Exploring the Dynamics of a Fractional Vector-Host Susceptible-Infected and Susceptible-Infected-recovered Models in Dengue Transmission

Dengue fever continues to pose a serious and persistent threat to public health and remains endemic in more than fifty countries worldwide. The disease is primarily transmitted to humans through the bite of infected Aedes mosquitoes, whose wide geographic distribution, adaptation to urban settings, and sensitivity to climatic variability contribute to sustained outbreaks. Although several prevention measures (such as vector control, environmental management, and community awareness) are widely implemented, dengue transmission remains difficult to suppress due to complex human-vector interactions, heterogeneous exposure, and limitations in controlling mosquito breeding habitats. For these reasons, epidemiological and mathematical modeling has become an essential tool for systematically describing transmission mechanisms, identifying dominant risk determinants, and assessing the expected impact of intervention strategies, thereby supporting evidence-based planning for prevention and control. In this work, we formulate a host-vector mathematical model for dengue virus transmission by coupling a mosquito Susceptible-Infected (SI) subsystem with a human Susceptible-Infected-Recovered (SIR) subsystem. The model captures the exchange of infection between vector and human populations and enables a quantitative investigation of threshold dynamics. In particular, the basic reproduction number R_0 is derived using the next-generation matrix technique, providing a key threshold quantity that characterizes whether an initial infection can invade the population. We then analyze the stability properties of the equilibria: the local stability analysis shows that the disease-free equilibrium is asymptotically stable when R_0<1 , implying eventual elimination of dengue, whereas dengue persists and an endemic equilibrium may arise when R_0>1 . Furthermore, global stability results are established using a suitable Lyapunov function, which strengthens the conclusions beyond local behavior. To validate the theoretical outcomes and to explore the effect of the principal parameters that promote or mitigate dengue spread, numerical simulations are carried out in MATLAB for the relevant compartments. These simulations illustrate the temporal evolution of the human and mosquito populations under different epidemiological scenarios and parameter settings. In addition, sensitivity analysis is performed to quantify how variations in model parameters influence R_0 and the overall transmission dynamics. This analysis highlights the most influential factors and provides insight into which control measures (e.g., reducing mosquito biting rate, lowering vector density, or increasing recovery) may be most effective for limiting dengue transmission.