Active Role of Self-Sustained Neural Activity on Sensory Input Processing: A Minimal Theoretical Model

A growing body of work has demonstrated the importance of ongoing oscillatory neural activity in sensory processing and the generation of sensorimotor behaviors. It has been shown, for several different brain areas, that sensory-evoked neural oscillations are generated from the modulation by sensory inputs of inherent self-sustained neural activity (SSA). This letter contributes to that strand of research by introducing a methodology to investigate how much of the sensory-evoked oscillatory activity is generated by SSA and how much is generated by sensory inputs within the context of sensorimotor behavior in a computational model. We develop an abstract model consisting of a network of three Kuramoto oscillators controlling the behavior of a simulated agent performing a categorical perception task. The effects of sensory inputs and SSAs on sensory-evoked oscillations are quantified by the cross product of velocity vectors in the phase space of the network under different conditions (disconnected without input, connected without input, and connected with input). We found that while the agent is carrying out the task, sensory-evoked activity is predominantly generated by SSA (93.10%) with much less influence from sensory inputs (6.90%). Furthermore, the influence of sensory inputs can be reduced by 10.4% (from 6.90% to 6.18%) with a decay in the agent's performance of only 2%. A dynamical analysis shows how sensory-evoked oscillations are generated from a dynamic coupling between the level of sensitivity of the network and the intensity of the input signals. This work may suggest interesting directions for neurophysiological experiments investigating how self-sustained neural activity influences sensory input processing, and ultimately affects behavior.

Dynamical analysis of coronavirus disease with crowding effect, and vaccination: a study of third strain

Countries affected by the coronavirus epidemic have reported many infected cases and deaths based on world health statistics. The crowding factor, which we named "crowding effects," plays a significant role in spreading the diseases. However, the introduction of vaccines marks a turning point in the rate of spread of coronavirus infections. Modeling both effects is vastly essential as it directly impacts the overall population of the studied region. To determine the peak of the infection curve by considering the third strain, we develop a mathematical model (susceptible–infected–vaccinated–recovered) with reported cases from August 01, 2021, till August 29, 2021. The nonlinear incidence rate with the inclusion of both effects is the best approach to analyze the dynamics. The model's positivity, boundedness, existence, uniqueness, and stability (local and global) are addressed with the help of a reproduction number. In addition, the strength number and second derivative Lyapunov analysis are examined, and the model was found to be asymptotically stable. The suggested parameters efficiently control the active cases of the third strain in Pakistan. It was shown that a systematic vaccination program regulates the infection rate. However, the crowding effect reduces the impact of vaccination. The present results show that the model can be applied to other countries' data to predict the infection rate.

Dynamical analysis, optimal control and spatial pattern in an influenza model with adaptive immunity in two stratified population

<abstract><p>Consistently, influenza has become a major cause of illness and mortality worldwide and it has posed a serious threat to global public health particularly among the immuno-compromised people all around the world. The development of medication to control influenza has become a major challenge now. This work proposes and analyzes a structured model based on two geographical areas, in order to study the spread of influenza. The overall underlying population is separated into two sub populations: urban and rural. This geographical distinction is required as the immunity levels are significantly higher in rural areas as compared to urban areas. Hence, this paper is a novel attempt to proposes a linear and non-linear mathematical model with adaptive immunity and compare the host immune response to disease. For both the models, disease-free equilibrium points are obtained which are locally as well as globally stable if the reproduction number is less than 1 (<italic>R</italic>₀₁ &lt; 1 &amp; <italic>R</italic>₀₂ &lt; 1) and the endemic point is stable if the reproduction number is greater then 1 (<italic>R</italic>₀₁ &gt; 1 &amp; <italic>R</italic>₀₂ &gt; 1). Next, we have incorporated two treatments in the model that constitute the effectiveness of antidots and vaccination in restraining viral creation and slow down the production of new infections and analyzed an optimal control problem. Further, we have also proposed a spatial model involving diffusion and obtained the local stability for both the models. By the use of local stability, we have derived the Turing instability condition. Finally, all the theoretical results are verified with numerical simulation using MATLAB.</p></abstract>

Bifurcation Analysis of a Four-Dimensional System of Two Symmetric Coupled Nonlinear Oscillators with Clearance

The research gradually highlights vibration and dynamical analysis of symmetric coupled nonlinear oscillators model with clearance. The aim of this paper is the bifurcation analysis of the symmetric coupled nonlinear oscillators modeled by a four-dimensional nonsmooth system. The approximate solution of this system is obtained with aid of averaging method and Krylov-Bogoliubov (KB) transformation presented by new notations of matrices. The bifurcation function is derived to investigate its dynamic behaviour by singularity theory. The results obtained provide guidance for the nonlinear vibration of symmetric coupled nonlinear oscillators model with clearance.