Mathematical Modeling of Tourism Development. An Application to Albanian Tourism
The article contains a comprehensive study of tourist arrivals in Albania in the years 1994 to 2020. During this period, the trend of tourism development has been studied, using the widely approved concept of Tourist Area Cycle Theory (TALC). During these years, the number of tourists has been growing rapidly, and, the touristic sites of Albania have been transformed to serve touristic purposes, especially the coastline. Recently the geographic touristic map has been enlarged to the mountain and rural areas, touristic villages, and cultural, archaeological, historical tourism. The dynamics of tourism development have been studied by many researchers, academics, and institutions to provide a complete and clear picture of the history and predict the future of the tourism industry. Econometric, mathematical or mixed models are applied to fit the tourism development and they have been helpful and have served the purpose. The model we have used to analyze the arrivals in Albania is the Logistical and the Gompertz model, largely used to estimate growth under limited resources. The tourist arrivals, i.e., the number of tourists entering the destination country have been considered as the most important variable to describe the tourism development. Several useful software is mostly used to fit the historical data and predict future arrivals such as Stata, Lab fit, Curve Expert, Spss, etc. In our case the Stata software to run the data provided for this article. The data for this article are provided from INSTAT (National Institute of Statistics), (http://www.instat.gov.al/) and other National Institutions such as the Ministry of Tourism and Environment of Albania, (https://turizmi.gov.al/), and several International Institutional such as the World Bank, (https://data.worldbank.org/indicator/ST.INT.ARVL?locations=AL), World Tourism Organization, (https://www.unwto.org/statistic/basic-tourism-statistics). The data, together with the growing numbers of tourists show the significant impact of tourism on the economic development of the country, income, contribution to the Gross Domestic Product (GDP), employment, etc.
 Butler, R. W. (2006). The concept of a tourist area cycle of evolution: Implications for management of resources. In The Tourism Area Life Cycle, 1: 3-12.
 Buttler, R. W. (1980). The concept of tourism area cycle of evolution: implications for management of resources”. Canadian Geographer, 24: 5-12.
 Čizmić, E., & Čaušević., A. (2017). Impact of event tourism in a tourist destination quality of experience–Case of the Sarajevo Film Festival. Universal Journal of Management, 5(7): 332-340.
 Correia, R., & Brito, C. (2016). Wine tourism and regional development. In Wine and tourism, 27-39.
 Kovaci et al. (2021). The Impact of Tourism on the Economic Development of Kosovo. Journal of Environmental Management and Tourism, 12(1): 146 – 153.
 Kulendran, N. and Witt, S.F. (2001). Cointegration versus least squares regression. Annals of Tourism Research, 28(2): 291-311.
 Lequeux- Dinca, A. I., & Preda, M. (2018). Festivals and cultural events–a destinFestivals and cultural events–a destination attractor and a triggering factor of change in the post-communist Romanian landscape. Journal of Environmental and Tourism Analyses, 5(1): 58-72.
 Lundtorp, S., & Wanhill., S. (2001). The resort lifecycle theory: Generating processes and estimation. Annals of tourism research, 28(4): 947-964.
 Malthus, T. R. (1872). An Essay on the Principle of Population.
 Martin, C. A., & Wit, S. F. (1989). Forecasting tourism demand: A comparison of the accuracy of several quantitative methods. International Journal of forecasting, 5(1): 7-19.
 Quetelet, L. A. (2013). A treatise on man and the development of his faculties. Cambridge University Press.
 Sambuu, A. (2019). Recreational assessment of landscapes of Tuva for the development of tourism. Journal of Environmental Management and Tourism (JEMT), 2 (34): 438-440.
 Shehu, V., Kosova, R., & Guxholli, D. (2016). Estimation of Foreign Arrivals in Albania Using Logistic Growth Model. “Information Systems and Technology Innovations: The New Paradigm for a smarter economy" (pp. 77-78). Tirana. Albania. ISBN: 978-9928-148-56-8.
 Song, H., Li, G., Witt, S. F., & Fei, B. (2010). Tourism demand modeling and forecasting: how should demand be measured? Tourism economics, 16(1): 63-81.
 Verhulst, P.-F. (1838). Notice sur la loi que la population suit dans son accroissement. Corresp. Math. Phys. 10: 113-126.
 INSTAT. (2021, 9). www.instat.gov.al/en/Home.asp. Retrieved from INSTAT. www.instat.gov.al/en/.
 worldbank.org. (2021, 9). worldbank. Retrieved from https://data.worldbank.org/indicator/ST.INT.ARVL?end=2019&locations=AL&start=1995&view=chart
The Copyright Transfer Form to ASERS Publishing (The Publisher)
This form refers to the manuscript, which an author(s) was accepted for publication and was signed by all the authors.
The undersigned Author(s) of the above-mentioned Paper here transfer any and all copyright-rights in and to The Paper to The Publisher. The Author(s) warrants that The Paper is based on their original work and that the undersigned has the power and authority to make and execute this assignment. It is the author's responsibility to obtain written permission to quote material that has been previously published in any form. The Publisher recognizes the retained rights noted below and grants to the above authors and employers for whom the work performed royalty-free permission to reuse their materials below. Authors may reuse all or portions of the above Paper in other works, excepting the publication of the paper in the same form. Authors may reproduce or authorize others to reproduce the above Paper for the Author's personal use or for internal company use, provided that the source and The Publisher copyright notice are mentioned, that the copies are not used in any way that implies The Publisher endorsement of a product or service of an employer, and that the copies are not offered for sale as such. Authors are permitted to grant third party requests for reprinting, republishing or other types of reuse. The Authors may make limited distribution of all or portions of the above Paper prior to publication if they inform The Publisher of the nature and extent of such limited distribution prior there to. Authors retain all proprietary rights in any process, procedure, or article of manufacture described in The Paper. This agreement becomes null and void if and only if the above paper is not accepted and published by The Publisher, or is with drawn by the author(s) before acceptance by the Publisher.