Dynamical analysis of a diffusive population-toxicant model with toxicant-taxis in polluted aquatic environments

This paper deals with a diffusive population-toxicant model in polluted aquatic environments, with a toxicant-taxis term describing a toxicant-induced behavior change, that is, the population tends to move away from locations with high-level toxicants. The global existence of solutions is established by the techniques of the semigroup estimation and Moser iteration. Based on a detailed study on the properties of the principal eigenvalue for non-self-adjoint eigenvalue problems, we investigated the local and global stability of the toxin-only steady-state solution and the existence of positive steady state, which yields sufficient conditions that lead to population persistence or extinction. Finally, by numerical simulations, we studied the effects of some key parameters, such as toxicant-taxis coefficient, advection rate, and effect coefficient of the toxicant on population growth, on population persistence. Both numerical and analytical results show that a weak chemotaxis effect, a small advection rate of the population, and a weak effect of the toxicant on population growth are favorable for population persistence.

Two predators, one prey model that integrates the effect of supplementary food resources due to one predator's kleptoparasitism under the possibility of retribution by the other predator

In ecology, foraging requires animals to expend energy in order to obtain resources. The cost of foraging can be reduced through kleptoparasitism, the theft of a resource that another individual has expended effort to acquire. Thus, kleptoparasitism is one of the most significant feeding techniques in ecology. The phenomenon of kleptoparasitism has garnered significant attention from scholars due to its substantial impact on the food chain. However, the proportionate amount of mathematical modelling to facilitate the analysis has made limited progress in the literature. This circumstance motivated us to develop mathematical models that could explain the population dynamics of the prey-predator food chain. This study explores a scenario with two predators and one prey, where one predator is a kleptoparasite and the other is a host. The energy depletion caused by the predator's counterattack subsequent to kleptoparasitism, notwithstanding the nonlethal nature of this antagonism, is an additional component incorporated into this model. It has been suggested that biologically viable equilibria must meet certain parametric conditions in order to exist and to be stable both locally and globally. This article delves deeply into the occurrences of various one-parametric bifurcations, such as saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation, as well as two-parametric bifurcations, such as Bautin bifurcation. A subcritical Hopf bifurcation happens when the growth rate of the first predator is relatively low, while a supercritical Hopf bifurcation occurs when the growth rate of the first predator is quite large, allowing for the coexistence of all three species. Numerical simulations have been conducted to validate our theoretical findings.

Infection-induced increases to population size during cycles in a discrete-time epidemic model

One-dimensional discrete-time population models, such as those that involve Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Expanding the system by one dimension to incorporate epidemiological interactions causes an interesting complexity of new behaviors. Here, we examine a discrete-time two-dimensional susceptible-infectious (SI) model with Ricker growth and show that the introduction of infection can not only produce a distinctly different bifurcation structure than that of the underlying disease-free system but also lead to counter-intuitive increases in population size. We use numerical bifurcation analysis to determine the influence of infection on the location and types of bifurcations. In addition, we examine the appearance and extent of a phenomenon known as the 'hydra effect,' i.e., increases in total population size when factors, such as mortality, that act negatively on a population, are increased. Previous work, primarily focused on dynamics at fixed points, showed that the introduction of infection that reduces fecundity to the SI model can lead to a so-called 'infection-induced hydra effect.' Our work shows that even in such a simple two-dimensional SI model, the introduction of infection that alters fecundity or mortality can produce dynamics can lead to the appearance of a hydra effect, particularly when the disease-free population is at a cycle.

Anatomical Features of Posterior Cerebral Arteries and Basilar Artery in 170 Anatolian Fresh Cadavers: Implications for Surgical Planning and Intervention

BACKGROUND

The posterior cerebral arteries (PCAs) are terminal branches of the basilar artery (BA) and are responsible for the primary supply of the occipital lobe. Saccular aneurysm is most commonly seen close to the bifurcation of the BA. Various surgical interventions are performed for aneurysms. Therefore, the anatomy and localization of the BA and PCA are crucial. The aim of this study was to determine the characteristics of these arteries in a large Anatolian population.

METHODS

The study included 170 Anatolian fresh cadavers. The diameters of the BA and PCA were measured. Correlations according to sex and age groups were analyzed. The Q1, Q2, and Q3 angles between the right and left PCA, between the right PCA and BA, and between the left PCA and BA, respectively, were measured. The location of the PCA relative to the sulcus pontocruralis (pontocrural groove) was also evaluated.

RESULTS

The diameter of the artery increased with age and was higher in males than in females. Q1 and Q2 diameters were larger in males, while the Q3 diameter was larger in females. The Q1 angle between the right and left PCAs was found to be higher in age range 40-59 years with a mean of 87.33 ± 17.91 mm. Finally, the bifurcation point of the PCA was most frequently located above the sulcus pontocruralis (pontocrural groove) and least frequently located on the sulcus pontocruralis (pontocrural groove).

CONCLUSIONS

The findings of our study will contribute to the planning of surgical approaches, the development of endovascular devices, the success of invasive procedures, and the reduction of complications.

Food-limited plant-herbivore model: Bifurcations, persistence, and stability

This research paper delves into the two-dimensional discrete plant-herbivore model. In this model, herbivores are food-limited and affect the plants' density in their environment. Our analysis reveals that this system has equilibrium points of extinction, exclusion, and coexistence. We analyze the behavior of solutions near these points and prove that the extinction and exclusion equilibrium points are globally asymptotically stable in certain parameter regions. At the boundary equilibrium, we prove the existence of transcritical and period-doubling bifurcations with stable two-cycle. Transcritical bifurcation occurs when the plant's maximum growth rate or food-limited parameter reaches a specific boundary. This boundary serves as an invasion boundary for populations of plants or herbivores. At the interior equilibrium, we prove the occurrence of transcritical, Neimark-Sacker, and period-doubling bifurcations with an unstable two-cycle. Our research also establishes that the system is persistent in certain regions of the first quadrant. We demonstrate that the local asymptotic stability of the interior equilibrium does not guarantee the system's persistence. Bistability exists between boundary attractors (logistic dynamics) and interior equilibrium for specific parameters' regions. We conclude that changes to the food-limitation parameter can significantly alter the system's dynamic behavior. To validate our theoretical findings, we conduct numerical simulations.

Impact of stent strut link location in proximal balloon edge dilation technique for bifurcation percutaneous coronary intervention

The single-stent strategy has generally been accepted as the default approach to bifurcation percutaneous coronary intervention. We have proposed the proximal balloon edge dilation (PBED) technique to prevent stent deformation during side branch (SB) dilation. This bench study aimed to evaluate the impact of stent link location and stent design on stent deformation, obstruction by stent struts at a jailed SB ostium, and incomplete stent apposition in the proximal optimization technique (POT)-PBED procedure. A coronary bifurcation model was used. We intentionally set the absence or presence of stent link on the carina (link-free or link-connect) under videoscope observation and compared stent parameters between 3- and 2-link stents (n = 5 each, n = 20 total). In the link-free group, the SB jailing rate of 3-link stents was significantly higher than that of 2-link stents (15.5 ± 5.1% vs. 6.6 ± 1.2%, p = 0.009). In the link-connect group, the SB jailing rate of 3-link stents was significantly lower than that of 2-link stents (30.0 ± 4.5% vs. 39.0 ± 2.6%, p = 0.009). In the bifurcation segment, the rate of incomplete stent apposition was significantly lower for 3-link stents of the link-connect group than for 2-link stents of the link-connect group (3.3 ± 4.2% vs. 19.0 ± 7.8%, p = 0.009). For both stent designs, ellipticity ratio was higher for link-connect group than link-free group. Link location as well as stent cell design greatly impacted stent deformation during the POT-PBED procedure.

