This study investigates a mathematical model of dengue virus transmission, focusing on the virus’s impact on humans and mosquitoes. The model classifies the entire population into seven categories: susceptible humans \(\mathcal {S}_h(t)\) , exposed humans \(\mathcal {E}_h(t)\) , infected humans \(\mathcal {I}_h(t)\) , recovered humans \(\mathcal {R}_h(t)\) , susceptible mosquitoes \(\mathcal {S}_m(t)\) , exposed mosquitoes \(\mathcal {E}_m(t)\) , and infected mosquitoes \(\mathcal {I}_m(t)\) . In this extended model, we reformulated the classical dengue transmission system using Caputo’s fractional derivative, resulting in a system of seven fractional-order differential equations. To investigate the influence of memory effects on disease progression, we solved the fractional model using the extended Euler method, whereas the classical model was analyzed using both the fourth-order Runge-Kutta (RK4) method and the Tamimi-Ansari method (TAM). Comparative analysis shows that as the fractional order approaches one, the results converge with those obtained from the classical methods, confirming the accuracy and consistency of the proposed methods. We also investigated the behavior of the model’s various compartments by altering the sensitive parameters. This study provides unique insights into the response of dengue transmission under diverse situations, revealing the potential of emerging classical and fractional approaches for investigating epidemiological models of infectious diseases, which will be extremely useful for researchers in this area.
