FRACTIONAL-ORDER DENGUE VIRUS MODEL WITH VECTOR AND NON-VECTOR TRANSMISSION: BIFURCATION ANALYSIS AND MEMORY EFFECTS

Abstract

Dengue fever, a major mosquito-borne disease, poses significant global health challenges, particularly in tropical and subtropical regions. Traditional epidemiological models often fail to capture the memory-dependent dynamics and complexities of disease transmission, limiting their effectiveness in informing public health strategies. This study introduces a novel fractional-order dengue transmission model using the Caputo fractional derivative to incorporate memory effects. The model considers both vector and non-vector transmission pathways, along with mosquito-to-mosquito transmission. The basic reproduction number  was derived using the next-generation matrix method. Stability analyses were performed to explore the conditions under which backward bifurcation occurs, with a particular focus on the influence of mosquito-to-mosquito transmission dynamics. Stability analysis revealed that backward bifurcation arises when the reproduction number associated with mosquito-to-mosquito transmission exceeds one, highlighting its critical role in dengue dynamics. Numerical simulations demonstrated that fractional-order models effectively delay epidemic peaks and extend the transition period of exposed populations, providing extended windows for timely interventions. Sensitivity analysis identified mosquito-to-human and mosquito-to-mosquito transmission rates as key drivers of  emphasizing the need for targeted control measures, including vector control and vaccination campaigns. This study demonstrates that fractional-order models are superior to traditional integer-order models in capturing the complex dynamics of dengue transmission. By integrating memory effects and analyzing critical transmission pathways, the model offers a more realistic framework for understanding dengue spread. These findings provide valuable insights for optimizing public health interventions, emphasizing the transformative potential of fractional-order models in sustainable dengue control and future research.