Efficacy and safety of low profile stents in Y-stent assisted coil embolization of wide-necked bifurcation aneurysms: a systematic review and meta-analysis

Low-profile stents may provide significant advantages in Y-stent-assisted coiling due to their miniaturized design and capability to be delivered through a 0.0165-inch microcatheter. We aim to investigate the safety and efficacy of using these newer versions of stents in Y-stent-assisted coiling for the treatment of wide-necked bifurcation aneurysms. We conducted a systematic review of the PubMed, Embase, Cochrane Library, and Web of Science databases up to September 2023, following the PRISMA guidelines. Eligible studies included  ≥ 5 patients with intracranial wide-necked bifurcation aneurysms treated with Y-stent-assisted coiling using low-profile stents, providing angiographic and clinical outcomes. Two authors independently handled the search and selection. Primary outcomes were immediate and follow-up aneurysm occlusion, procedure-related complications, aneurysm recanalization, and retreatment. Secondary outcomes included technical success, procedure-related morbidity, procedure-related mortality, procedure-related stroke, and in-stent stenosis at follow-up. We analyzed the data using random-effects meta-analysis. In total, 19 studies including 507 patients with 509 aneurysms were included. 95% of the treated aneurysms were managed using the crossing Y-configuration. Technical success rate was 99%. Immediate adequate aneurysm occlusion was 90%. Follow-up angiographies were available for 443 aneurysms. The mean angiographic follow-up duration was 15.6 ± 1.9 months. The rates for follow-up adequate aneurysm occlusion and complete occlusion were 98% and 89%, respectively. After a mean clinical follow-up of 15 ± 2.4 months, a good clinical outcome was observed in 98% of patients. Overall, procedure-related morbidity and mortality rates were 1.3%, and 0.4%, respectively. Low-profile stents in Y-stent-assisted coiling outperform previous stent versions in terms of safety, efficacy, and technical success rates.

Transradial Versus Transfemoral Access for Bifurcation Percutaneous Coronary Intervention Using Second-Generation Drug-Eluting Stent

BACKGROUND

The benefits of transradial access (TRA) over transfemoral access (TFA) for bifurcation percutaneous coronary intervention (PCI) are uncertain because of the limited availability of device selection. This study aimed to compare the procedural differences and the in-hospital and long-term outcomes of TRA and TFA for bifurcation PCI using second-generation drug-eluting stents (DESs).

METHODS

Based on data from the Coronary Bifurcation Stenting Registry III, a retrospective registry of 2,648 patients undergoing bifurcation PCI with second-generation DES from 21 centers in South Korea, patients were categorized into the TRA group (n = 1,507) or the TFA group (n = 1,141). After propensity score matching (PSM), procedural differences, in-hospital outcomes, and device-oriented composite outcomes (DOCOs; a composite of cardiac death, target vessel-related myocardial infarction, and target lesion revascularization) were compared between the two groups (772 matched patients each group).

RESULTS

Despite well-balanced baseline clinical and lesion characteristics after PSM, the use of the two-stent strategy (14.2% vs. 23.7%, P = 0.001) and the incidence of in-hospital adverse outcomes, primarily driven by access site complications (2.2% vs. 4.4%, P = 0.015), were significantly lower in the TRA group than in the TFA group. At the 5-year follow-up, the incidence of DOCOs was similar between the groups (6.3% vs. 7.1%, P = 0.639).

CONCLUSION

The findings suggested that TRA may be safer than TFA for bifurcation PCI using second-generation DESs. Despite differences in treatment strategy, TRA was associated with similar long-term clinical outcomes as those of TFA. Therefore, TRA might be the preferred access for bifurcation PCI using second-generation DES.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT03068494.

A general description of criticality in neural network models

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A comprehensive study of how criticality emerges and how to reproduce it is still lacking. In this study, we investigate coupled networks with conductance-based neurons and illustrate the co-existence of different spiking patterns, including asynchronous irregular (AI) firing and synchronous regular (SR) state, along with a scale-invariant neuronal avalanche phenomenon (criticality). We show that fast-acting synaptic coupling can evoke neuronal avalanches in the mean-dominated regime but has little effect in the fluctuation-dominated regime. In a narrow region of parameter space, the network exhibits avalanche dynamics with power-law avalanche size and duration distributions. We conclude that three stages which may be responsible for reproducing the synchronized bursting: mean-dominated subthreshold dynamics, fast-initiating a spike event, and time-delayed inhibitory cancellation. Remarkably, we illustrate the mechanisms underlying critical avalanches in the presence of noise, which can be explained as a stochastic crossing state around the Hopf bifurcation under the mean-dominated regime. Moreover, we apply the ensemble Kalman filter to determine and track effective connections for the neuronal network. The method is validated on noisy synthetic BOLD signals and could exactly reproduce the corresponding critical network activity. Our results provide a special perspective to understand and model the criticality, which can be useful for large-scale modeling and computation of brain dynamics.

The impact of radio-chemotherapy on tumour cells interaction with optimal control and sensitivity analysis

Oncologists and applied mathematicians are interested in understanding the dynamics of cancer-immune interactions, mainly due to the unpredictable nature of tumour cell proliferation. In this regard, mathematical modelling offers a promising approach to comprehend this potentially harmful aspect of cancer biology. This paper presents a novel dynamical model that incorporates the interactions between tumour cells, healthy tissue cells, and immune-stimulated cells when subjected to simultaneous chemotherapy and radiotherapy for treatment. We analysed the equilibria and investigated their local stability behaviour. We also study transcritical, saddle-node, and Hopf bifurcations analytically and numerically. We derive the stability and direction conditions for periodic solutions. We identify conditions that lead to chaotic dynamics and rigorously demonstrate the existence of chaos. Furthermore, we formulated an optimal control problem that describes the dynamics of tumour-immune interactions, considering treatments such as radiotherapy and chemotherapy as control parameters. Our goal is to utilize optimal control theory to reduce the cost of radiotherapy and chemotherapy, minimize the harmful effects of medications on the body, and mitigate the burden of cancer cells by maintaining a sufficient population of healthy cells. Cost-effectiveness analysis is employed to identify the most economical strategy for reducing the disease burden. Additionally, we conduct a Latin hypercube sampling-based uncertainty analysis to observe the impact of parameter uncertainties on tumour growth, followed by a sensitivity analysis. Numerical simulations are presented to elucidate how dynamic behaviour of model is influenced by changes in system parameters. The numerical results validate the analytical findings and illustrate that a multi-therapeutic treatment plan can effectively reduce tumour burden within a given time frame of therapeutic intervention.

The role of natural recovery category in malaria dynamics under saturated treatment

In the process of malaria transmission, natural recovery individuals are slightly infectious compared with infected individuals. Our concern is whether the infectivity of natural recovery category can be ignored in areas with limited medical resources, so as to reveal the epidemic pattern of malaria with simpler analysis. To achieve this, we incorporate saturated treatment into two-compartment and three-compartment models, and the infectivity of natural recovery category is only reflected in the latter. The non-spatial two-compartment model can admit backward bifurcation. Its spatial version does not possess rich dynamics. Besides, the non-spatial three-compartment model can undergo backward bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. For spatial three-compartment model, due to the complexity of characteristic equation, we apply Shengjin's Distinguishing Means to realize stability analysis. Further, the model exhibits Turing instability, Hopf bifurcation and Turing-Hopf bifurcation. This makes the model may admit bistability or even tristability when its basic reproduction number less than one. Biologically, malaria may present a variety of epidemic trends, such as elimination or inhomogeneous distribution in space and periodic fluctuation in time of infectious populations. Notably, parameter regions are given to illustrate substitution effect of two-compartment model for three-compartment model in both scenarios without or with spatial movement. Finally, spatial three-compartment model is used to present malaria transmission in Burundi. The application of efficiency index enables us to determine the most effective method to control the number of cases in different scenarios.

