Stability and sensitivity analysis of Be-CoDiS, an epidemiological model to predict the spread of human diseases between countries. Validation with data from the 2014-16 West African Ebola Virus Disease epidemic.

Ebola virus disease is a lethal human and primate disease that requires a particular attention from the international health authorities due to important recent outbreaks in some Western African countries and isolated cases in European and North-America continents. Regarding the emergency of this situation, various decision tools, such as mathematical models, were developed to assist the authorities to focus their efforts in important factors to eradicate Ebola. In a previous work, we have proposed an original deterministic spatial-temporal model, called Be-CoDiS (Between-Countries Disease Spread), to study the evolution of human diseases within and between countries by taking into consideration the movement of people between geographical areas. This model was validated by considering numerical experiments regarding the 2014-16 West African Ebola Virus Disease epidemic. In this article, we propose to perform a stability analysis of Be-CoDiS. Our first objective is to study the equilibrium states of simplified versions of this model, limited to the cases of one an two countries, and to determine their basic reproduction ratios. Then, in order to give some recommendations for the allocation of resources used to control the disease, we perform a sensitivity analysis of those basic reproduction ratios regarding the model parameters. Finally, we validate the obtained results by considering numerical experiments based on data from the 2014-16 West African Ebola Virus Disease epidemic.

Temperatures at the last interglacial simulated by a coupled ocean-atmosphere climate model

The last interglacial (Eemian, 125,000 years ago) has generally been considered the warmest time period in the last 200,000 years and thus sometimes been used as a reference for greenhouse projections. Herein we report results from a coupled ocean-atmosphere climate model of the surface temperature response to changes in the radiative forcing at the last interglacial. Although the model generates the expected summer warming in the northern hemisphere, winter cooling of a comparable magnitude occurs over North Africa and tropical Asia. The global annual mean temperature for the Eemian run is 0.3 degrees C cooler than the control run. Validation of simulated sea surface temperatures (SSTs) against reconstructed SSTs supports this conclusion and also the assumption that the flux correction, fitted for the present state, operates satisfactorily for modest perturbations. Our results imply that contrary to conventional expectations, Eemian global temperatures may already have been reached by the mid 20th century.

The transducer model for contrast detection and discrimination: formal relations, implications, and an empirical test.

The transducer function mu for contrast perception describes the nonlinear mapping of stimulus contrast onto an internal response. Under a signal detection theory approach, the transducer model of contrast perception states that the internal response elicited by a stimulus of contrast c is a random variable with mean mu(c). Using this approach, we derive the formal relations between the transducer function, the threshold-versus-contrast (TvC) function, and the psychometric functions for contrast detection and discrimination in 2AFC tasks. We show that the mathematical form of the TvC function is determined only by mu, and that the psychometric functions for detection and discrimination have a common mathematical form with common parameters emanating from, and only from, the transducer function mu and the form of the distribution of the internal responses. We discuss the theoretical and practical implications of these relations, which have bearings on the tenability of certain mathematical forms for the psychometric function and on the suitability of empirical approaches to model validation. We also present the results of a comprehensive test of these relations using two alternative forms of the transducer model: a three-parameter version that renders logistic psychometric functions and a five-parameter version using Foley's variant of the Naka-Rushton equation as transducer function. Our results support the validity of the formal relations implied by the general transducer model, and the two versions that were contrasted account for our data equally well.