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Publications

Publications by Alberto Pinto

2015

Mathematics of Energy and Climate Change

Authors
Bourguignon, J; Jeltsch, R; Pinto, AA; Viana, M;

Publication
CIM Series in Mathematical Sciences

Abstract

2018

Cournot duopolies with investment in R&D: Regions of nash investment equilibria

Authors
Oliveira, BMPM; Becker Paulo, J; Pinto, AA;

Publication
Springer Proceedings in Mathematics and Statistics

Abstract
We study a model of a Cournot duopoly where firms invest in R&D to reduce their production costs. Depending on the parameters, we may find regions with one, two or three Nash equilibria of the investment. Here, we study the effect of the parameters in these regions, in particular, we study the effect of the possible market saturation, the maximum relative cost reduction and the product differentiation, giving special attention to regions with multiple Nash equilibria. We observed that, in general, the competitive region, where both firms invest, is reduced as we increase the possible market saturation and the differentiation of the products and is enlarged when we increase the maximum relative cost reduction. © 2018, Springer International Publishing AG, part of Springer Nature.

2018

Operational Research

Authors
Vaz, AIF; Almeida, JP; Oliveira, JF; Pinto, AA;

Publication
Springer Proceedings in Mathematics & Statistics

Abstract

2018

Modelling the suppression of autoimmunity after pathogen infection

Authors
Oliveira, BMPM; Trinchet, R; Otero Espinar, MVO; Pinto, A; Burroughs, N;

Publication
MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Abstract
We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 (IL-2) secretion. We model the suppression of the autoimmune line of T cells after a different line of T cells responded to a pathogen infection. In this paper, we show that if the population of the pathogen responding line of T cells becomes large enough, the competition for IL-2 and the increase in the death rates may lead to a depletion in the concentration of autoimmune T cells. Provided this lasts for a sufficiently long time, the concentration of autoimmune T cells can be brought down to values inside the basin of attraction of the controlled state, and autoimmunity can be suppressed.

2017

Geometric Approaches and Bifurcations in the Dichotomous Decision Model = ????? ???????? ?????????? ?? ????? ?????? ?? ??????

Authors
Mousa, AS; Pinto, AA;

Publication
Journal of the Arab American University

Abstract

2019

A fit of CD4(+) T cell immune response to an infection by lymphocytic choriomeningitis virus

Authors
Afsar, A; Martins, F; Oliveira, BMPM; Pinto, AA;

Publication
MATHEMATICAL BIOSCIENCES AND ENGINEERING

Abstract
We fit an immune response model to data reporting the CD4(+) T cell numbers from the 28 days following the infection of mice with lymphocytic choriomeningitis virus LCMV. We used an ODE model that was previously used to describe qualitatively the behaviour of CD4(+) T cells, regulatory T cells (Tregs) and interleukine-2 (IL-2) density. The model considered two clonotypes of T cells in order to fit simultaneously the two time series for the gp61 and NP309 epitopes. We observed the proliferation of T cells and, to a lower extent, Tregs during the immune activation phase following infection and subsequently, during the contraction phase, a smooth transition from faster to slower death rates. The six parameters that were optimized were: the beginning and ending times of the immune response, the growth rate of T cells, their capacity, and the two related with the homeostatic numbers of T cells that respond to each epitope. We showed that the ODE model was able to be calibrated thus providing a quantitative description of the data.

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