The SIS epidemic model with Markovian switching

Population systems are often subject to environmental noise. Motivated by Takeuchi et al. (2006), we will discuss in this paper the effect of telegraph noise on the well-known SIS epidemic model. We establish the explicit solution of the stochastic SIS epidemic model, which is useful in performing computer simulations. We also establish the conditions for extinction and persistence for the stochastic SIS epidemic model and compare these with the corresponding conditions for the deterministic SIS epidemic model. We first prove these results for a two-state Markov chain and then generalise them to a finite state space Markov chain. Computer simulations based on the explicit solution and the Euler--Maruyama scheme are performed to illustrate our theory. We include a more realistic example using appropriate parameter values for the spread of Streptococcus pneumoniae in children

Parameter estimation for the stochastic SIS epidemic model

In this paper we estimate the parameters in the stochastic SIS epidemic model by using pseudo-maximum likelihood estimation (pseudo-MLE) and least squares estimation. We obtain the point estimators and 100(1 − α)% confidence intervals as well as 100(1 − α)% joint confidence regions by applying least squares techniques. The pseudo-MLEs have almost the same form as the least squares case. We also obtain the exact as well as the asymptotic 100(1 − α)% joint confidence regions for the pseudo-MLEs. Computer simulations are performed to illustrate our theory

Tetrahedrally coordinated carbonates in Earth's lower mantle

Carbonates are the main species that bring carbon deep into our planet through subduction. They are an important rock-forming mineral group, fundamentally distinct from silicates in Earth's crust in that carbon binds to three oxygen atoms, while silicon is bonded to four oxygens. Here, we present experimental evidence that under the sufficiently high pressures and high temperatures existing in the lower mantle, ferromagnesian carbonates transform to a phase with tetrahedrally coordinated carbons. Above 80 GPa, in situ synchrotron infrared experiments show the unequivocal spectroscopic signature of the high-pressure phase of (Mg,Fe)CO$_3$. Using ab-initio calculations, we assign the new IR signature to C-O bands associated with tetrahedrally coordinated carbon with asymmetric C-O bonds. Tetrahedrally coordinated carbonates are expected to exhibit substantially different reactivity than low pressure three-fold coordinated carbonates, as well as different chemical properties in the liquid state. Hence this may have significant implications on carbon reservoirs and fluxes and the global geodynamic carbon cycle

Constructing the cultural repertoire in a natural disaster: The role of social media in the Thailand flood of 2011

In 2011, Thailand witnessed its worst flooding catastrophe in half a century. In this study, we explored social media as a new and promising weapon to address the physical and morale challenges caused by the natural disaster. A case study was conducted in the context of crisis response, whichinvestigated the use of social media to contribute to the collective cultural repertoire during the natural disaster. By investigating two paths toward the cultural repertoire construction considering different social groups, this study also identified the roles of social media as an information market and an information threshold in the crisis response