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About

About

I am a lecturer at the Department of Mathematics of the School of Technology and Management, Polytechnic Institute of Leiria, since 2004.

My PhD was taken at University of Minho, in 2010, under the supervision of Professor Alberto Adrego Pinto and Professor Nico Stollenwerk. The title of my PhD thesis was "Thresholds for epidemiological outbreaks".

Interest
Topics
Details

Details

  • Name

    José Martins
  • Cluster

    Computer Science
  • Role

    Senior Researcher
  • Since

    01st January 2012
Publications

2017

Bistability of Evolutionary Stable Vaccination Strategies in the Reinfection SIRI Model

Authors
Martins, J; Pinto, A;

Publication
BULLETIN OF MATHEMATICAL BIOLOGY

Abstract
We use the reinfection SIRI epidemiological model to analyze the impact of education programs and vaccine scares on individuals decisions to vaccinate or not. The presence of the reinfection provokes the novelty of the existence of three Nash equilibria for the same level of the morbidity relative risk instead of a single Nash equilibrium as occurs in the SIR model studied by Bauch and Earn (PNAS 101:13391-13394, 2004). The existence of three Nash equilibria, with two of them being evolutionary stable, introduces two scenarios with relevant and opposite features for the same level of the morbidity relative risk: the low-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a low probability; and the high-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a high probability. We introduce the evolutionary vaccination dynamics for the SIRI model and we prove that it is bistable. The bistability of the evolutionary dynamics indicates that the damage provoked by false scares on the vaccination perceived morbidity risks can be much higher and much more persistent than in the SIR model. Furthermore, the vaccination education programs to be efficient they need to implement a mechanism to suddenly increase the vaccination coverage level.

2016

A repeated strategy for dumping

Authors
Martins, J; Banik, N; Pinto, AA;

Publication
Springer Proceedings in Mathematics and Statistics

Abstract
In this work, we study the phenomena of dumping in a duopoly market through an infinitely repeated game. We consider two firms of different countries competing in the same country. When both firms are cooperating, if the foreign firm deviates from cooperation this can be interpreted as dumping and a period of punishment can be imposed to the foreign firm. After this, firms can play continuously the deviation-punishment game or compete à la Cournot. Previously, we observe that the repeated strategy of deviation-punishment is not adopted in the case of symmetric demand equations. Here, we observe that this strategy of repeated dumping can appear as the best repeated strategy when the demand equations are non-symmetric. © Springer-Verlag Berlin Heidelberg 2016.

2012

Stationarity in Moment Closure and Quasi-Stationarity of the SIS model

Authors
José Martins; Alberto Pinto; N. Stollenwerk

Publication
Mathematical Biosciences - Mathematical Biosciences, vol.236, no.2, pp.126-131

Abstract

2012

Scaling of Stochasticity in Dengue Hemorrhagic Fever Epidemics

Authors
M. Aguiar; B. W. Kooi; José Martins; N. Stollenwerk

Publication
MATH MODEL NAT PHENO - Mathematical Modelling of Natural Phenomena, vol.7, no.3, pp.1-11

Abstract

2011

An Economical Model For Dumping by Dumping in a Cournot Model

Authors
Nilanjan Banik; Fernanda.A. Ferreira; José Martins; Alberto Pinto

Publication
vol.2, pp.141-153

Abstract