Identifying critical regulatory interactions in cell fate decision and transition by systematic perturbation analysis

One of the most significant challenges in biology is to elucidate the roles of various regulatory interactions in cell fate decision and transition. However, it remains to be fully clarified how they cooperate and determine fate transition. Here, a general framework based on statistical analysis and bifurcation theory is proposed to identify crucial regulatory interactions and how they play decisive roles in fate transition. More exactly, specific feedback loops determine occurrence of bifurcations by which cell fate transition can be realized. While regulatory interactions in the feedback loops determine the direction of transition. In addition, two-parameter bifurcation analysis further provides detailed understanding of how the fate transition based on statistical analysis occurs. Statistical analysis can also be used to reveal synergistic combinatorial perturbations by which fate transition can be more efficiently realized. The integrative analysis approach can be used to identify critical regulatory interactions in cell fate transition and reveal how specific cell fate transition occurs. To verify feasibility of the approach, the epithelial to mesenchymal transition (EMT) network is chosen as an illustrative example. In agreement with experimental observations, the approach reveals some critical regulatory interactions and underlying mechanisms in cell fate determination and transitions between three states. The approach can also be applied to analyze other regulatory networks related to cell fate decision and transition.

Interventions in chronic total occlusions with bifurcation lesions: incidence, treatment, and in-hospital outcome

INTRODUCTION AND OBJECTIVES

Coronary chronic total occlusions (CTO) involving bifurcation lesions are a challenging lesion subset that is understudied in the literature. This study analyzed the incidence, procedural strategy, in-hospital outcomes and complications of percutaneous coronary interventions (PCI) for bifurcation-CTO (BIF-CTO).

METHODS

We assessed data from 607 consecutive CTO patients treated at the Institut Cardiovasculaire Paris Sud (ICPS), Massy, France between January 2015 and February 2020. Procedural strategy, in-hospital outcomes and complication rates were compared between 2 patient subgroups: BIF-CTO (n=245=and non-BIF-CTO (n=362).

RESULTS

The mean patient age was 63.2±10.6 years; 79.6% were men. Bifurcation lesions were involved in 40.4% of the procedures. Overall lesion complexity was high (mean J-CTO score 2.30±1.16, mean PROGRESS-CTO score 1.37±0.94). The preferred bifurcation treatment strategy was a provisional approach (93.5%). BIF-CTO patients presented with higher lesion complexity, as assessed by J-CTO score (2.42±1.02 vs 2.21±1.23 in the non-BIF-CTO patients, P=.025) and PROGRESS-CTO score (1.60±0.95 vs 1.22±0.90 in the non-BIF-CTO patients, P<.001). Procedural success was 78.9% and was not affected by the presence of bifurcation lesions (80.4% in the BIF-CTO group, 77.8% in the non-BIF-CTO-CTO group, P=.447) or the bifurcation site (proximal BIF-CTO 76.9%, mid-BIF-CTO 83.8%, distal BIF-CTO 85%, P=.204). Complication rates were similar in BIF-CTO and non-BIF-CTO.

CONCLUSIONS

The incidence of bifurcation lesions is high in contemporary CTO PCI. Patients with BIF-CTO present with higher lesion complexity, with no impact on procedural success or complication rates when the predominant strategy is provisional stenting.

Optimization of ictal aborting stimulation using the dynamotype taxonomy

Electrical stimulation is an increasingly popular method to terminate epileptic seizures, yet it is not always successful. A potential reason for inconsistent efficacy is that stimuli are applied empirically without considering the underlying dynamical properties of a given seizure. We use a computational model of seizure dynamics to show that different bursting classes have disparate responses to aborting stimulation. This model was previously validated in a large set of human seizures and led to a description of the Taxonomy of Seizure Dynamics and the dynamotype, which is the clinical analog of the bursting class. In the model, the stimulation is realized as an applied input, which successfully aborts the burst when it forces the system from a bursting state to a quiescent state. This transition requires bistability, which is not present in all bursters. We examine how topological and geometric differences in the bistable state affect the probability of termination as the burster progresses from onset to offset. We find that the most significant determining factors are the burster class (dynamotype) and whether the burster has a DC (baseline) shift. Bursters with a baseline shift are far more likely to be terminated due to the necessary structure of their state space. Furthermore, we observe that the probability of termination varies throughout the burster's duration, is often dependent on the phase when it was applied, and is highly correlated to dynamotype. Our model provides a method to predict the optimal method of termination for each dynamotype. These results lead to the prediction that optimization of ictal aborting stimulation should account for seizure dynamotype, the presence of a DC shift, and the timing of the stimulation.

Matrix stability and bifurcation analysis by a network-based approach

In this paper, we develop a network-based methodology to investigate the problems related to matrix stability and bifurcations in nonlinear dynamical systems. By matching a matrix with a network, i.e., interaction graph, we propose a new network-based matrix analysis method by proving a theorem about matrix determinant under which matrix stability can be considered in terms of feedback loops. Especially, the approach can tell us how a node, a path, or a feedback loop in the interaction graph affects matrix stability. In addition, the roles played by a node, a path, or a feedback loop in determining bifurcations in nonlinear dynamical systems can also be revealed. Therefore, the approach can help us to screen optimal node or node combinations. By perturbing them, unstable matrices can be stabilized more efficiently or bifurcations can be induced more easily to realize desired state transitions. To illustrate feasibility and efficiency of the approach, some simple matrices are used to show how single or combinatorial perturbations affect matrix stability and induce bifurcations. In addition, the main idea is also illustrated through a biological problem related to T cell development with three nodes: TCF-1, GATA3, and PU.1, which can be considered to be a three-variable nonlinear dynamical system. The approach is especially helpful in understanding crucial roles of single or molecule combinations in biomolecular networks. The approach presented here can be expected to analyze other biological networks related to cell fate transitions and systematic perturbation strategy selection.

Risk Assessment of Side Branch Compromise After Coronary Bifurcation Stenting - A Substudy of the 3D-OCT Bifurcation Registry

BACKGROUND

Side branch (SB) occlusion during bifurcation stenting is a serious complication. This study aimed to predict SB compromise (SBC) using optical coherence tomography (OCT).Methods and Results: Among the 168 patients who enrolled in the 3D-OCT Bifurcation Registry, 111 bifurcation lesions were analyzed to develop an OCT risk score for predicting SBC. SBC was defined as worsening of angiographic SB ostial stenosis (≥90%) immediately after stenting. On the basis of OCT before stenting, geometric parameters (SB diameter [SBd], length from proximal branching point to carina tip [BP-CT length], and distance of the polygon of confluence [dPOC]) and 3-dimensional bifurcation types (parallel or perpendicular) were evaluated. SBC occurred in 36 (32%) lesions. The parallel-type bifurcation was significantly more frequent in lesions with SBC. The receiver operating characteristic curve indicated SBd ≤1.77 mm (area under the curve [AUC]=0.73, sensitivity 64%, specificity 75%), BP-CT length ≤1.8 mm (AUC=0.83, sensitivity 86%, specificity 68%), and dPOC ≤3.96 mm (AUC=0.68, sensitivity 63%, specificity 69%) as the best cut-off values for predicting SBC. To create the OCT risk score, we assigned 1 point to each of these factors. As the score increased, the frequency of SBC increased significantly (Score 0, 0%; Score 1, 8.7%; Score 2, 28%; Score 3, 58%; Score 4, 85%; P<0.0001).

CONCLUSIONS

Prediction of SBC using OCT is feasible with high probability.

Follow-up optical coherence tomography to evaluate circumflex ostium after fenestration of left main Papyrus covered stent: a case report

Background

Left main (LM) perforations necessitating a covered stent risk sacrificing the side branch. The lost side branch can be promptly recovered by fenestration of the covered stent, using a stiff wire. However, it is unclear whether subsequent balloon angioplasty of the recovered side branch ostium is sufficient to preserve side branch patency. We report the longer-term patency of the circumflex (LCx) ostium after LM covered stenting.

Case summary

A 78-year-old lady, with stable angina, presented for elective angiography. Percutaneous coronary intervention of the left anterior descending (LAD) artery to LM was complicated by a distal LM perforation. A covered stent across the LM sealed the perforation but resulted in acute occlusion of the LCx. The LCx was rescued by fenestration of the covered stent with a stiff wire, followed by balloon angioplasty to the LCx ostium. At follow-up, the angina had resolved. However, follow-up angiography demonstrated a new severe stenosis at the LCx ostium, with remnants of the polyurethane membrane seen protruding into the LCx ostium on optical coherence tomography. Therefore, the LCx ostium was stented, using the reverse Culotte technique.

