A novel mathematical model and Optimal Control Strategies for Polio Transmission Incorporating Security Challenges and Public Awareness

Poliomyelitis remains a pressing public health concern in endemic regions, particularly in countries like Pakistan, where misinformation, healthcare access barriers, and resistance to vaccination campaigns undermine eradication efforts. This study presents a novel eight-compartment mathematical model incorporating key epidemiological and social dimensions, including virus carriers, partially and fully vaccinated individuals, misinformed populations, and healthcare workers. The model integrates optimal control strategies—vaccination, public awareness campaigns, and protection for health workers—formulated using Pontryagin's Maximum Principle to minimize both infection levels and associated intervention costs. To validate the model's real-world applicability, parameter fitting was performed using observed or assumed epidemiological data. The fitting process achieved high goodness-of-fit metrics (e.g., R 2 = 0.9942, RMSE = 2.09), confirming the model's accuracy in capturing polio dynamics across multiple compartments, including infected, recovered, and virus carriers. Sensitivity analysis highlighted the dominant role of virus carriers and partial vaccination in influencing the basic reproduction number R 0 , while 3D simulations illustrated nonlinear interactions among the control variables. Numerical simulations, implemented via the MATLAB environment, demonstrate that multi-faceted control strategies significantly reduce infection prevalence and improve immunity coverage. This integrated modeling and data-fitting framework offers policymakers a robust, evidence-based tool for designing context-sensitive interventions tailored to high-risk polio-endemic areas.