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We introduce and analyze a within-host dynamical model of the coevolution between rapidly mutating pathogens and the adaptive immune response. Pathogen mutation and a homeostatic constraint on lymphocytes both play a role in allowing the…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
The Susceptible-Infected-Susceptible (SIS) model is one of the simplest memoryless system for describing information/epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched…
From critical infrastructure, to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Despite advances…
Although timely sepsis diagnosis and prompt interventions in Intensive Care Unit (ICU) patients are associated with reduced mortality, early clinical recognition is frequently impeded by non-specific signs of infection and failure to detect…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
In this paper we study the susceptible-infectious (SI) epidemiological model using dynamical graphs. Dynamical structures have been recently applied in many areas including complex systems. Dynamical structures include the mutual…
Sepsis is a life-threatening host response to infection associated with high mortality, morbidity, and health costs. Its management is highly time-sensitive since each hour of delayed treatment increases mortality due to irreversible organ…
One of the key challenges in modeling the dynamics of contagion phenomena is to understand how the structure of social interactions shapes the time course of a disease. Complex network theory has provided significant advances in this…
Network interactions that are nonlinear in the state of more than two nodes - also known as higher-order interactions - can have a profound impact on the collective network dynamics. Here we develop a coupled cell hypernetwork formalism to…
A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics…
Our brain is a complex information processing network in which the nervous system receives information from the environment to quickly react to incoming events or learns from experience to sharp our memory. In the nervous system, the brain…
Parkinson's disease (PD) belongs to the class of neurodegenerative disorders that affect the central nervous system. It is usually defined as the gradual loss of dopaminergic neurons in the substantia nigra pars compacta, which causes both…
Mathematical models of infectious disease transmission typically neglect within-host dynamics. Yet within-host dynamics - including pathogen replication, host immune responses, and interactions with microbiota - are crucial not only for…
Sepsis remains one of the most complex and heterogeneous syndromes in intensive care, characterized by diverse physiological trajectories and variable responses to treatment. While deep learning models perform well in the early prediction…
We investigate the dynamics of an epidemiological susceptible-infected-susceptible (SIS) model on an adaptive network. This model combines epidemic spreading (dynamics on the network) with rewiring of network connections (topological…
Under many physiological and pathological conditions such as division and migration, cells undergo dramatic deformations, under which their mechanical integrity is supported by cytoskeletal networks (i.e. intermediate filaments, F-actin,…
Synchronization of brain activity fluctuations is believed to represent communication between spatially distant neural processes. These inter-areal functional interactions develop in the background of a complex network of axonal connections…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the…