ABSTRACT
In this article, we develop a mathematical model considering susceptible, exposed, infected, asymptotic, quarantine/isolation and recovered classes as in case of COVID-19 disease. The facility of quarantine/isolation have been provided to both exposed and infected classes. Asymptotic individuals either recovered without undergo treatment or moved to infected class after some duration. We have formulated the reproduction number for the proposed model. Elasticity and sensitivity analysis indicates that model is more sensitive towards the transmission rate from exposed to infected classes rather than transmission rate from susceptible to exposed class. Analysis of global stability for the proposed model is studied through Lyapunov's function.
ABSTRACT
OBJECTIVE: Absence epilepsy is a common seizure disorder in children which can produce chronic psychosocial sequelae. Human patients and rat absence models show bilateral spike-wave discharges (SWD) in cortical regions. We employed diffusion tensor imaging (DTI) in rat absence models to detect abnormalities in white matter pathways connecting regions of seizure activity. METHODS: We studied Wistar albino Glaxo rats of Rijswijk (WAG/Rij), genetic absence epilepsy rats of Strasbourg (GAERS), and corresponding nonepileptic control strains. Ex vivo DTI was performed at 9.4 T with diffusion gradients applied in 16 orientations. We compared fractional anisotropy (FA), perpendicular (lambda(perpendicular)) and parallel (lambda(||)) diffusivity between groups using t-maps and region of interest (ROI) measurements. RESULTS: Adult epileptic WAG/Rij rats exhibited a localized decrease in FA in the anterior corpus callosum. This area was confirmed by tractography to interconnect somatosensory cortex regions most intensely involved in seizures. This FA decrease was not present in young WAG/Rij rats before onset of SWD. GAERS, which have more severe SWD than WAG/Rij, exhibited even more pronounced callosal FA decreases. Reduced FA in the epileptic animals originated from an increased lambda(perpendicular) with no significant changes in lambda(||). INTERPRETATION: Reduced FA with increased lambda(perpendicular) suggests that chronic seizures cause reduction in myelin or decreased axon fiber density in white matter pathways connecting regions of seizure activity. These DTI abnormalities may improve the understanding of chronic neurological difficulties in children suffering with absence epilepsy, and may also serve as a noninvasive biomarker for monitoring beneficial effects of treatment.
