Harmonizing epidemic dynamics: A fractional calculus approach to optimal control strategies for cholera transmission

Abstract

Cholera remains a persistent global health challenge, demanding innovative approaches for effective control and mitigation. In this groundbreaking study, I delve into the intricate interplay between mathematical modeling, fractional calculus theory, and optimal control strategies to elucidate the dynamics of cholera transmission and propose evidence-based interventions. My investigation begins by establishing foundational principles of fractional calculus theory, providing a robust framework for analyzing infectious disease dynamics. Through a comprehensive epidemiological model, I delineate the transmission dynamics of cholera, stratifying populations into susceptible, infected, and recovered cohorts. I integrate parameters such as contact rates, mortality rates, and re-susceptibility rates to capture the complexity of cholera dynamics within human and vector populations. Central to my analysis are the derived Caputo fractional differential equations, which elegantly capture the fractional fluctuations inherent in disease propagation. Leveraging mathematical analysis, I demonstrate the positivity and boundedness of solutions, establishing non-negative invariants crucial for understanding disease dynamics. Furthermore, I explore optimal control strategies aimed at mitigating cholera transmission. By introducing vaccination campaigns and prompt treatment modalities, I elucidate their profound impact on susceptible, infected, and recovered populations. My findings underscore the transformative potential of targeted interventions, despite initial observations of counterintuitive trends, such as increases in susceptible populations with intensified control efforts. Through numerical simulations, I provide visual representations of cholera dynamics, offering insights into the temporal evolution of the disease and the effectiveness of control measures. My results demonstrate the efficacy of vaccination campaigns and prompt treatment strategies in curbing cholera incidence, paving the way for evidence-based interventions. In conclusion, my study offers a paradigm shift in understanding and controlling cholera transmission. By integrating mathematical modeling, fractional calculus theory, and optimal control strategies, I provide a comprehensive framework for tackling infectious diseases. This groundbreaking approach holds promise for informing public health policies and mitigating the global burden of cholera and beyond.