Conclusion

This case demonstrates that stenting the LCx ostium should be considered after covered stent implantation from LM to LAD, because balloon angioplasty of the LCx ostium may not provide a durable result in this scenario.

Nonlinear mechanism for the enhanced bursting activities induced by fast inhibitory autapse and reduced activities by fast excitatory autapse

The paradoxical phenomena that excitatory modulation does not enhance but reduces or inhibitory modulation not suppresses but promotes neural firing activities have attracted increasing attention. In the present study, paradoxical phenomena induced by both fast excitatory and inhibitory autapses in a "Fold/Big Homoclinic" bursting are simulated, and the corresponding nonlinear and biophysical mechanisms are presented. Firstly, the enhanced conductance of excitatory autapse induces the number of spikes per burst and firing rate reduced, while the enhanced inhibitory autapse cause both indicators increased. Secondly, with fast-slow variable dissection, the burst of bursting is identified to locate between a fold bifurcation and a big saddle-homoclinic orbit bifurcation of the fast subsystem. Enhanced excitatory or inhibitory autapses cannot induce changes of both bifurcation points, i.e., burst width. However, width of slow variable between two successive spikes within a burst becomes wider for the excitatory autapse and narrower for the inhibitory autapse, resulting in the less and more spikes per burst, respectively. Last, the autaptic current of fast autapse mainly plays a role during the peak of action potential, differing from the slow autaptic current with exponential decay, which can play roles following the peak of action potential. The fast excitatory autaptic current enhances the amplitude of the action potential and reduces the repolarization of the action potential to lengthen the interspike interval (ISI) of the spiking of the fast subsystem, resulting in the wide width of slow variable between successive spikes. The fast inhibitory autaptic current reduces the amplitude of action potential and ISI of spiking, resulting in narrow width of slow variable. The novel example of the paradoxical responses for both fast modulations and nonlinear mechanism extend the contents of neurodynamics, which presents potential functions of the fast autapse.

Slender Bi-Radial Ping-Pong Technique for Complete Revascularisation of Concomitant CTO and Non-LM Bifurcation Lesions: A Report of Two Cases

The "ping-pong" technique entails the use of two different guide catheters to alternately engage the same coronary artery during percutaneous coronary intervention (PCI). Bi-arterial vascular access for dual injection is the standard of care in contemporary chronic total occlusion (CTO) PCI. Two-stent bifurcation PCI strategies require a minimum of 6 French (F) guide catheter. In this report, we describe two cases where dual access initially made for CTO PCI was leveraged for subsequent bifurcation PCI in the same setting, by means of two 5F Judkin's Left (JL) guides in a transradial "slender" double-guiding catheter "ping-pong" strategy. In both cases, two 5F JL guides were initially navigated via bi-radial access for antegrade and retrograde injection from left anterior descending artery (LAD) and right coronary artery (RCA) respectively, to facilitate PCI to CTO of LAD. After successful crossing of the LAD CTO lesions, we took advantage of the two 5F JL guides already present via this dual access created for CTO PCI, to adopt the novel use of the "ping-pong" guide technique in order to perform bifurcation PCI by two-stent strategy. In the first case, PCI of the left circumflex (LCx)/obtuse marginal (OM) bifurcation was performed by the DK-Culotte technique with two JL 5F guides used to alternately engage the left main (LM) coronary artery, with wiring and passage of equipment to the LCx and OM done via separate "ping-pong" guides engaging the LM. In the second case, LAD/Diagonal bifurcation PCI was performed by T and protrusion (TAP) technique in a similar slender fashion via "ping-pong" guides. This approach has limited indications. As described in our case report, the CTO lesion was relatively less complex, the LM was not diseased and importantly, narrow radial artery diameters of the patients precluded the use of larger 6F guide transradially. Advantages of this ping-pong technique in bifurcation PCI include the avoidance of wire wrap, accommodation and easy delivery of multiple hardware, and the non-necessity of changing multiple guides, thus reducing radial artery spasm, particularity among those with narrower radial artery diameters.

Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure

A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use mathematical frameworks like fractional calculus, which is capable of doing so. Here, we first present a fractional-order memristor synapse-coupling Hopfield neural network on two neurons and then extend the model to a neural network with a ring structure that consists of n sub-network neurons, increasing the synchronization in the network. Necessary and sufficient conditions for the stability of equilibrium points are investigated, highlighting the dependency of the stability on the fractional-order value and the number of neurons. Numerical simulations and bifurcation analysis, along with Lyapunov exponents, are given in the two-neuron case that substantiates the theoretical findings, suggesting possible routes towards chaos when the fractional order of the system increases. In the n-neuron case also, it is revealed that the stability depends on the structure and number of sub-networks.

Optimal control of pneumonia transmission model with seasonal factor: Learning from Jakarta incidence data

Pneumonia is a dangerous disease that can lead to death without proper treatment. It is caused by a bacterial infection that leads to the inflammation of the air sacs in human lungs and potentially results in a lung abscess if not properly untreated. Here in this article we introduced a novel mathematical model to investigate the potential impact of Pneumonia treatments on disease transmission dynamics. The model is then validated against data from Jakarta City, Indonesia. In the model, the infection stage in infected individuals is categorized into three stages: the Exposed, Congestion and Hepatization, and the Resolution stage. Mathematical analysis shows that the disease-free equilibrium is always locally asymptotically stable when the basic reproduction number is less than one and unstable when larger than one. The endemic equilibrium only exists when the basic reproduction number is larger than one. Our proposed model always exhibits a forward bifurcation when the basic reproduction number is equal to one, which indicates local stability of the endemic equilibrium when the basic reproduction number is larger than one but close to one. A global sensitivity analysis shows that the infection parameter is the most influential parameter in determining the size of the total infected individual in the endemic equilibrium point. Furthermore, we also found that the hospitalization and the acceleration of the treatment duration can be used to control the level of endemic size. An optimal control problem was constructed from the earlier model and analyzed using the Pontryagin Maximum Principle. We find that the implementation of treatment in the earlier stage of infected individuals is needed to avoid a more significant outbreak of Pneumonia in a long-term intervention.

Co-dynamics of COVID-19 and TB with COVID-19 vaccination and exogenous reinfection for TB: An optimal control application

COVID-19 and Tuberculosis (TB) are among the major global public health problems and diseases with major socioeconomic impacts. The dynamics of these diseases are spread throughout the world with clinical similarities which makes them difficult to be mitigated. In this study, we formulate and analyze a mathematical model containing several epidemiological characteristics of the co-dynamics of COVID-19 and TB. Sufficient conditions are derived for the stability of both COVID-19 and TB sub-models equilibria. Under certain conditions, the TB sub-model could undergo the phenomenon of backward bifurcation whenever its associated reproduction number is less than one. The equilibria of the full TB-COVID-19 model are locally asymptotically stable, but not globally, due to the possible occurrence of backward bifurcation. The incorporation of exogenous reinfection into our model causes effects by allowing the occurrence of backward bifurcation for the basic reproduction number R₀ < 1 and the exogenous reinfection rate greater than a threshold (η > η∗). The analytical results show that reducing R₀ < 1 may not be sufficient to eliminate the disease from the community. The optimal control strategies were proposed to minimize the disease burden and related costs. The existence of optimal controls and their characterization are established using Pontryagin's Minimum Principle. Moreover, different numerical simulations of the control induced model are carried out to observe the effects of the control strategies. It reveals the usefulness of the optimization strategies in reducing COVID-19 infection and the co-infection of both diseases in the community.

