Chaos: An Interdisciplinary Journal of Nonlinear Science

We have studied the emergence of slow relaxation oscillations in next generation neural mass models with spike frequency adaptation. Relaxation oscillations connect low firing state (Down state) to high firing state (Up state) via the slow adaptation. In the examined cases, the orbit relaxes towards the Up State via a sequence of collective damped oscillations (peaks of activity), thus revealing population bursting dynamics. The slower is the adaptation time scale the higher is the complexity (number of peaks) displayed by the relaxation oscillations. In particular, a chaos-induced spike-adding mechanism regulates the increase in the number of peaks. In analogy to what found in the Hidmarsh-Rose neuron model, two different types of chaotic behaviors have been identified: Population Spiking and Population Bursting Chaos. The increase of the adaptation strength leads to shorter (longer) Up (Down) state durations somehow mimicking the effect of charbachol in in vitro experiments, where spontaneous slow waves are observed. Indeed, the scenario depicted in [1], where an increase of the concentration of carbachol induces a transition from anesthesia-like to sleep-like dynamics is consistent with our results based on the variation of the adaptation strength. HighlightsO_LISpike Frequency Adaptation (SFA) promotes the emergence of Slow Relaxation Oscillations C_LIO_LISpike-adding mechanisms, controlled by SFA, lead to Relaxation Oscillations of increasing complexity C_LIO_LITwo types of chaotic behaviours: Population Spiking and Population Bursting Chaos C_LIO_LISFA regulates Up and Down States durations and their correlation C_LI

Allergic conjunctivitis is an inflammation of the conjunctiva caused by allergen; it is common disorder affecting up to 40% of the population. In this work, we study seasonal allergic conjunctivitis (SAC), also called "hay fever eyes", which is caused by exposure to airborne pollens. We develop a mathematical model quantifying the ocular immune system response to the allergens. First, we present a simplified qualitative description of the immunopathogenesis of SAC. Then, we express each chosen immunopathological mechanism mathematically to construct a system of thirty-one ordinary differential equations. We compare summary statistics of the predicted observable immune signals to experimental measurements and find our model captures key qualitative features of SAC progression. We then compare our predicted time series of histamine concentration to symptom scores and find a strong correlation suggesting the model predicts relevant clinically trends. Next, we calibrate the model through multi-step process. We find the most influential parameters are the production and depletion rates of IL-4, and the production rates of IL-5 and IL-8. These cytokines are targeted in treatments for asthma, atopic dermatitis, and severe eosinophilic associated disorder and suggest potential therapeutic targets for SAC. Our calibrated model mimics most of the summary statistics of the experimentally observable immune signals with discrepancies for IL-5 and IL-13 indicating that additional immunopathological mechanisms could be important.

Efficient operation of neural networks has been linked to criticality in their underlying non-equilibrium excitation dynamics. However, obtaining experimental evidence of this conjecture remains challenging due to limited control and undersampling in biological systems. Here, we experimentally explore neural network criticality using an ultracold Rydberg gas as a highly controllable simulator. We highlight the similarity of the excitation spreading via Rydberg facilitation and the synaptic connection of spiking activity of neurons, giving rise to distinct absorbing and active phases. We systematically explore and resolve criticality criteria, including power-law scaling of excitation avalanches and the emergence of universal avalanche shape collapse. Crucially, we implement a controlled gain mechanism to compensate for atom loss, mimicking metabolic resource replenishment and stabilizing the system in a controlled non-equilibrium steady state. We find peak temporal correlations at the critical point and stochastic oscillations with dragon king avalanches in the active phase, consistent with predictions for systems orbiting criticality. Our work establishes facilitated Rydberg gases as a platform for investigating criticality, resource dynamics, and emergent oscillations in neural networks.

