FRACTIONAL-ORDER MATHEMATICAL MODELING OF INFECTIOUS DISEASE DYNAMICS WITH OPTIMAL CONTROL STRATEGIES FOR RESOURCE-LIMITED SETTINGS IN PAKISTAN

Abstract

Infectious diseases continue to pose significant public health challenges in Pakistan, where limited healthcare resources often hinder timely and effective epidemic response. Conventional integer-order epidemiological models frequently fail to capture the memory-dependent characteristics of disease transmission, resulting in reduced predictive accuracy. This study developed a fractional-order mathematical model integrated with optimal control strategies to analyze infectious disease dynamics in resource-limited healthcare settings in Pakistan. The proposed model employed a system of fractional differential equations based on the Caputo derivative to describe disease transmission while incorporating optimal intervention measures, including vaccination, treatment, isolation, and public awareness campaigns. Model stability was examined through equilibrium and basic reproduction number (R₀) analyses, while sensitivity analysis identified the most influential epidemiological parameters. Numerical simulations demonstrated that the fractional-order model provided superior predictive performance compared with conventional integer-order models by effectively accounting for memory effects in disease progression. The results further indicated that integrated optimal control strategies substantially reduced disease transmission, lowered the basic reproduction number below the epidemic threshold, and improved healthcare resource utilization. The findings highlight the potential of fractional-order mathematical modeling as a robust decision-support tool for optimizing infectious disease control policies and strengthening epidemic preparedness in Pakistan. The proposed framework offers valuable theoretical and practical contributions to mathematical epidemiology and supports evidence-based public health planning in resource-constrained environments.