Bifurcation analysis on ion sound and Langmuir solitary waves solutions to the stochastic models with multiplicative noises

This article explores on a stochastic couple models of ion sound as well as Langmuir surges propagation involving multiplicative noises. We concentrate on the analytical stochastic solutions including the travelling and solitary waves by using the planner dynamical systematic approach. To apply the method, First effort is to convert the system of equations into the ordinary differential form and present it in form of a dynamic structure. Next analyze the nature of the critical points of the system and obtain the phase portraits on various conditions of the corresponding parameters. The analytic solutions of the system in an account of distinct energy states for each phase orbit are performed. We also show how the results are highly effective and interesting to realize their exciting physical as well as the geometrical phenomena based on the demonstration of the stochastic system involving ion sound as well as Langmuir surges. Descriptions of effectiveness of the multiplicative noise on the obtained solutions of the model, and its corresponding figures are demonstrated numerically.

A dynamical systems treatment of transcriptomic trajectories in hematopoiesis

Inspired by Waddington's illustration of an epigenetic landscape, cell-fate transitions have been envisioned as bifurcating dynamical systems, wherein exogenous signaling dynamics couple to a cell's enormously complex signaling and transcriptional machinery, to elicit qualitative transitions in the cell's collective state. Single-cell RNA sequencing (scRNA-seq), which measures the distributions of possible transcriptional states in large populations of differentiating cells, provides an alternate view, in which development is marked by the variations of a myriad of genes. Here, we present a mathematical formalism for rigorously evaluating, from a dynamical systems perspective, whether scRNA-seq trajectories display statistical signatures consistent with bifurcations and, as a case study, pinpoint regions of multistability along the neutrophil branch of hematopoeitic differentiation. Additionally, we leverage the geometric features of linear instability to identify the low-dimensional phase plane in gene expression space within which the multistability unfolds, highlighting novel genetic players crucial for neutrophil differentiation. Broadly, we show that a dynamical systems treatment of scRNA-seq data provides mechanistic insights into the high-dimensional processes of cellular differentiation, taking a step toward systematic construction of mathematical models for transcriptomic dynamics.

A stochastic agent-based model to evaluate COVID-19 transmission influenced by human mobility

The COVID-19 pandemic has created an urgent need for mathematical models that can project epidemic trends and evaluate the effectiveness of mitigation strategies. A major challenge in forecasting the transmission of COVID-19 is the accurate assessment of the multiscale human mobility and how it impacts infection through close contacts. By combining the stochastic agent-based modeling strategy and hierarchical structures of spatial containers corresponding to the notion of geographical places, this study proposes a novel model, Mob-Cov, to study the impact of human traveling behavior and individual health conditions on the disease outbreak and the probability of zero-COVID in the population. Specifically, individuals perform power law-type local movements within a container and global transport between different-level containers. It is revealed that frequent long-distance movements inside a small-level container (e.g., a road or a county) and a small population size reduce both the local crowdedness and disease transmission. It takes only half of the time to induce global disease outbreaks when the population increases from 150 to 500 (normalized unit). When the exponent c 1 of the long-tail distribution of distance k moved in the same-level container, p ( k ) ∼ k - c 1 · level , increases, the outbreak time decreases rapidly from 75 to 25 (normalized unit). In contrast, travel between large-level containers (e.g., cities and nations) facilitates global spread of the disease and outbreak. When the mean traveling distance across containers 1 d increases from 0.5 to 1 (normalized unit), the outbreak occurs almost twice as fast. Moreover, dynamic infection and recovery in the population are able to drive the bifurcation of the system to a "zero-COVID" state or to a "live with COVID" state, depending on the mobility patterns, population number and health conditions. Reducing population size and restricting global travel help achieve zero-COVID-19. Specifically, when c 1 is smaller than 0.2, the ratio of people with low levels of mobility is larger than 80% and the population size is smaller than 400, zero-COVID can be achieved within fewer than 1000 time steps. In summary, the Mob-Cov model considers more realistic human mobility at a wide range of spatial scales, and has been designed with equal emphasis on performance, low simulation cost, accuracy, ease of use and flexibility. It is a useful tool for researchers and politicians to apply when investigating pandemic dynamics and when planning actions against disease.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11071-023-08489-5.

Slow negative feedback enhances robustness of square-wave bursting

Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.

Dynamical systems model of development of the action differentiation in early infancy: a requisite of physical agency

Young infants are sensitive to whether their body movements cause subsequent events or not during the interaction with the environment. This ability has been revealed by empirical studies on the reinforcement of limb movements when a string is attached between an infant limb and a mobile toy suspended overhead. A previous study reproduced the experimental observation by modeling both the infant's limb and a mobile toy as a system of coupled oscillators. The authors then argued that emergence of agency could be explained by a phase transition in the dynamical system: from a weakly coupled state to a state where the both movements of the limb and the toy are highly coordinated. However, what remains unexplained is the following experimental observation: When the limb is connected to the mobile toy by a string, the infant increases the average velocity of the arm's movement. On the other hand, when the toy is controlled externally, the average arm's velocity is greatly reduced. Since young infants produce exuberant spontaneous movements even with no external stimuli, the inhibition of motor action to suppress the formation of spurious action-perception coupling should be also a crucial sign for the emergence of agency. Thus, we present a dynamical system model for the development of action differentiation, to move or not to move, in the mobile task. In addition to the pair of limb and mobile oscillators for providing positive feedback for reinforcement in the previous model, bifurcation dynamics are incorporated to enhance or inhibit self-movements in response to detecting contingencies between the limb and mobile movements. The results from computer simulations reproduce experimental observations on the developmental emergence of action differentiation between 2 and 3 months of age in the form of a bifurcation diagram. We infer that the emergence of physical agency entails young infants' ability not only to enhance a specific action-perception coupling, but also to decouple it and create a new mode of action-perception coupling based on the internal state dynamics with contingency detection between self-generated actions and environmental events.

Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments

A nonlinear partial differential equation containing a nonlocal advection term and a diffusion term is analyzed to study wound closure outcomes in wound healing experiments. There is an extensive literature of similar models for wound healing experiments. In this paper we study the character of wound closure in these experiments in terms of the sensing radius of cells and the force of cell-cell adhesion. We prove a bifurcation result which differentiates uniform closure of the wound from nonuniform closure of the wound, based on a critical value [Formula: see text] of the force of cell-cell adhesion parameter [Formula: see text]. For [Formula: see text] the steady state solution [Formula: see text] of the model is stable and the wound closes uniformly. For [Formula: see text] the steady state solution [Formula: see text] of the model is unstable and the wound closes nonuniformly. We provide numerical simulations of the model to illustrate our results.

Bi-stability and critical transitions in mental health care systems: a model-based analysis

BACKGROUND

Delayed initiation and early discontinuation of treatment due to limited availability and accessibility of services may often result in people with mild or moderate mental disorders developing more severe disorders, leading to an increase in demand for specialised care that would be expected to further restrict service availability and accessibility (due to increased waiting times, higher out-of-pocket costs, etc.).

METHODS

We developed a simple system dynamics model of the interaction of specialised services capacity and disease progression to examine the impact of service availability and accessibility on the effectiveness and efficiency of mental health care systems.

RESULTS

Model analysis indicates that, under certain conditions, increasing services capacity can precipitate an abrupt, step-like transition from a state of persistently high unmet need for specialised services to an alternative, stable state in which people presenting for care receive immediate and effective treatment. This qualitative shift in services system functioning results from a 'virtuous cycle' in which increasing treatment-dependent recovery among patients with mild to moderate disorders reduces the number of severely ill patients requiring intensive and/or prolonged treatment, effectively 'releasing' services capacity that can be used to further reduce the disease progression rate. We present an empirical case study of tertiary-level child and adolescent mental health services in the Australian state of South Australia demonstrating that the conditions under which such critical transitions can occur apply in real-world services systems.

CONCLUSIONS

Policy and planning decisions aimed at increasing specialised services capacity have the potential to dramatically increase the effectiveness and efficiency of mental health care systems, promoting long-term sustainability and resilience in the face of future threats to population mental health (e.g., economic crises, natural disasters, global pandemics).

