ABSTRACT
The virologically confirmed cases of a new coronavirus disease (COVID-19) in the world are rapidly increasing, leading epidemiologists and mathematicians to construct transmission models that aim to predict the future course of the current pandemic. The transmissibility of a virus is measured by the basic reproduction number ( R0 ), which measures the average number of new cases generated per typical infectious case. This review highlights the articles reporting rigorous estimates and determinants of COVID-19 R0 for the most affected areas. Moreover, the mean of all estimated R0 with median and interquartile range is calculated. According to these articles, the basic reproduction number of the virus epicentre Wuhan has now declined below the important threshold value of 1.0 since the disease emerged. Ongoing modelling will inform the transmission rates seen in the new epicentres outside of China, including Italy, Iran and South Korea.
Subject(s)
Coronavirus Infections , Coronavirus , Pandemics , Pneumonia, Viral , Severe acute respiratory syndrome-related coronavirus , Basic Reproduction Number , Betacoronavirus , COVID-19 , China , Humans , SARS-CoV-2ABSTRACT
In this paper, we consider a ring neural network with one-way distributed-delay coupling between the neurons and a discrete delayed self-feedback. In the general case of the distribution kernels, we are able to find a subset of the amplitude death regions depending on even (odd) number of neurons in the network. Furthermore, in order to show the full region of the amplitude death, we use particular delay distributions, including Dirac delta function and gamma distribution. Stability conditions for the trivial steady state are found in parameter spaces consisting of the synaptic weight of the self-feedback and the coupling strength between the neurons, as well as the delayed self-feedback and the coupling strength between the neurons. It is shown that both Hopf and steady-state bifurcations may occur when the steady state loses stability. We also perform numerical simulations of the fully nonlinear system to confirm theoretical findings.