With 302 neurons and a rigorously characterized connectome, the nematode Caenorhabditis elegans represents a powerful model organism to study the fundamental roles of neuronal circuits in behavior. However, despite the breadth of research, many questions remain unanswered regarding how these organisms are able to successfully navigate their environment. Here, we present a biologically grounded dynamical circuit model for the investigation of sensory-guided behavior during C. elegans chemotaxis. Our mathematical model consists of the chemosensory neuron AWA, interneurons RIM and RIA, motor neurons, including SMDs and RMDs, and body wall muscles that provide proprioceptive feedback through stretch receptors. After optimization with an evolutionary algorithm, the model locomotes effectively toward a chemical attractant, realistically capturing nematode chemotactic behavior. Chemotaxis is ensured by sharp turns, which resemble the omega turns of living nematodes, as a key emergent property of the model. The sharp turning behavior is triggered by decreases in the concentration of the attractant. These result in reduced AWA activity, which in turn triggers disinhibition of RIM and subsequent changes in RIA oscillations. The ensuing coordinated changes in downstream motor neurons activity patterns produce sharp turns, which correct the nematodes path, so that the model worm heads toward the attractant, and remains at its proximity, after it reaches the gradient peak. The proposed framework, along with its emergent dynamics, provides new insights into the minimum requirements for C. elegans circuitry to display major features of its chemotactic behavior, including omega turns. In parallel, it generates experimentally testable hypotheses with respect to the participating neuronal elements.

Extensive studies suggest the brain performs Bayesian inference to infer the latent world states. It is a fundamental neuroscience question that how canonical recurrent neural circuits in the brain implement Bayesian inference. Many existing theoretical studies focused on how the recurrent circuits compute the posterior, while largely overlooking how the circuits compute the model evidence (normalization constant in Bayes' theorem), a key quantity that measures how well a model explains the observed data.Thus, it remains largely unknown about how the recurrent circuits compute the model evidence. The present study performs rigorous theoretical analyses of the continuous attractor networks, a canonical recurrent circuit model, and reveals that the nonlinear circuit dynamics can simultaneously compute the posterior and model evidence in first two dominant subspaces within the circuit dynamics. Specifically, the circuit dynamics in the stimulus feature subspace implements the Langevin posterior sampling, and the circuit dynamics in the subspace of total neuronal activity computes the model evidence in a way analogous to the evidence lower bound in stochastic variational inference. We further extend the circuit model to compute the model evidence of multiple inputs, and simulations validate the computation in the network. Our work for the first time reveals the concurrent model evidence and posterior sampling in subspaces in continuous attractor networks, significantly deepen our understanding of the computational algorithms adopted by the neural circuits.

Sequestration of gene products through diverse mechanisms forms a fundamental layer of regulation in intracellular biochemical processes, including post-translational modification, promiscuous binding to genomic decoy sites, and partitioning into membraneless compartments formed through phase separation. Here, we develop a unified stochastic framework to quantify how such sequestration-type processes, when coupled to noisy gene expression, modulate cell-to-cell variation in protein levels. In this model, protein molecules reversibly switch between active (free) and inactive (sequestered) states, whose switching rates are arbitrary functions of the molecular counts. Using exact analytical calculations and the linear noise approximation, we derive expressions for the Fano factor of the active-protein level and identify fluctuation attenuation regimes in terms of the logarithmic sensitivities of the switching rates to protein abundances. We show that inactive-protein-dependent switching, of which genomic decoy binding is a natural example, can preserve Poisson-level fluctuations in the active-protein level under appropriate conditions. Enzymatic inactivation, a type of post-translational modification, emerges as a special case of active-protein-dependent sequestration, where greater responsiveness of the inactivation propensity attenuates active-protein fluctuations. In both decoy binding and enzymatic inactivation, protecting the inactive protein from decay lowers active-protein fluctuations. Finally, a noise-buffering regime associated with intracellular phase separation is recovered when the inactive-to-active switching rate depends inversely on the inactive-protein level. Together, the examples of genomic decoy binding, enzymatic inactivation, and intracellular phase separation suggest that noise buffering observed across diverse intracellular processes is rooted in a broader class of reversible sequestration mechanisms that attenuate protein-level fluctuations.

Interception of moving objects is a universal pattern of animal behavior with many industrial applications. Inspired by the behavior of the characid fish Brycon guatemalensis, which catches fruits falling onto the surface of a river, we study one-shot (i.e., open-loop) interceptions using both stochastic optimal control theory and reinforcement learning. In the first instance, an agent actuates a control (wait time before launch and heading angle) to meet its target, given a noisy estimate of the target initial state. In a minimal setting, where launch velocity and actuated control are constants, we show that the optimal wait time is attenuated by noise in both the target measurement and control actuation, as well as agent energy conservation. We then derive an upper bound for the heading angle variance which scales as the ratio of the non-vanishing optimal interception error to the initial planar separation. Complementing our control framework, our deep reinforcement learning approach shows that the neural network representing the fish first learns the value function for the interception, then learns how to aim, and finally learns the optimal wait time. Beyond the specific problem at hand, our results may also have applications to problems with little time for feedback or corrections such as perching, landing, and docking.

