Plenary Lecture

Tourism Sustainability Models with Time Delay

Professor Mihaela Neamtu
Faculty of Economics and Business Administration
West University of Timisoara
Romania
E-mail: mihaela.neamtu@e-uvt.ro

Abstract: Nowadays, the tourism industry gains attention all over the world. The development of a touristic site could have a negative impact on the natural environment; therefore a balance must be maintained for the protection of the surrounding areas. Casagrandi and Rinaldi (2002) developed the minimal model that characterizes a touristic site, by considering the number of tourists, the quality of the environment and the capital. It is proved that there are no policies that guarantee a sustainable tourism without a negative and direct impact of the environment. In 2013, Wei et al. determined the equilibrium points and for different values of the investment parameter a stability analysis is provided. Lacitignola et al.(2007) and Afsharnezhad et al. (2017) took into account two main tourist categories (mass and eco-tourists) and studied different scenarios for the sustainability of tourism. Motivated by the existing minimal models that describe a touristic site, our contribution is to study their dynamics when the realistic features are introduced. On one hand, the distributed time delay highlights the effect of previous tourists in the number of present visitors, environment and capital flow. On the other hand, the fractional derivative accounts for the memory of the tourists. For the associated mathematical models the positive solutions and positive equilibrium points are investigated. The local stability analysis is given and bifurcation analysis is carried out with respect to the average time delay. The numerical results illustrate the theoretical findings.

Brief Biography of the Speaker: Mihaela Neamtu was born in Timisoara (Romania) on 1971. She graduated in 1995 the Faculty of Mathematics, West University of Timisoara. In 2001 she obtained the title of Ph.D in mathematics. She followed a didactic career at the Faculty of Economics and Business Administration, West University of Timisoara, Romania and she is currently Professor. She has been a visiting Professor for short periods of time at The Nottingham Trent University, Economics & Politics (Great Britain), Faculty of Mathematics, Bonn (Germany), University of Perpignan (France) and University of La Rochelle (France). Professor Mihaela Neamtu published over 100 articles in journals and proceedings of international conferences and 6 books with 106 citations in ISI and BDI journals. Moreover, she has been a regular referee of papers for ISI and BDI journals and a reviewer of Mathematical Reviews (MathSciNet). She has been participating in 11 multiannual grants (1 of them is international), in 9 as a member and in 2 as a director.

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