Parameter Identification in a Tuberculosis Model for Cameroon

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency-and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.

Rapid hydrothermal cooling above the axial melt lens at fast-spreading mid-ocean ridge

Axial melt lenses sandwiched between the lower oceanic crust and the sheeted dike sequences at fast-spreading mid-ocean ridges are assumed to be the major magma source of oceanic crust accretion. According to the widely discussed "gabbro glacier'' model, the formation of the lower oceanic crust requires efficient cooling of the axial melt lens, leading to partial crystallization and crystal-melt mush subsiding down to lower crust. These processes are believed to be controlled by periodical magma replenishment and hydrothermal circulation above the melt lens. Here we quantify the cooling rate above melt lens using chemical zoning of plagioclase from hornfelsic recrystallized sheeted dikes drilled from the East Pacific at the Integrated Ocean Drilling Program Hole 1256D. Weestimate the cooling rate using a forward modelling approach based on CaAl-NaSi interdiffusion in plagioclase. The results show that cooling from the peak thermal overprint at 1000-10506 degrees C to 6006 degrees C are yielded within about 10-30 years as a result of hydrothermal circulation above melt lens during magma starvation. The estimated rapid hydrothermal cooling explains how the effective heat extraction from melt lens is achieved at fast-spreading mid-ocean ridges.