Diverse branching forms regulated by a core auxin transport mechanism in plants

Diverse branching forms have evolved multiple times across the tree of life to facilitate resource acquisition and exchange with the environment. In the vascular plant group, the ancestral pattern of branching involves dichotomy of a parent shoot apex to form two new daughter apices. The molecular basis of axillary branching in Arabidopsis is well understood, but few regulators of dichotomous branching are known. Through analyses of dichotomous branching in the lycophyte, Selaginella kraussiana, we identify PIN-mediated auxin transport as an ancestral branch regulator of vascular plants. We show that short-range auxin transport out of the apices promotes dichotomy and that branch dominance is globally coordinated by long-range auxin transport. Uniquely in Selaginella, angle meristems initiate at each dichotomy, and these can develop into rhizophores or branching angle shoots. We show that long-range auxin transport and a transitory drop in PIN expression are involved in angle shoot development. We conclude that PIN-mediated auxin transport is an ancestral mechanism for vascular plant branching that was independently recruited into Selaginella angle shoot development and seed plant axillary branching during evolution.

Numerical assessment of recellularization conditions to vessel occlusion

To ensure the functional properties of an organ generated by the process of decellularization and recellularization, the initial density and distribution of seeding cells in the parenchymal space should be maximized. However, achieving a uniform distribution of cells across the entire organ is not straightforward because of vessel occlusion. This study assessed vessel occlusion during recellularization under different conditions. A combination of the electrical analog permeability (EPA) model, computational fluid dynamics (CFD), and discrete element method (DEM) was employed to describe the vessel occlusion phenomenon. In particular, realistic flow distributions in vascular trees of the decellularized organ were indicated by the EPA model. The cell suspension flow was modeled by a coupled CFD-DEM model, whereby living cells were presented as a discrete phase (solved by the DEM solver), and the culture medium was modeled as the fluid phase (solved by CFD solver). The cell suspension velocity was reduced up to 47% after decellularization, which directly affected cell movement. Simulation results also indicate that the occurrence of vessel occlusion was promoted by gravity direction in the asymmetric bifurcation and increased as the cell concentration increased. The assessment of vessel occlusion under different conditions was quantitatively investigated. The model provides insights into the dynamics of cells in the vessel compartment, allowing for the selection of optimum seeding parameters for the recellularization process.

On the nonlinear dynamics of a piezoresistive based mass switch based on catastrophic bifurcation

This research investigates the feasibility of mass sensing in piezoresistive MEMS devices based on catastrophic bifurcation and sensitivity enhancement due to the orientation adjustment of the device with respect to the crystallographic orientation of the silicon wafer. The model studied is a cantilever microbeam at the end of which an electrostatically actuated tip mass is attached. The piezoresistive layers are bonded to the vicinity of the clamped end of the cantilever and the device is set to operate in the resonance regime by means of harmonic electrostatic excitation. The nonlinearities due to curvature, shortening and electrostatic excitation have been considered in the modelling process. It is shown that once the mass is deposited on the tip mass, the system undergoes a cyclic fold bifurcation in the frequency domain, which yields a sudden jump in the output voltage of the piezoresistive layers; this bifurcation is attributed to the nonlinearities governing the dynamics of the response. The partial differential equations of the motion are derived and discretized to give a finite degree of freedom model based on the Galerkin method, and the limit cycles are captured in the frequency domain by using the shooting method. The effect of the orientation of the device with respect to the crystallographic coordinates of the silicon and the effect of the orientation of the piezoresistive layers with respect to the microbeam length on the sensitivity of the device is also investigated. Thanks to the nonlinearity and the orientation adjustment of the device and piezoresistive layers, a twofold sensitivity enhancement due to the added mass was achieved. This achievement is due to the combined amplification of the sensitivity in the vicinity of the bifurcation point, which is attributed to the nonlinearity and maximizing the sensitivity by orientation adjustment of the anisotropic piezoresistive coefficients.

A discrete Huber-Braun neuron model: from nodal properties to network performance

Many of the well-known neuron models are continuous time systems with complex mathematical definitions. Literatures have shown that a discrete mathematical model can effectively replicate the complete dynamical behaviour of a neuron with much reduced complexity. Hence, we propose a new discrete neuron model derived from the Huber-Braun neuron with two additional slow and subthreshold currents alongside the ion channel currents. We have also introduced temperature dependent ion channels to study its effects on the firing pattern of the neuron. With bifurcation and Lyapunov exponents we showed the chaotic and periodic regions of the discrete model. Further to study the complexity of the neuron model, we have used the sample entropy algorithm. Though the individual neuron analysis gives us an idea about the dynamical properties, it's the collective behaviour which decides the overall behavioural pattern of the neuron. Hence, we investigate the spatiotemporal behaviour of the discrete neuron model in single- and two-layer network. We have considered obstacle as an important factor which changes the excitability of the neurons in the network. Literatures have shown that spiral waves can play a positive role in breaking through quiescent areas of the brain as a pacemaker by creating a coherence resonance behaviour. Hence, we are interested in studying the induced spiral waves in the network. In this condition when an obstacle is introduced the wave propagation is disturbed and we could see multiple wave re-entry and spiral waves. In a two-layer network when the obstacle is considered only in one layer and stimulus applied to the layer having the obstacle, the wave re-entry is seen in both the layer though the other layer is not exposed to obstacle. But when both the layers are inserted with an obstacle and stimuli also applied to the layers, they behave like independent layers with no coupling effect. In a two-layer network, stimulus play an important role in spatiotemporal dynamics of the network.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-022-09806-1.

A general pattern of non-spiking neuron dynamics under the effect of potassium and calcium channel modifications

Electrical activity of excitable cells results from ion exchanges through cell membranes, so that genetic or epigenetic changes in genes encoding ion channels are likely to affect neuronal electrical signaling throughout the brain. There is a large literature on the effect of variations in ion channels on the dynamics of spiking neurons that represent the main type of neurons found in the vertebrate nervous systems. Nevertheless, non-spiking neurons are also ubiquitous in many nervous tissues and play a critical role in the processing of some sensory systems. To our knowledge, however, how conductance variations affect the dynamics of non-spiking neurons has never been assessed. Based on experimental observations reported in the biological literature and on mathematical considerations, we first propose a phenotypic classification of non-spiking neurons. Then, we determine a general pattern of the phenotypic evolution of non-spiking neurons as a function of changes in calcium and potassium conductances. Furthermore, we study the homeostatic compensatory mechanisms of ion channels in a well-posed non-spiking retinal cone model. We show that there is a restricted range of ion conductance values for which the behavior and phenotype of the neuron are maintained. Finally, we discuss the implications of the phenotypic changes of individual cells at the level of neuronal network functioning of the C. elegans worm and the retina, which are two non-spiking nervous tissues composed of neurons with various phenotypes.

Multi-timescale analysis of midbrain dopamine neuronal firing activities

Midbrain dopamine (DA) neurons exhibit spiking and bursting patterns under physiological conditions. Based on the data on electrophysiological recordings, Yu et al. developed a 13-dimensional mathematical model to capture the detailed characteristics of the DA neuronal firing activities. We use the fitting method to simplify the original model into a 4-dimensional model. Then, the spiking-to-bursting transition is detected from a simple and robust mathematical condition. Physiologically, this condition is a balance of the restorative and the regenerative ion channels at resting potential. Geometrically, this condition imposes a transcritical bifurcation. Moreover, we combine singularity theory and singular perturbation methods to capture the geometry of three-timescale firing attractors in a universal unfolding of a cusp singularity. In particular, the planar description of the corresponding firing patterns can generate the corresponding firing attractors. This analysis provides a new idea for understanding the firing activities of the DA neuron and the specific mechanisms for the switching and dynamic regulation among different patterns.

Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis

A considerable number of research works has been devoted to the study of tumor models. Several biophysical factors, such as cell proliferation, apoptosis, chemotaxis, angiogenesis and necrosis, have been discovered to have an impact on the complicated biological system of tumors. An indicator of the aggressiveness of tumor development is the instability of the shape of the tumor boundary. Complex patterns of tumor morphology have been explored in Lu et al. (J Comput Phys 459:111153, 2022). In this paper, we continue to carry out a bifurcation analysis on such a vascular tumor model with a controlled necrotic core and chemotaxis. This bifurcation analysis, to the parameter of cell proliferation, is built on the explicit formulas of radially symmetric steady-state solutions. By perturbing the tumor free boundary and establishing rigorous estimates of the free boundary system, we prove the existence of the bifurcation branches with Crandall-Rabinowitz theorem. The parameter of chemotaxis is found to influence the monotonicity of the bifurcation point as the mode l increases both theoretically and numerically.

Global dynamic modes of peristaltic-ciliary flow of a Phan-Thien-Tanner hybrid nanofluid model

In this paper, the tools of dynamical systems theory are applied to examine the streamline patterns and their local and global bifurcations for ciliary-induced peristalsis of non-Newtonian fluid (blood) with the suspension of hybrid nanoparticles (Cu-Ag/Phan-Thien-Tanner based fluid) in a tube with heat source effect. The thermodynamics of this model are recently described by Ali et al. (Biomech Model Mechanobiol 20:2393-2412, 2021), where the fluid flows through a tube whose inner walls are considered to be ciliated with small hair-like structures. However, our novel approach allows us to create a complete picture of the model's overall dynamic behavior in terms of bifurcation point analysis exhibiting qualitatively different flow modes. Special attention is paid to the computing, analysis and simulation of equilibrium points in terms of capturing the global dynamics, such as evaluating the heteroclinic bifurcation, which is used to identify trapping phenomena in response to biological characteristics such as wave amplitude, Weissenberg and wave numbers. The main novelty here is the ability to control the position of the equilibrium points in the domain of interest, allowing one to identify global bifurcations that reflect key dynamic properties of the model. Based on the advantages of this technique, the maximum trapping volume and symmetric trapping zones adjacent to the walls are determined as a novel result. We also show that as the solid volume fraction of copper and the Brinkman number increases, the isotherm patterns become more distorted. Our findings highlight a novel class of complex behavior that governs transitions between qualitatively different modes and trapping phenomena.

Evolution of cooperation in multigame with environmental space and delay

Replicator dynamics is widely used in evolutionary game theory, however, most previous studies on replicator dynamics focus on single games and ignore multiple social dilemmas encountered by individuals in a population. This paper uses replicator dynamics to construct a multigame system with environmental space and delay based on three social dilemmas. For the non-delayed and delayed multigame systems, rich dynamics for stability, bistability, transcritical bifurcation, Hopf bifurcation, and the direction, stability and periodic variation of periodic solutions are comprehensively investigated. Accordingly, we use numerical simulations to assist in exploring the effects of multigame, environmental space, and time delay on strategic dynamics. The results show that large proportions of snowdrift game and stag hunt game are conducive to the prosperity of cooperators, and defectors are easy to survive when the proportion of prisoner's dilemma is large. The cooperator gains the advantage of benefit distribution from environmental space, or the defector gets less benefit distribution as punishment, which will make pure cooperation the dominant strategy. Furthermore, environmental space can allow cooperation and defection to coexist oscillatingly. Interestingly, large delays reverse the coexistence of cooperation and defection to a situation dominated by the purely cooperative strategy.

Collective cell migration is spatiotemporally regulated during mammary epithelial bifurcation

Branched epithelial networks are generated through an iterative process of elongation and bifurcation. We sought to understand bifurcation of the mammary epithelium. To visualize this process, we utilized three-dimensional (3D) organotypic culture and time-lapse confocal microscopy. We tracked cell migration during bifurcation and observed local reductions in cell speed at the nascent bifurcation cleft. This effect was proximity dependent, as individual cells approaching the cleft reduced speed, whereas cells exiting the cleft increased speed. As the cells slow down, they orient both migration and protrusions towards the nascent cleft, while cells in the adjacent branches orient towards the elongating tips. We next tested the hypothesis that TGF-β signaling controls mammary branching by regulating cell migration. We first validated that addition of TGF-β1 (TGFB1) protein increased cleft number, whereas inhibition of TGF-β signaling reduced cleft number. Then, consistent with our hypothesis, we observed that pharmacological inhibition of TGF-β1 signaling acutely decreased epithelial migration speed. Our data suggest a model for mammary epithelial bifurcation in which TGF-β signaling regulates cell migration to determine the local sites of bifurcation and the global pattern of the tubular network.

Dynamical behaviour of single photobioreactor with variable yield coefficient

Scholars studied chemostat model with variable yield coefficient and a growth rate in Monod expression for the existence of natural oscillations in a bioreactor. This article explores dynamical properties of a similar simple model, analytically and numerically, in which the growth rate is a modified Haldane expression. Study includes determination of analytic conditions for existence of steady-state washout and no washout solutions, optimization of the performance of the bioreactor when no washout solution occurs, stability of the optimized steady state solution, and the ranges of the parameter values for which natural oscillations (Hopf Bifurcation) take place. Investigation shows that it is possible to gain natural oscillations for much smaller values of the substrate concentration compared to Monod-based earlier works.

Nonlinear dynamic epidemiological analysis of effects of vaccination and dynamic transmission on COVID-19

This paper is concerned with nonlinear modeling and analysis of the COVID-19 pandemic. We are especially interested in two current topics: effect of vaccination and the universally observed oscillations in infections. We use a nonlinear Susceptible, Infected, & Immune model incorporating a dynamic transmission rate and vaccination policy. The US data provides a starting point for analyzing stability, bifurcations and dynamics in general. Further parametric analysis reveals a saddle-node bifurcation under imperfect vaccination leading to the occurrence of sustained epidemic equilibria. This work points to the tremendous value of systematic nonlinear dynamic analysis in pandemic modeling and demonstrates the dramatic influence of vaccination, and frequency, phase, and amplitude of transmission rate on the persistent dynamic behavior of the disease.

Discrete-time COVID-19 epidemic model with chaos, stability and bifurcation

In this paper, we explore local behavior at fixed points, chaos and bifurcations of a discrete COVID-19 epidemic model in the interior of R + 5 . It is explored that for all involved parametric values, COVID-19 model has boundary fixed point and also it has an interior fixed point under certain parametric condition(s). We have investigated local behavior at boundary and interior fixed points of COVID-19 model by linear stability theory. It is also explored the existence of possible bifurcations at respective fixed points, and proved that at boundary fixed point there exists no flip bifurcation but at interior fixed point it undergoes both flip and hopf bifurcations, and we have explored said bifurcations by explicit criterion. Moreover, chaos in COVID-19 model is also investigated by feedback control strategy. Finally, theoretical results are verified numerically.

The Mid-Pleistocene Transition: a delayed response to an increasing positive feedback?

Glacial-interglacial cycles constitute large natural variations in Earth's climate. The Mid-Pleistocene Transition (MPT) marks a shift of the dominant periodicity of these climate cycles from ∼ 40 to ∼ 100  kyr. Recently, it has been suggested that this shift resulted from a gradual increase in the internal period (or equivalently, a decrease in the natural frequency) of the system. As a result, the system would then have locked to ever higher multiples of the external forcing period. We find that the internal period is sensitive to the strength of positive feedbacks in the climate system. Using a carbon cycle model in which feedbacks between calcifier populations and ocean alkalinity mediate atmospheric CO2 , we simulate stepwise periodicity changes similar to the MPT through such a mechanism. Due to the internal dynamics of the system, the periodicity shift occurs up to millions of years after the change in the feedback strength is imposed. This suggests that the cause for the MPT may have occurred a significant time before the observed periodicity shift.

