Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model.

In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and transmission of weak stimuli generated at distal synapses. To support the experimental findings from the perspective of multicompartment model analysis, this paper aimed to elucidate the phenomenon of SR in a noisy two-compartment hippocampal pyramidal neuron model, which was a variant of the Pinsky-Rinzel neuron model with smooth activation functions and a hyperpolarization-activated cation current. With a bifurcation analysis of the model, we demonstrated the underlying dynamical structure responsible for the occurrence of SR. Furthermore, using a stochastically generated biphasic pulse train and broadband noise generated by the Orenstein-Uhlenbeck process as noise perturbation, both SR and suprathreshold SR were observed and quantified. Spectral analysis revealed that the distribution of spectral power under noise perturbations, in addition to inherent neurodynamics, is the main factor affecting SR behavior. The research results suggested that noise enhances the transmission of weak stimuli associated with elongated dendritic structures of hippocampal pyramidal neurons, thereby providing support for related laboratory findings.

Emergence of Beta Oscillations of a Resonance Model for Parkinson's Disease.

In Parkinson's disease, the excess of beta oscillations in cortical-basal ganglia (BG) circuits has been correlated with normal movement suppression. In this paper, a physiologically based resonance model, generalizing an earlier model of the STN-GPe circuit, is employed to analyze critical dynamics of the occurrence of beta oscillations, which correspond to Hopf bifurcation. With the experimentally measured parameters, conditions for the occurrence of Hopf bifurcation with time delay are deduced by means of linear stability analysis, center manifold theorem, and normal form analysis. It is found that beta oscillations can be induced by increasing synaptic transmission delay. Furthermore, it is revealed that the oscillations originate from interaction among different synaptic connections. Our analytical results are consistent with the previous experimental and simulating findings, thus may provide a more systematic insight into the mechanisms underlying the transient beta bursts.

Modeling the effects of the contaminated environments on COVID-19 transmission in India.

COVID-19 is an infectious disease caused by the SARS-CoV-2 virus that caused an outbreak of typical pneumonia first in Wuhan and then globally. Although researchers focus on the human-to-human transmission of this virus but not much research is done on the dynamics of the virus in the environment and the role humans play by releasing the virus into the environment. In this paper, a novel nonlinear mathematical model of the COVID-19 epidemic is proposed and analyzed under the effects of the environmental virus on the transmission patterns. The model consists of seven population compartments with the inclusion of contaminated environments means there is a chance to get infected by the virus in the environment. We also calculated the threshold quantity R 0 to know the disease status and provide conditions that guarantee the local and global asymptotic stability of the equilibria using Volterra-type Lyapunov functions, LaSalle's invariance principle, and the Routh-Hurwitz criterion. Furthermore, the sensitivity analysis is performed for the proposed model that determines the relative importance of the disease transmission parameters. Numerical experiments are performed to illustrate the effectiveness of the obtained theoretical results.