Emerging research on desynchronization reveals strong relations to memory formation and recollection with much of the evidence originating from studies of the hippocampus, a brain region central to memory processing. However, growing evidence emphasizing the role of desynchronization is accompanied by challenges, most notably the synchronization/desynchronization conundrum. The conundrum arises from an apparent contradiction between learning and Shannon's information theory: spike-timing-dependent plasticity (STDP) acquires information via synchronized populational activity whereas information theory suggests that information channel is encoded through higher variability. Both frameworks are well-founded. Learning is widely accepted as the mathematical abstraction of STDP while Shannon's information theory showcases its power ubiquitously across fields from communication systems to neuroscience. Here, we propose that learning and Shannon's information theory are not necessarily opposing principles. Rather, learning plays a critical role in the process of synchronization and desynchronization. To justify our claim, we conduct computational simulations based on a Hodgkin-Huxley neuronal model coupled with NMDA, AMPA, and GABA synapses with inputs of biologically realistic spiking data. Our results show that enabling STDP significantly influences synchronization and desynchronization dynamics. Specifically, we find that STDP and desynchronization form a regulatory loop, in which STDP regulates the level of synchrony, and synchrony regulates subsequent learning strength. Further study reveals STDP is capable of switching neurons from synchronization to desynchronization. This framework mitigates the synchronization/desynchronization conundrum by clarifying the relationship between desynchronization and learning, and offers a new perspective on how synchrony contributes to memory formation and recollection.

SynGAP and PSD-95 undergo liquid-liquid phase separation in vitro, motivating models of the postsynaptic density (PSD) as a biomolecular condensate. However, how their association kinetics and intermolecular interactions shape activity-dependent partitioning remains unclear. We develop a multicomponent framework that couples equilibrium Flory-Huggins calculations in conserved total-composition space to four-species Cahn-Hilliard-reaction dynamics for free SynGAP, free PSD-95, the SynGAP-PSD-95 complex, and solvent. Complex formation and dissociation are represented by explicit forward and reverse activity-based mass-action rates. These calculations show that the equilibrium association constant and self- and cross-interaction energies jointly control the extent and composition of the two-phase region. For an illustrative LTP-like parameter switch, decreasing the equilibrium association constant and altering selected interaction energies redistributes SynGAP from the PSD-95-rich phase to the PSD-95-poor phase without eliminating the PSD-95-rich phase. A separate equilibrium comparison represents haploinsufficiency as a 50% reduction in total SynGAP. For the illustrative parameter sets, the reduced-SynGAP composition remains within the two-phase region but has different tie-line endpoints and phase compositions than the control composition.

Obesity is a major health concern worldwide and is caused by an excessive fat accumulation in the body due to adipogenesis. Recent studies suggest that excessive stress or disruption of circadian rhythms can enhance adipogenic commitment and lead to obesity. Moreover, this adipogenic commitment occurs at a specific time of day, highlighting a correlation with the circadian rhythm. However, the dynamical nature of this kind of stress-induced adipogenic differentiation remains an unresolved puzzle. Herein, we proposed a mathematical model centred on the key transcription factor PPAR{gamma}, associated with adipogenic differentiation, and demonstrated that adipogenic commitment is a bistable, irreversible differentiation process in which slow positive feedback regulation of PPAR{gamma} primarily controls the differentiation commitment threshold. The model reproduced the experimental observations regarding the extent of adipogenesis induced by constant and pulsatile stress input signals and explained the correlation between adipogenic differentiation time and circadian phase. It further predicts how to control the adipogenic commitment even under stressful conditions. Overall, our study elucidates how stress signalling dynamically governs adipogenesis.

