Search

In this paper, we provide a simple ODEs model with a generic nonlinear incidence rate function and incorporate two treatments, blocking the virus binding and inhibiting the virus replication to investigate the impact of calibration on model predictions for the SARS-CoV-2 infection dynamics. We derive conditions of the infection eradication for the long-term dynamics using the basic reproduction number, and complement the characterization of the dynamics at short-time using the resilience and reactivity of the virus-free equilibrium are considered to inform on the average time of recovery and sensitivity to perturbations in the initial virus free stage. Then, we calibrate the treatment model to clinical datasets for viral load in mild and severe cases and immune cells in severe cases. Based on the analysis, the model calibrated to these different datasets predicts distinct scenarios: eradication with a non reactive virus-free equilibrium, eradication with a reactive virus-free equilibrium, and failure of infection eradication. Moreover, severe cases generate richer dynamics and different outcomes with the same treatment. Calibration to different datasets can lead to diverse model predictions, but combining long- and short-term dynamics indicators allows the categorization of model predictions and determination of infection severity. [ABSTRACT FROM AUTHOR]

• We propose an epidemic model of imperfect vaccination with a latent period a general nonmonotone incidence rate function. • We study the threshold dynamics with respect to the effective reproduction number. • We discuss the critical vaccination coverage rate that is required to eliminate the disease. • We apply the model to data on measles disease transmission and provide sensitivity analysis. • The latent period shows a noticeable effect on system dynamics but not on the effective reproduction number. In this paper, we investigate the effects of the latent period on the dynamics of infectious disease with an imperfect vaccine. We assume a general incidence rate function with a non-monotonicity property to interpret the psychological effect in the susceptible population when the number of infectious individuals increases. After we propose the model, we provide the well-posedness property by verifying the non-negativity and boundedness of the models solutions. Then, we calculate the effective reproduction number R E. The threshold dynamics of the system is obtained with respect to R E. We discuss the global stability of the disease-free equilibrium when R E < 1 and explore the system persistence when R E > 1. Moreover, we prove the coexistence of an endemic equilibrium when the system persists. Then, we discuss the critical vaccination coverage rate that is required to eliminate the disease. Numerical simulations are provided to: (i) implement a case study regarding the measles disease transmission in the United States from 1963 to 2016; (ii) study the local and global sensitivity of R E with respect to the model parameters; (iii) discuss the stability of endemic equilibrium; and (iv) explore the sensitivity of the proposed model solutions with respect to the main parameters. [ABSTRACT FROM AUTHOR]

In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current I a p p , the maximal conductance of the M-current g M and the conductance of the leak current g L . We give precise conditions for the model that ensure the existence of a Bogdanov–Takens (BT) point and show that such a point can occur by varying I a p p and g M . We discuss the case when the BT point becomes a Bogdanov–Takens–cusp (BTC) point and show that such a point can occur in the three-dimensional parameter space. The results of the bifurcation analysis are applied to different neuronal models and are verified and supplemented by numerical bifurcation diagrams generated using the package MATCONT. We conclude that there is a transition in the neuronal excitability type organised by the BT point and the neuron switches from Class-I to Class-II as conductance of the M-current increases. [ABSTRACT FROM AUTHOR]

Sea lice infection is one of the major threats in the marine fishery, especially for farmed salmon. In this paper, we propose a mathematical model for the growth of sea lice with a three-stage structure: non-infectious immature, infectious immature and adults where the level of non-infectious immature development depends on the size of the adult population. We first describe the nonlinear dynamics by a system of partial differential equations, then, by mathematical techniques and an appropriate change of variables transform it into a system of delay differential equations with constant delay. We address the system threshold dynamics in the established model with respect to the adult reproduction number R s , including the global stability of the trivial steady state when R s < 1 , persistence and global attractivity of the unique positive steady state when R s > 1 . Numerical simulations are provided to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the global dynamics of a periodic disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. We first derive the model system with a general nonlinear incidence rate function by stage-structure. Then, we identify the basic reproduction ratio R0 for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the disease-free state when R0<1 and discuss the disease persistence when R0>1. We also explore the coexistence of endemic state in the nonautonomous system and prove the uniqueness with constants coefficients. Numerical simulations are provided to present a case study regarding the meningococcal meningitis disease transmission and discuss the influence of carriers on R0. [ABSTRACT FROM AUTHOR]

