FRACTIONAL-ORDER MATHEMATICAL MODELING OF CLIMATE-DRIVEN VECTOR-BORNE DISEASE DYNAMICS IN PAKISTAN

Abstract

Climate change is altering the environmental conditions that influence vector-borne disease transmission, creating major public-health challenges in climate-sensitive settings such as Pakistan. This study proposes a fractional-order mathematical model for climate-driven dengue transmission by integrating human–vector dynamics, climatic variability, and temporal memory. Temperature, rainfall, and relative humidity are incorporated into biologically meaningful transmission and vector parameters, while a Caputo fractional derivative represents nonlocal temporal dependence. The framework includes model calibration, equilibrium and stability analysis, the basic reproduction number (R₀), sensitivity and uncertainty analysis, validation, comparison with an equivalent integer-order model, and climate and intervention scenario simulations. The approach is intended to identify climate-sensitive transmission mechanisms and assess whether fractional dynamics improve empirical representation and prediction. The framework may support climate-informed surveillance, early-warning systems, and targeted vector-control planning in Pakistan. Because the supplied manuscript does not contain finalized empirical estimates or model outputs, numerical findings and hypothesis decisions remain placeholders and should be completed only after the dataset and simulations are finalized.