for the system to approach the edge of chaos, which, with sufficient early warning time, will make it possible to take preventive measures to prevent the system from reaching the edge. Real-time early warning systems typically use temporal and/or spatiotemporal early warning measures of self-organization to the edge of chaos. Temporal measures are calculated in a sliding window of a time series corresponding to some dynamic variable, such as the number of reposts on an online social network. Such measures are computationally less complex and more accessible for calculations than spatiotemporal measures, the calculation of which requires information about the interactions between elements of the system in space and time. Recently, it has become increasingly common to hear the assertion that temporary measures are ineffective for the early warning. Moreover, some researchers claim that early warning using such measures is impossible. Therefore, we investigated the effectiveness of temporal and spatiotemporal measures associated with critical slowdown of a complex system as it approaches the edge of chaos. First, we introduce the concept of the effectiveness of an early warning measure in terms of the time of early warning and the number of false warning. Next, we calculate the spatiotemporal and corresponding temporal early warning measures associated with the critical slowdown of the sandpile cellular automaton as a system isomorphic to some real-world systems in the context of systems theory. Finally, we compare the effectiveness of the respective measures. We were able to establish that temporary measures are no less effective than the corresponding spatiotemporal measures.

Data-driven machine learning framework to predict dynamics of complex infectious disease models incorporating human behavior

PADMANABHAN SESHAIYER George Mason University USA Co-Author(s):

Abstract: A complex system refers to a collection of interconnected elements or components that exhibit emergent behaviors and properties arising from their interactions. The COVID-19 pandemic, as an example of such a complex system, highlighted the significance of mathematical epidemiological modeling and data analysis in understanding disease dynamics. It also highlighted the importance of interdisciplinary collaborations integrating research on behavioral and/or social processes in mathematical epidemiological models with a goal to minimize unintended outcomes of public health interventions in response to pandemics. In this work we aim to enhance complex epidemiological models by integrating insights from social and behavioral sciences with data-driven predictive analytics. The proposed work will present a hybrid framework combining Agent-Based Modeling, Compartmental Models, and Physics-Informed Neural Networks applied to benchmark problems to efficiently conduct parameter estimation and data-driven decision-making.

Brain Complex Data Analytics To Identify Epileptic Activity Using EEG Source Localization Methods

Jianzhong Su University of Texas at Arlington USA Co-Author(s):    Julio Ensico-Elva, Talon Johnson

Abstract: Data analytics plays an increasing role in brain research and medicine. The well-known Hodgkin-Huxley theory for neurons laid a foundation for computational neuroscience. However, understanding activities in the whole brain remains a focus of active research for this very complex system. Full brain Electroencephalography (EEG) and its source localization is a brain imaging modality based on multi-channel EEG signals. It measures the brain field potential fluctuations on the entire scalp for a period of time, and then we can compute the electric current density inside the brain by solving an inverse problem for an electric field equation on the 3-D brain finite element model. In this talk, we introduce computational methods for the EEG imaging problems, their validations through experimental data, and discuss its applications. One application is in identifying brain activity abnormalities and the sequence of excitation in brain anatomic areas during seizures of infant patients with Glucose Transporter Deficiency Syndrome. Our research shows the EEG data sets can be used to glean into the inner working of brain normal and pathological functions in specific brain areas using data analytic algorithms.

The Stability of Memory Storage in the Hippocampus

Honghui Zhang Northwestern polytechnical university Peoples Rep of China Co-Author(s):    Lei Yang, Zhongkui Sun

Abstract: Based on the physiological mechanism underlying the hippocampus for memory storage, we have developed a CA3CA1 synaptic network memory model that elucidates the stored process of sensory information. Once information is stored in long-term memory, the model encodes it into trajectories within a stable heteroclinic network (SHN) in the phase space. Saddle points within the SHN represent the information blocks that information is divided into in the process of short-term memory. In this paper, memory strength and lifetime are introduced to measure the stability of memory storage in hippocampus. We track the storage process of initial memory, which is stored in distinct synaptic pattern, resulting in a durable memory engram. Subsequent memories are stored in either tracked or untracked synapses, which can cause decay and interference on the engram of the initial memory. We discussed the dynamics of AMPA receptors efficacy on tracked synapses based on the CA3CA1 synaptic network model. And estimated the decay effect of untracked synapses based on a synaptic plasticity discrete model. Numerical results indicate that the memory strength is dependent on the relative activation level of the PKA cascade within the postsynaptic neurons during encoding. This strength is further augmented during the consolidation process, which is induced by the decay effect. In the process of consolidation, the complexity of information and the number of synaptic inputs, as well as the excitatory-inhibitory balance, are important factors influencing the memory strength. The forgetting process for long-term memory is driven by the decay effect, and the memory information, efficiency, and various neurodegenerative diseases can alter the lifetime of initial memory by regulating the decay effect.

Dynamic analysis of beta oscillation in Parkinsonian neural networks with pedunculopntine nucleus under optogenetic control

Yuzhi Zhao Northwestern Polytechnical University Peoples Rep of China Co-Author(s):    Yuzhi Zhao, Honghui Zhang, Ying Yu, Lin Du, Zichen Deng

Abstract: Clinical experiments have proven that the pedunculopontine nucleus (PPN) plays a crucial role in the modulation of beta oscillations in Parkinson`s disease (PD). Here, we propose a new computational framework by introducing the PPN and related synaptic connections to the classic basal ganglia-thalamo-cortical (BGTC) model. Fascinatingly, the improved model can not only simulate the basic saturated and beta activities mentioned in previous studies but also produce the normal alpha rhythm that is much closer to physiological phenomena. Specifically, the results show that parkinsonian oscillation activities can be controlled and modulated by the connection strength between the PPN and the globus pallidus internal nucleus (GPi) and the subthalamic nucleus (STN), supporting the fact that PPN is overinhibited in PD. Meanwhile, the internal mechanism underlying these state transitions is further explained from the perspective of dynamics. Additionally, both deep brain stimulation (DBS) and optogenetic technology are considered effective in terms of abnormal oscillations. Especially when a low-frequency DBS is added to the PPN, beta oscillations can be suppressed, but it is excited again as the DBS`s frequency gradually increases to a larger value. These results coincide with the experimental results that low frequency stimulation of the PPN is effective, and verify the rationality of the model. Furthermore, we show that optogenetic stimulation of the globus pallidus external (GPe) expressing excitatory channelrhodopsin (ChR2) can effectively inhibit beta oscillations, whereas exciting the STN and PPN has a limited effect. These results are consistent with experimental reports suggesting that the symptoms of PD`s movement disorder can be alleviated under the GPe-ChR2, but not STN-ChR2, situation. Although the functional role of the PPN and the feasibility of optogenetic stimulation remain to be clinically explored, the results obtained help us understand the mechanisms of beta oscillations in PD.