Abstract
We make two fits of an ODE system with 5 equations that model immune response by CD4 + T cells with the presence of regulatory T cells (Tregs). We fit the simulations to data regarding gp61 and NP309 epitopes from mice infected with lymphocytic choriomeningitis virus LCMV. We optimized parameters relating to: the T cell maximum growth rate; the T cell capacity; the T cell homeostatic level; and the ending time of the immune activation phase after infection. We quantitatively and qualitatively compare the obtained results with previous fits in the literature using different ODE models and we show that we are able to calibrate the model and obtain good fits describing the data. © 2021, Springer Nature Switzerland AG.

Abstract
We propose a refinement process of dynamic equilibria based on small random perturbations (SRPs) of the backward perfect foresight (bpf) equilibrium map in a class of one-step, forward-looking dynamic models. An equilibrium is selected if its stationary measure is the limit of the stationary measures associated with the processes generated by the SRPs of the bpf maps, as the perturbation size approaches 0. We show that, for full measure sets of parameter values of a large class of one-parameter families of unimodal bpf maps, only determinate cycles or the chaotic sunspot equilibrium defined by Araujo and Maldonado (2000) is selected. Two examples are provided illustrating such refinement process.

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Abstract
The subprime crisis was a global financial crisis that affected a large number of countries and, in particular, the European economies. In this paper we considered fourteen variables associated to the public, private and financial sectors, in order to analyze the main vulnerabilities, differences and similarities observed in twenty-seven European countries. The statistical analysis was performed with the STATIS methodology, with data collected in the period 2002-2011, including some years before and some after the historical crisis of 2007-2008. The study led us to conclude that European countries are different in which concerns to investment, savings, sustainability of public accounts and public investment.

Abstract
An important problem in directional statistics is to test the null hypothesis of a common mean direction for several populations. The Analysis of Variance (ANOVA) test for vectorial data may be used to test the hypothesis of the equality of the mean directions for several von Mises-Fisher populations. As this test is valid only for large concentrations, we propose in this paper to apply the resampling techniques of bootstrap and permutation to the ANOVA test. We carried out an extensive simulation study in order to evaluate the performance of the ANOVA test with the resampling techniques, for several sphere dimensions and different sample sizes and we compare with the usual ANOVA test for data from von Mises-Fisher populations. The purpose of this simulation study is also to investigate whether the proposed tests are preferable to the ANOVA test, for low concentrations and small samples. Finally, we present an example with spherical data.