Network synchronization, stability and rhythmic processes in a diffusive mean-field coupled SEIR model

Connectivity and rates of movement have profound effect on the persistence and extinction of infectious diseases. The emerging disease spread rapidly, due to the movement of infectious persons to some other regions, which has been witnessed in case of novel coronavirus disease 2019 (COVID-19). So, the networks and the epidemiology of directly transmitted infectious diseases are fundamentally linked. Motivated by the recent empirical evidence on the dispersal of infected individuals among the patches, we present the epidemic model SEIR (Susceptible-Exposed-Infected-Recovered) in which the population is divided into patches which form a network and the patches are connected through mean-field diffusive coupling. The corresponding unstable epidemiology classes will be synchronized and achieve stable state when the patches are coupled. Apart from synchronization and stability, the coupled model enables a range of rhythmic processes such as birhythmicity and rhythmogenesis which have not been investigated in epidemiology. The stability of Disease Free Equilibrium (or Endemic Equilibrium) is attained through cessation of oscillation mechanism namely Oscillation Death (OD) and Amplitude Death (AD). Corresponding to identical and non-identical epidemiology classes of patches, the different steady states are obtained and its transition is taking place through Hopf and transcritical bifurcation.

The funny current in genetically modified mice

Since its first description in 1979, the hyperpolarization-activated funny current (I_f) has been the object of intensive research aimed at understanding its role in cardiac pacemaker activity and its modulation by the sympathetic and parasympathetic branches of the autonomic nervous system. I_f was described in isolated tissue strips of the rabbit sinoatrial node using the double-electrode voltage-clamp technique. Since then, the rabbit has been the principal animal model for studying pacemaker activity and I_f for more than 20 years. In 2001, the first study describing the electrophysiological properties of mouse sinoatrial pacemaker myocytes and those of I_f was published. It was soon followed by the description of murine myocytes of the atrioventricular node and the Purkinje fibres. The sinoatrial node of genetically modified mice has become a very popular model for studying the mechanisms of cardiac pacemaker activity. This field of research benefits from the impressive advancement of in-vivo exploration techniques of physiological parameters, imaging, genetics, and large-scale genomic approaches. The present review discusses the influence of mouse genetic on the most recent knowledge of the funny current's role in the physiology and pathophysiology of cardiac pacemaker activity. Genetically modified mice have provided important insights into the role of I_f in determining intrinsic automaticity in vivo and in myocytes of the conduction system. In addition, gene targeting of f-(HCN) channel isoforms have contributed to elucidating the current's role in the regulation of heart rate by the parasympathetic nervous system. This review is dedicated to Dario DiFrancesco on his retirement.

Rhythmic wrist movements facilitate the soleus H-reflex and non-voluntary air-stepping in humans

Neural coupling between the upper and lower limbs during human walking is supported by modulation of cross-limb reflexes and the presence of rhythmic activity in the proximal arm muscles. Nevertheless, the involvement of distal arm muscles in cyclic movements and sensorimotor neuromodulation is also suggested given their step-synchronized activation in many locomotor-related tasks (e.g., swimming, skiing, climbing, cycling, crawling, etc.). Here we investigated the effect of rhythmic wrist movements, separately and in conjunction with arm swinging, on the characteristics of non-voluntary cyclic leg movements evoked by muscle vibration in a gravity neutral position and on the soleus H-reflex of the stationary legs. For the H-reflex modulation, five conditions were compared: stationary arms, voluntary alternating upper limb swinging, combined upper limb and wrist motion, wrist movements only and motion of the upper limbs with addition of load. Rhythmic wrist movements significantly facilitated the amplitude of non-voluntary leg oscillations, including ankle joint oscillations, and the H-reflex. The latter effect was related to rhythmicity of wrist motion rather than to a simple extra tension in the upper limb muscles (a kind of the Jendrassik manoeuvre) since adding resistance to arm oscillations (without flexion-extension in the wrist joint) had an opposite inhibitory effect on the H-reflex. Our results further support the existence of connections between the distal parts of the upper and lower extremities at the neural level, suggesting that wrist joint movements can be an important component of motor neurorehabilitation.