Simultaneous Kissing Balloon Stenting Technique in Management of Two Branches of Right Renal Artery Bifurcation: A Case Report

Atherosclerosis and fibromuscular dysplasia are the commonest types of diseases associated with renovascular hypertension, with atherosclerosis accounting for 70%-80% of all cases and the latter accounting for 10% of cases. We report a case of a 65-year-old asian male with stenosis of the right renal artery with early bifurcation treated by percutaneous balloon dilation and simultaneous kissing balloon stenting technique.

Symmetry-breaking longitude bifurcations for a free boundary problem modeling small plaques in three dimensions

Atherosclerosis, one of the leading causes of death in USA and worldwide, begins with a lesion in the intima of the arterial wall, allowing LDL to penetrate into the intima where they are oxidized. The immune system considers these oxidized LDL as a dangerous substance and tasks the macrophages to attack them; incapacitated macrophages become foam cells and leads to the formation of a plaque. As the plaque continues to grow, it progressively restricts the blood flow, possibly triggering heart attack or stroke. Because the blood vessels tend to be circular, two-space dimensional cross section model is a good approximation, and the two-space dimensional models are studied in Friedman et al. (J Differ Equ 259(4):1227-1255, 2015) and Zhao and Hu (J Differ Equ 288:250-287, 2021). It is interesting to see whether a true three-space dimensional stationary solution can be developed. We shall establish a three-space dimensional stationary solution for the mathematical model of the initiation and development of atherosclerosis which involves LDL and HDL cholesterols, macrophages and foam cells. The model is a highly nonlinear and coupled system of PDEs with a free boundary, the interface between the plaque and the blood flow. We establish infinite branches of symmetry-breaking stationary solutions which bifurcate from the annular stationary solution in the longitude direction.

Complex dynamics of hair bundle of auditory nervous system (II): forced oscillations related to two cases of steady state

The forced oscillations of hair bundle of inner hair cells of auditory nervous system evoked by external force from steady state are related to the fast adaption of hair cells, which are very important for auditory amplification. In the present paper, comprehensive and deep understandings to nonlinear dynamics of forced oscillations are acquired in four aspects. Firstly, the complex dynamics underlying the twitch (fast recoil of displacement X which is fast variable) induced from Case-1 and Case-2 steady states by external pulse force are obtained. With help of vector fields and nullclines, the phase trajectory of forced oscillations is identified to be an evolution process between two equilibrium points corresponding to zero force and pulse force, respectively, and then the twitch is obtained as the behavior running along the nonlinear part of X-nullcline. Especially, twitch observed in experiment are classified into 6 types, which are induced by negative change of force, negative and positive changes of force, and positive change of force, respectively, and further build relationships to three subcases of Case-2 steady state with N-shaped X-nullcline (equilibrium point locates on the left, middle, and right branches of X-nullcline, respectively). Secondly, the experimental observation of fatigue of twitch induced by continual two pulse forces, i.e. the reduced amplitude of the latter twitch when interval between two forces is short, is also explained as a nonlinear behavior beginning from an initial value different from that of the former one. Thirdly, the experimental observation of transition between sustained oscillations and steady state induced by pulse force can be simulated for Case-1 steady state with Z-shaped X-nullcline instead of Case-2, due to that there exists bifurcations with respect to external force for Case-1 while no bifurcations for Case-2. Last, the threshold phenomenon induced by simple pulse stimulation exists for Case-1 steady state rather than Case-2, due to that the upper and lower branches of Z-shaped X-nullcline close to the middle branch exhibit coexisting behaviors of variable X while N-shaped X-nullcline does not. The nonlinear dynamics of forced oscillations are helpful for explanations to the complex experimental observations, which presents potential measures to modulate the functions of twitch such as the fast adaption.

Effect of Stenting Strategy on the Outcome in Patients with Non-Left Main Bifurcation Lesions

Previous studies have not compared outcomes between different percutaneous coronary intervention (PCI) strategies and lesion locations in non-left main (LM) bifurcation lesions. We enrolled 2044 patients from a multicenter registry with an LAD bifurcation lesion (n = 1551) or non-LAD bifurcation lesion (n = 493). The primary outcome was target lesion failure (TLF), a composite of cardiac death, myocardial infarction, and target lesion revascularization (TLR). During a median follow-up period of 38 months, non-LAD bifurcation lesions treated with the two-stent strategy, compared with the one-stent strategy, were associated with more frequent TLF (20.7% vs. 6.3%, p < 0.01), TLR (16.7% vs. 4.7%, p < 0.01), and target vessel revascularization (TVR; 18.2% vs. 6.3%, p < 0.01). There was no significant difference in outcome among LAD bifurcation lesions treated with different PCI strategies. The two-stent strategy was associated with a higher risk of TLF (adjusted HR 4.34, CI 1.93−9.76, p < 0.01), TLR (adjusted HR 4.30, CI 1.64−11.27, p < 0.01), and TVR (adjusted HR 5.07, CI 1.69−9.74, p < 0.01) in the non-LAD bifurcation lesions. The planned one-stent strategy is preferable to the two-stent strategy for the treatment of non-LAD bifurcation lesions.

Mathematical modeling for COVID-19 with focus on intervention strategies and cost-effectiveness analysis

The realistic assessments of public health intervention strategies are of great significance to effectively combat the COVID-19 epidemic and the formation of intervention policy. In this paper, an extended COVID-19 epidemic model is devised to assess the severity of the pandemic and explore effective control strategies. The model is characterized by ordinary differential equations with seven-state variables, and it incorporates some parameters associated with the interventions (i.e., media publicity, home isolation, vaccination and face-mask wearing) to investigate the impacts of these interventions on the spread of the COVID-19 epidemic. Some dynamic behaviors of the model, such as forward and backward bifurcation, are analyzed. Specifically, we calibrate the model parameters using actual COVID-19 infected data in Brazil by Markov Chain Monte Carlo algorithm such that we can study the effects of interventions on a practical case. Through a comprehensive exploration of model design and analysis, model calibration, sensitivity analysis, implementation of optimal control problems and cost-effectiveness analysis, the rationality of our model is verified, and the effective strategies to combat the epidemic in Brazil are revealed. The results show that the asymptomatic infected individuals are the main drivers of COVID-19 transmission, and rapid detection of asymptomatic infections is critical to combat the COVID-19 epidemic in Brazil. Interestingly, the effect of the vaccination rate associated with pharmaceutical intervention on the basic reproduction number is much lower than that of non-pharmaceutical interventions (NPIs). Our study also highlights the importance of media publicity. To reduce the infected individuals, the multi-pronged NPIs have considerable positive effects on controlling the outbreak of COVID-19. The infections are significantly decreased by the early implementation of media publicity complemented with home isolation and face-mask wearing strategy. When the cost of implementation is taken into account, the early implementation of media publicity complemented with a face-mask wearing strategy can significantly mitigate the second wave of the epidemic in Brazil. These results provide some management implications for controlling COVID-19.

Dynamic of a two-strain COVID-19 model with vaccination

COVID-19 is a respiratory illness caused by an ribonucleic acid (RNA) virus prone to mutations. In December 2020, variants with different characteristics that could affect transmissibility emerged around the world. To address this new dynamic of the disease, we formulate and analyze a mathematical model of a two-strain COVID-19 transmission dynamics with strain 1 vaccination. The model is theoretically analyzed and sufficient conditions for the stability of its equilibria are derived. In addition to the disease-free and endemic equilibria, the model also has single-strain 1 and strain 2 endemic equilibria. Using the center manifold theory, it is shown that the model does not exhibit the phenomenon of backward bifurcation, and global stability of the model equilibria are proved using various approaches. Simulations to support the model theoretical results are provided. We calculate the basic reproductive number R 1 and R 2 for both strains independently. Results indicate that - both strains will persist when R 1 > 1 and R 2 > 1 - Stain 2 could establish itself as the dominant strain if R 1 < 1 and R 2 > 1 , or when R 2 > R 1 > 1 . However, because of de novo herd immunity due to strain 1 vaccine efficacy and provided the initial stain 2 transmission threshold parameter R 2 is controlled to remain below unity, strain 2 will not establish itself/persist in the community.