Mathematical Modelling of Real-World Problems

Abstract

Mathematical modeling has become one of the most influential interdisciplinary methods of understanding, analyzing, 
predicting, and optimizing various phenomena of reality. Today, complex, uncertain, interdependent, and dynamic 
features mark most social, economic, environmental, industrial, technological, and biological systems. This means 
that people can no longer make decisions based solely on intuition. Use of mathematical modeling allows for the 
transformation of phenomena of reality into mathematical models that include variables, parameters, equations, 
inequalities, functions, probability distributions, and optimization criteria, thus providing one with clear guidelines 
for understanding, analyzing, predicting and optimizing real-world phenomena. The current paper discusses the 
principles, methods, and applications of mathematical modeling in solving real-world problems and the importance 
of the process of problem definition, abstraction, assumption-making, variable selection, mathematical modeling, 
parameter estimation. The methodology used in the research is analytical and conceptual to analyze the relevant 
problems in transportation, population growth, epidemic dynamics, environmental management, agriculture, 
business, finance, education, and supply-chain systems. Datasets that are hypothetical in nature were produced in 
order to show how deterministic, statistical, differential equations, and optimization models should be used and 
interpreted. It was concluded in this article that mathematical modeling must be viewed not as one mathematical case 
but as a process giving rise to several mathematical formulations. The connection between mathematical modeling 
and computational methods, data analysis, and interdisciplinary knowledge can improve forecasting, resource 
allocation, risk assessment, and policy making.