Japanese Encephalitis Virus (JEV) belongs to the Flavivirus family, and the RNA dependent RNA polymerase (RdRp) domain located at the C terminus of non structural protein 5 (NS5) regulates de novo viral genome synthesis. The conserved priming loop inserted in the thumb domain of RDRP initiates de novo genome synthesis. Interestingly, the reported replication process initiates with an interaction between NS5 (methyltransferase/RDRP) and NS3 (protease/helicase), and inhibiting this interaction directly correlates with the inhibition of viral replication. The function of the priming loop in the context of the NS5 NS3 interaction is not yet known. In this study, we studied the priming loop function in the NS5 NS3 interaction and viral replication. Using a structure based drug design approach, we screened the Maybridge compound library against the RdRp priming loop and identified 15 candidate compounds based on binding energy. Among them, DSHS00151 showed significant dose dependent inhibition of the NS5 NS3 interaction with an IC50 of 3.5 micromolar in the mammalian two hybrid assay, inhibited viral infectivity with an IC50 of 2.54 micromolar, and reduced viral RNA load with an IC50 of 2.9 micromolar, compared to CD10712. Molecular Dynamics (MD) simulations revealed that DSHS00151 exhibits stronger and more stable binding with the priming loop residues (790 to 812) compared to CD10712. The molecular mechanism suggested by the docking of the NS5 and NS3 proteins showed that the priming loop tends to rotate toward the NS3 protein to stabilize the complex, and compound binding restricts this loop rotation, thus compromising the stability of the NS5 and NS3 complex and affecting viral replication. Overall, our study validated the function of the NS5 priming loop as an allosteric site, and compounds binding to this allosteric site belong to the Non Nucleoside Reverse Transcriptase Inhibitors (NNRTI) class of inhibitors, which disrupt the NS5 and NS3 interaction and could be developed as novel anti JEV therapeutics.

The global potential of a chemical reaction network has many applications and is closely related to the stochastic detailed balance. However, many fundamental questions concerning stochastic detailed balance remain unresolved, such as whether it depends on the system volume and how to construct new systems that satisfy it. In this paper, we show that stochastic detailed balance may depend on the system volume. We therefore introduce four types of stochastic detailed balance according to their dependence on volume and rate constants, and systematically investigate the relationships among them. Our results distinguish detailed balance arising from particular choices of volume and parameters from that enforced by network structure, and identify conditions under which detailed balance at one volume extends to all volumes. We further obtain a class of networks satisfying stochastic detailed balance for every volume and every positive choice of rate constants, and construct new systems whose global potentials exhibit double-well structures.

Trigger waves are positive feedback-mediated traveling waves that propagate without slowing down or diminishing in amplitude, enabling biochemical coordination over distances where diffusion alone would be insufficient. Apoptosis can spread as trigger waves of caspase activity, as demonstrated in Xenopus eggs and egg extracts. We measured apoptotic wave speeds in extracts at two cell cycle states and found that waves propagated more slowly in M-phase arrested cytostatic factor (CSF) extracts than in interphase extracts (21 versus 27 m min-1). Luther's equation, v=2{surd}D{kappa}, predicts wave speed from the diffusion coefficient D and the positive-feedback doubling rate {kappa}. However, D and {kappa} were comparable between the two extracts and could not explain the speed difference. This discrepancy highlighted a key limitation of the classical equation: it does not account for an activation threshold in trigger wave initiation, and in fact the threshold required to trigger apoptosis was found to differ between cell cycle states. We therefore extended Luther's equation to include such a threshold, obtaining v{propto}{surd}(AD/Uc ), where A is the reaction rate and Uc is the activation threshold. Perturbing apoptotic sensitivity confirmed the predicted threshold-speed relationship. These findings establish the activation threshold as a key determinant of trigger wave speed and provide a broadly applicable scaling law for predicting the spread of switch-like biochemical signals.

Astrocytes actively regulate synaptic transmission and neuronal excitability, yet their role in orchestrating macroscopic cortical network regimes and slow-wave oscillations remains an active area of reasearch. This study investigates how bidirectional neuron astrocyte interactions shape emergent population dynamics using a computational network model of excitatory and inhibitory neurons coupled to an astrocyte. The results identify astrocytic feedback topology, rather than astrocytic coupling strength alone, as a key determinant of emergent cortical network dynamics. By systematically dissecting pathway-specific connectivity, it has been shown that the neuronal population driving astrocytic activation and the neuronal population receiving gliotransmission jointly determine whether the network occupies asynchronous irregular (AI), synchronous irregular (SI), synchronous regular(SR), asynchronous regular(AR) or quiescent regimes.Directing gliotransmission selectively onto excitatory neurons consistently promotes population synchrony regardless of the population influencing astrocytic dynamics, whereas selective modulation of inhibitory interneurons induces network quiescence via strong suppression. Under dual-target gliotransmission, network synchrony is dictated by the population driving astrocytic dynamics: excitatory-only drive promotes synchrony, while combined or inhibitory-specific drive preserves asynchronous states. Furthermore, the model reveals that astrocytic signaling kinetics provide an additional temporal control mechanism that regulates the frequency and persistence of self sustained up states.

