A Mathematical Model to Assess the Impact of Tourism Activities on the Economy of Vendors at Bukit Maras, Terengganu, Malaysia

Ummu Atiqah Mohd Roslan; Muhamad Fairus Noor Hassim; Siti Marsila Mhd Ruslan

doi:10.11113/mjfas.v20n1.2885

Authors

Ummu Atiqah Mohd Roslan ᵃSpecial Interest Group of Modelling and Data Analytics (SIGMDA), Faculty of Computer Science and Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia; ᵇInstitute of Oceanography and Environment, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
Muhamad Fairus Noor Hassim Biological Security and Sustainability (BIOSES) Research Group, Faculty of Science and Marine Environment, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia
Siti Marsila Mhd Ruslan Faculty of Maritime Studies, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, Malaysia

DOI:

https://doi.org/10.11113/mjfas.v20n1.2885

Keywords:

Mathematical model, ordinary differential equation, tourism, economy

Abstract

Bukit Maras is one of the recreational spots that has been identified as having great potential to be promoted as a tourist destination in Terengganu. In this study, it is intriguing to see the whether the tourism activities that occurred at Bukit Maras have a positive impact on the economic activity of the local vendors from the point of view of mathematical modelling. The objective of this paper is to formulate a mathematical model in the form of ordinary differential equations (ODEs), inspired by the concept of symbiosis interaction in ecology. Further, some mathematical analyses of this model such as finding the steady states and their stability, were also proved. In addition, some numerical simulations are performed using Maple software to produce the plots of time series as well as phase portraits. To prove the positive impact of the presence of tourists on the economics of vendors, a parameter called the spending rate by the tourists was varied. The results showed that as the spending rate increased, it was expected that the number of vendors would increase too. This indicated that the economics of the vendors have improved. Moreover, it is also predicted that the number of tourists will continuously increase in the future, provided that the attractiveness factors of the Bukit Maras are well preserved. These results are significant for the local government to provide more funding for the development of Bukit Maras so that both tourists and vendors can be sustained in the future.

References

Mohd Roslan, U. A., Mohd Radzi, M. N. F., Mhd Ruslan, S. M., Noor Hassim, M. F., Mohd A. Wahid, M. I. & Ahmad, A. (2021). Proximity matrix analysis for a study on the impact of tourism activity on the economic of vendors at Bukit Maras, Terengganu, Malaysia. AIP Conference Proceedings, 2138(41649), 1-6.

Casagrandi, R. & Rinaldi, S. (2002). A theoretical approach to tourism sustainability. Conservation Ecology, 6(1), 1-13.

Johnston, R. J. & Tyrrell, T. J. (2005). A dynamic model of sustainable tourism. Journal of Travel Research, 44, 124-134.

Johnston, R. J. & Tyrrell, T. J. (2007). Sustainability and tourism dynamics. In A. Woodside & D. Martin (Eds.), Tourism Management: Analysis, Behaviour and Strategy (Chapter 26). CABI.

Sinay, L. and Sinay, L. (2006). A simple mathematical model for the effects of the growth of tourism on environment. New Perspectives and Values in World Tourism & Tourism Management in the Future, Turkey, November 2006.

Kaslik, E. & Neamtu, M. (2020). Dynamics of a tourism sustainability model with distributed delay. Chaos, Solitons and Fractals, 133(109610), 1-9.

Liu, J., An, K., & Jang, S. C. (Shawn). (2020). A model of tourists’ civilized behaviors: Toward sustainable coastal tourism in China. Journal of Destination Marketing and Management, 16(April), 1-10.

Dimitrovski, D., Lemmetyinen, A., Nieminen, L., & Pohjola, T. (2021). Understanding coastal and marine tourism sustainability - A multi-stakeholder analysis. Journal of Destination Marketing and Management, 19(January), 1-12.

Nguyen, T. Q. T., Young, T., Johnson, P., & Wearing, S. (2019). Conceptualising networks in sustainable tourism development. Tourism Management Perspectives, 32(September), 1-11.

Nesticò, A., & Maselli, G. (2020). Sustainability indicators for the economic evaluation of tourism investments on islands. Journal of Cleaner Production, 248, 1-24.

Zha, J., Dai, J., Xu, H., Zhao, C., Tan, T., & Li, Z. (2021). Assessing efficiency and determinants of tourist attractions based on a two-subprocess perspective: A case of Chengdu, southwestern China. Journal of Destination Marketing and Management, 19(October 2020), 1-16.

Pulido-Fernández J. I., Cárdenas-García, P. J., & Espinosa-Pulido, J. A. (2019). Does environmental sustainability contribute to tourism growth? An analysis at the country level. Journal of Cleaner Production, 213, 309-319.

Sambasiavm, M. (2013). Dynamical behavior of logistic equation through symbiosis model. International Journal of Scientific and Research Publications, 3(6), 1-6.

Zhu, Z., Wu, R., Chen, F. & Li, Z. (2019). Dynamic behaviors of a Lotka-Volterra commensal symbiosis model with non-selective Michelis-Menten type harvesting. International Journal of Applied Mathematics, 50(2), 1-9.

Kooi, B. W., Kuijper, L. D. J. & Kooijman, S. A. L. M. (2004). Consequences of symbiosis for food web dynamics. Mathematical Biology, 49, 227-271.

Lynch, S. (2014). Dynamical Systems with Applications using MATLAB. Switzerland: Springer.

Lim, K. C., Ramli, K. I., Yusof, N. S., & Cheah, S. T. (2015). Examining young Malaysians travel behaviour and expenditure patterns in domestic tourism. Asian Social Science, 11(9), 77-88.