Fractional order modeling of dengue transmission dynamics in Bangladesh

Abstract

Over the past three decades, the epidemiological characteristics of dengue fever in Bangladesh have raised significant public health concerns, with the disease progressively spreading across the country’s subtropical and tropical regions since 2004. This study introduces a fractional-order mathematical model that incorporates both human and mosquito populations using Caputo derivatives to account for memory and hereditary effects in disease transmission. Analytical solutions are approximated using the Laplace–Adomian decomposition method, while the Adams–Bashforth-Moulton predictor–corrector (PECE) scheme is applied for numerical solutions. Model parameters are estimated via the maximum likelihood method, using dengue case data from Bangladesh (June 1, 2022–September 30, 2022). Our findings indicate that the fractional-order model effectively captures a range of transmission scenarios, with lower derivative orders correlating with reduced outbreak severity. Moreover, numerical solutions exhibit higher accuracy compared to analytical approximations, particularly for complex nonlinear systems. Additionally, the results suggest that controlling mosquito populations, reducing transmission rates, and improving treatment measures are critical strategies for dengue mitigation.