A FRACTIONAL-ORDER MATHEMATICAL MODEL OF DENGUE TRANSMISSION INCORPORATING CLIMATE VARIABILITY AND VECTOR-CONTROL INTERVENTIONS IN PAKISTAN

Abstract

Dengue transmission in Pakistan is influenced by climatic variability, mosquito ecology, and the effectiveness of vector-control interventions. This study developed a climate-sensitive fractional-order mathematical framework to examine dengue transmission dynamics across selected dengue-endemic cities in Pakistan. The model incorporated susceptible, exposed, infectious, and recovered human populations alongside susceptible, exposed, and infectious mosquito populations. Temperature, rainfall, and relative humidity were incorporated as climate-dependent factors influencing mosquito development, survival, biting activity, and transmission. A Caputo fractional derivative was employed to represent potential memory effects, while a conventional integer-order model provided a comparative benchmark. The analytical framework included reproduction-number estimation, equilibrium and stability analysis, parameter sensitivity, and numerical simulations of individual and combined vector-control strategies. Model performance was designed to be evaluated through goodness-of-fit measures and out-of-sample predictive validation using dengue surveillance and meteorological data. The proposed framework provides a basis for investigating climate-sensitive transmission patterns and evaluating targeted intervention strategies. Its empirical effectiveness and the potential predictive advantage of fractional-order modelling require confirmation using verified Pakistan-specific data.