Mathematical Models for Enhancing Humanitarian Aid in Road Accidents: A Comprehensive Literature Review

Road accidents are a source of enormous human, social, and financial losses in general, and in particular, swift and effective response mechanisms are needed to reduce loss of lives and enhance the recovery rates. Mathematical modeling, including optimization, stochastic, fuzzy and especially feedback-based System Dynamics techniques, provides potent data driven tools to enhance the speed, precision and fairness of humanitarian assistance allocation. The study provides an in-depth analysis of the application of these models to tailor the post-accident humanitarian plans and outlines the key factors that influence their outcomes, which are questionable. System Dynamics in particular is unique in that it modelled the nonlinear feedback structures, delays and interdependencies of the road accident systems including the interactions between traffic volume, driver behaviour, weather, and emergency response capacity. As opposed to the static optimization models which give one-off solutions, SD can be used to simulate changes in system behavior with time and can be used to explore what-if scenarios to identify unintended consequences. Combination of SD and stochastic optimization or AI-driven decision-making can as well make models more robust, incorporating uncertainty management with feedback systems, which lead to big changes in the efficiency of resource allocation and triage prioritization as well as the reduction of reaction time. These combined models prove to be useful in real-world decision support, such as emergency vehicle routes, hotspots detection, and proactive preventative policy construction. The databases of Scopus and Web of Science were properly searched according to PICOS and PRISMA criteria to define the inclusion criteria. The survey was principally centered on peer-reviewed studies in road-accident situations. Evaluation of studies was based on the type of data (stochastic, deterministic, fuzzy), modeling techniques (exact vs. heuristic), and the ability to deal with uncertainty, sensitivity analysis, and dynamic decision-making capabilities, with special consideration given to System Dynamics as a tool to document the nonlinear feedbacks, delays, and causal relationships. The review indicates a clear trend towards predictive emerging technologies such as IoT, machine learning, and fog computing; analytics and adaptive algorithms are all more effective than the fixed ones in time-sensitive settings and contribute to the quality and speed of response. Besides, the synthesis of the reviewed literature demonstrates the definite research gaps and future directions. The current models have the habit of addressing single constituents of the accident response and in most cases do not consider the interrelationships of the pre-crash prevention, real-time emergency management and post-crash recovery. Future studies are needed to tie up these silos by constructing comprehensive SD-based frameworks that encompass end to end system behavior and operational decision-making that are congruent to the strategic policy objectives. Secondly, integrating SD with real-time sensor information, predictive forecasting via machine learning, and resource planning via robust optimization will make available adaptive and self-improving humanitarian aid systems, learning and updating with the arrival of new data. These developments can change existing reactive strategies to proactive, resilience-based strategies that have the potential to save more lives and reduce the long-term social and economic consequences. The findings emphasize the ability of such a radical approach to the integration of System Dynamics and mathematical modeling to change resource allocation, reduce the response time, and enhance strategic planning. The evidence-based, flexible, and feedback-based humanitarian help will make evidence-based, flexible, and resilient science-driven emergency response systems possible.