In this paper, we propose a mathematical model for a single species fish stock with a three-stage structure: Juveniles, small adults, and large adults with two harvesting strategies for mature classes, maturity, and size selectivities. The purpose of the work is to investigate the dynamical behavior of the model and discuss the effect of harvesting. We identify the adult reproduction number RA for the model; obtain the local and global stability of the trivial equilibrium when RA < 1; and discuss the population persistence and existence of a unique positive equilibrium when RA > 1. Numerical simulations are provided to investigate the inuence of harvesting functions, discuss the optimal harvesting rates, and explore the effect of periodic coefficients on the dynamical system. [ABSTRACT FROM AUTHOR]

In this paper, we propose a delayed mathematical model for the transmission of Ebola in humans. We consider the transmission of infection between the living humans and from infectious corpses to the living individuals in which the latent period of Ebola is incorporated. We identify the basic reproduction number R 0 for the model, prove that the disease-free equilibrium is always globally asymptotically stable when R 0 < 1, the disease is persistence and a unique endemic equilibrium exists when R 0 > 1. We show that the endemic steady state is locally asymptotically stable under certain condition and globally asymptotically stable in a special case of the model. Numerical simulations are provided to demonstrate and complement the theoretical results. [ABSTRACT FROM AUTHOR]

We give an explicit formula for the signature of any rational link in terms of the denominators of the canonical continued fraction of its slope. [ABSTRACT FROM AUTHOR]

We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has an explicit delay and phase shift in the argument of the phases and connection function, respectively. Using the phase model, we prove that for any type of oscillators and any coupling, the in-phase and anti-phase phase-locked solutions always exist and give conditions for their stability. We show that for small delay these solutions are unique, but with large enough delay multiple solutions of each type with different frequencies may occur. We give conditions for the existence and stability of other types of phase-locked solutions. We discuss the various bifurcations that can occur in the phase model as the time delay is varied. The results of the phase model analysis are applied to Morris–Lecar oscillators with diffusive coupling and compared with numerical studies of the full system of delay differential equations. We also consider the case of small time delay and compare the results with the existing ones in the literature. • We study existence of phase-locked solutions of a phase model with large time delay. • We give conditions for the stability of phase-locked solutions. • We compare our results with existing ones for phase models with small time delay. • We study the bifurcations that cause transitions between phaselocked solutions. • We consider an application to Morris–Lecar oscillators with diffusive coupling. [ABSTRACT FROM AUTHOR]

This study proposes a new rate-dependent feedforward compensator for compensation of hysteresis nonlinearities in smart materials-based actuators without considering the analytical inverse model. The proposed rate-dependent compensator is constructed with the inverse multiplicative structure of the rate-dependent Prandtl–Ishlinskii (RDPI) model. The study also presents an investigation for the compensation error when the proposed compensator is applied in an open-loop feedforward manner. Then, an internal model-based feedback control design is applied with the proposed feedforward compensator to a piezoelectric cantilever actuator. The experimental results illustrate that the proposed feedforward–feedback control scheme can be used in micro-positioning motion control applications to enhance the tracking performance of the piezoelectric cantilever actuator under different operating conditions. [ABSTRACT FROM AUTHOR]

The core G protein signaling module, which consists of Gα and extra-large Gα (XLG) subunits coupled with the Gβγ dimer, is a master regulator of various stress responses. In this study, we compared the basal and salt stress-induced transcriptomic, metabolomic and phenotypic profiles in Gα, Gβ, and XLG-null mutants of two plant species, Arabidopsis thaliana and Marchantia polymorpha , and showed that G protein mediates the shift of transcriptional and metabolic homeostasis to stress readiness status. We demonstrated that such stress readiness serves as an intrinsic protection mechanism against further stressors through enhancing the phenylpropanoid pathway and abscisic acid responses. Furthermore, WRKY transcription factors were identified as key intermediates of G protein-mediated homeostatic shifts. Statistical and mathematical model comparisons between A. thaliana and M. polymorpha revealed evolutionary conservation of transcriptional and metabolic networks over land plant evolution, whereas divergence has occurred in the function of plant-specific atypical XLG subunit. Taken together, our results indicate that the shifts in transcriptional and metabolic homeostasis at least partially act as the mechanisms of G protein-coupled stress responses that are conserved between two distantly related plants. Heterotrimeric G protein mutants show altered plant responses to various abiotic and biotic stresses, but the underlying molecular mechanisms remain largely unclear. This study shows that G protein regulates cell stress readiness through modulating WRKY transcriptional pathways and phenylpropanoid metabolic homeostasis. The transcriptional and metabolic networks regulated by G proteins are largely conserved between Arabidopsis thaliana and Marchantia polymorpha. [ABSTRACT FROM AUTHOR]