The initial response of populations to the SARS-CoV-2 virus reduced the incidence of COVID-19 cases. However, this success was shorted lived once most populations relaxed most restrictions, resulting in an increase in infections. This feedback contributed to additional pandemic waves. The temporal unfolding of behavioural changes in populations present a challenge to mathematical models for disease dynamics. Coupled behaviour-disease models with varying levels of complexity accounting for several factors have been used to capture behavioural dynamics and SARS-CoV-2 transmission, with varying results. To study the impact of model complexity on the predictive power of models, here we formulate five coupled behaviour-disease models with varying structure and number of parameters. We fit the models to SARS-CoV-2 infection incidence and stringency of control interventions from five European countries in the first wave, and study how well these fitted models predict the second wave. We show that models with more parameters do not necessarily have a greater ability to explain and predict key features of a pandemic wave. Hence, our results show that a relatively simple coupled behaviour-disease model with important parameters can do an adequate job of providing information about the pandemic wave. Additionally, our findings show that complex models can be country-specific, working better for some countries and poorly for others. We conclude that modellers should not always opt for the most complicated possible models, if the data do not support their use.

The circadian clock allows living systems to anticipate environmental daily variations by scheduling cellular mechanisms according to the time of the day. The reciprocal interplay between metabolism and circadian clock is essential for energy homeostasis, and the disruption of metabolic clock inputs contributes to dysfunction of clocks in peripheral tissues. However, the molecular mechanisms through which the feeding/fasting cycle entrains peripheral clocks remain incompletely understood. Here, we investigate experimentally and theoretically the role of AMP-dependent kinase (AMPK), a key fasting sensor, in metabolic regulation of the circadian clock. Using a luciferase reporter driven by the Bmal1 promoter to monitor molecular clock activity in human U2OS cells, and thanks to a signal processing method based on the Hilbert transform to retrieve the instantaneous phase and period of circadian signals, we show that pharmacological activation of AMPK by AICAR significantly elevates Bmal1 promoter activity and markedly lengthens the clock period in a dose-dependent manner. Conversely, the clock period is shortened by the pharmacological inhibition by SR18292 of Peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC-1-alpha). Importantly, the action of AICAR is abolished by FK866, a nicotinamide phosphoribosyltransferase (NAMPT) inhibitor, demonstrating that AMPK-dependent modulation of Bmal1 promoter activity requires NAD+ availability. These experimental results are recapitulated by numerical simulations of our previously published mathematical model, where PGC-1-alpha plays a key role in mediating AMPK activity to the clock. Moreover, the comparison of experimentally measured and theoretically predicted phase response curves, following AMPK activation at different circadian phases, provides an additional validation of the model. By integrating biological experiments with mathematical modeling, our results identify a key mechanism through which metabolic factors can entrain and regulate the circadian clock via NAD+-dependent AMPK-mediated regulation of Bmal1 promoter activity.

In the two-process model of sleep-wake regulation, circadian-modulated thresholds time every sleep onset and awakening, yet they remain free parameters rather than quantities derived from neuronal dynamics. This limitation leaves the framework unable to predict how sleep patterns change when neuromodulatory drive is altered, as in aging and narcolepsy. Here we close that gap by deriving closed-form, circadian-modulated threshold expressions from the Phillips-Robinson model with explicit orexinergic excitation of the wake-promoting population. Within this single threshold geometry, aging and narcolepsy appear as opposite deformations along the orexinergic axis: age-related hyperexcitability of orexin neurons elevates the sleep-onset boundary and creates a fragility regime in which minor nocturnal disturbances trigger premature awakenings, whereas orexin loss depresses the same boundary toward the wake-onset threshold and produces the rapid state fragmentation of narcolepsy. Concurrently, reduced circadian amplitude compresses the inter-threshold corridor, advancing sleep onset and shortening sleep duration. These results convert the classical two-process thresholds from descriptive conveniences into mechanistic organizers of sleep-wake dynamics across healthy aging and orexin deficiency. Author summaryThe classical two-process model of sleep relies on a pair of switching thresholds that have been imposed by hand rather than derived from the neurons that actually stabilize sleep and wakefulness. Here we remove this limitation: starting from a biophysical mean-field model of the sleep- and wake-promoting populations, and adding the orexin system that stabilizes arousal, we derive the sleep-onset and awakening thresholds analytically from the bifurcation geometry of the underlying dynamical system. These closed-form thresholds depend explicitly on circadian phase, homeostatic state, and orexinergic tone, revealing that aging and narcolepsy are opposite deformations of a single threshold corridor along one orexinergic axis. In aging, orexin hyperexcitability raises the sleep-onset barrier past a sharp "arousal fragility boundary," beyond which a minor disturbance triggers irreversible awakening; in narcolepsy, orexin loss collapses the same barrier and fragments sleep while paradoxically preserving total sleep time. We further find, contrary to common assumption, that orexin sustains wakefulness chiefly by raising the barrier to falling asleep rather than by resisting awakening. This work turns phenomenological sleep thresholds into physics-derived organizers of behavior, providing a mechanistic bridge from neuronal circuitry to whole-organism sleep dynamics.

