Abstract:
Bangladesh is one of the most overcrowded and densely populated countries globally. Thus, in recent years, the population problem has been a great concern of the policymakers of Bangladesh. For the development and progress of the country, it would be crucial to perceive and estimate the increasing trend of the population. This research work principally focuses on the analysis through data fitting using the nonlinear least square curve fitting method and forecast of the future population growth of the country by considering mathematical methods. Available actual and adjusted census data (1974-2022) of Bangladesh population applied in the well-known autonomous logistic population growth model and fund that all data sets of logistic (exact), deterministic (Adam-Bashforths-Multon predictor-corrector (PECE) method), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach, and logistic multi-scaling approximation fits with a good agreement. Again the existence and uniqueness of the solution for deterministic and fractional-order and Hyers-Ulam stability have been studied. Generally, the growth rate and carrying capacity of the population of any country slowly fluctuate with time. This analysis provides several advantages to assessing an approximate closed-form of straightforward solutions, as most previous studies conducted with population models of single species employed constant growth rates and carrying capacity, and no fractional-order method is studied. Finally, our projection adheres with an excellent agreement to the estimate (2012-2061) of the Bangladesh Ministry of Planning and Bureau of Statistics (BBS). Thus, we bank on the findings of this research work will assist in successful population forecast and planning, development, and progression of the nation.