A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or bifurcations, the approach focuses on the geometry of membrane potential trajectories. The changes in concavity during the upstroke of an action potential can be directly obtained from a time series of voltages. The concavity criterion is then extended to models based on autonomous dynamical systems where the changes in concavity can be obtained analytically from a curve of inflection points in phase space. The inflection point manifold defines a region required for excitability: all the orbits that cross it contain action potentials, and all the trajectories that contain action potentials are in it. This analytical principle can then be used to define excitability in a dynamical system, and also a measure of excitability that enables quantification and comparisons of excitability across dynamical system. The measure provides a way to compare the excitabilities of systems that model neurons with different electrophysiological phenotypes and consider different stimulus conditions. The traditionally vague physiological concept of electrical excitability is transformed into a rigorous analytical description by considering the time-dependent curvature of the membrane potential. The criterion is robust across smooth, single compartment models of electrical excitability and can be can be extended to single compartment models in higher dimensions, and multicompartment models as well.

Aoki et al. (2023) proposed that the sharp difference in microblade distribution between the north and south of the Qinling-Huaihe (H-Q) line before the early Holocene could have been due to a higher frequency of pathogens in the south. Greater susceptibility to pathogen-induced disease among northerners could have effectively prevented migration across the H-Q line. Here, we explore the possibility that migration between the north and south could have been stalled by a vector-borne disease whose vector distribution was climate dependent. The original wave equation approach is extended to include climate variation in the forms of (i) a period of linear warming; (ii) a period of linear cooling; and (iii) a period of temperature oscillations. Simulations of this extended model are carried out using published estimates of the climate record for the Northern Hemisphere since the Upper Paleolithic. This analysis suggests possible time intervals during which microblades could have reached the south.

Background: Tuberculosis remains a persistent infectious disease whose control is complicated by latent infection, delayed treatment, incomplete recovery, reinfection, and continuing transmission from infectious individuals. Although treatment is central to tuberculosis management, it is frequently represented only as a transition parameter in mathematical models rather than as a separate epidemiological state. In this study, treatment was therefore incorporated explicitly as an independent compartment so that its influence on transmission, recovery, disease-induced mortality, and long-term disease persistence could be evaluated. Methods: A deterministic nonlinear compartmental model was formulated by dividing the total population into susceptible, exposed, actively infected, treated, and recovered classes. Reinfection of recovered individuals, progression from latent infection to active disease, movement of infectious individuals into treatment, treatment-associated recovery, natural mortality, and disease-induced mortality were included. Positivity and boundedness of the solutions were examined to establish biological validity. The basic reproduction number, R0, was derived through the next-generation matrix approach. Disease-free and endemic equilibria were determined, and their local and conditional global stability properties were investigated using Jacobian analysis, the Routh-Hurwitz criterion, center manifold theory, Lyapunov functions, and LaSalles invariance principle. Normalized sensitivity indices, Latin hypercube sampling, partial rank correlation coefficients, and numerical simulations were also applied. Results: The disease-free equilibrium was shown to be locally asymptotically stable when ,R0<1 whereas sustained transmission and a unique endemic equilibrium were associated with R0>1. Under the stated reduced-model assumptions, stability of the endemic equilibrium was established. Transmission-related parameters were identified as the strongest positive contributors to disease persistence. In contrast, treatment and recovery parameters were found to reduce the reproduction number and infectious burden. Numerical simulations indicated that stronger treatment implementation and reduced transmission opportunities produced substantial reductions in active tuberculosis cases. Conclusion: Treatment was shown to function as both a clinical pathway and an epidemiological control mechanism. The proposed framework may support the design of treatment-centered strategies for reducing tuberculosis prevalence and preventing long-term endemic persistence.