Dengue infection results in a significant number of deaths, mostly in the tropical and subtropical regions across the world. Yet, despite the seriousness of this disease, vaccine, and antiviral drugs that could be employed in dengue treatment remain elusive. The desire to establish the factors determining the disease severity and the growing need for efficient drugs has prompted extensive research interest in within-host viral dynamics. However, very few mathematical models of within-host dengue dynamics pertaining to secondary dengue infection with another serotype are presently available. To address this gap in the pertinent literature, in this work, a secondary dengue infection model with T-cell mediated adaptive immunity and antibody-dependent enhancement was developed by considering the memory cell and heterogeneous antibody as the main factor. In particular, the explicit role of cytokines is considered for both virus and infected cell clearance, along with both extrinsic and intrinsic mechanisms for antibody-dependent enhancement. In case of secondary dengue infection, both the virus and homogeneous antibody production are enhanced due to the influence of memory cells remaining from the previous (primary) dengue infection. Owing to the high model sensitivity, it was possible to establish that, among antibody-dependent enhancement mechanisms, the increased virus replication inside the infected cell, which increases the overall virus burst size, exerts the maximum effect on disease severity during secondary infection. Moreover, the role of initial memory cell concentrations and half-saturation constant in the secretion of memory cell in the disease severity was studied. The obtained results concur with the clinical observations and may be helpful in further research on antibody-dependent enhancements aimed at producing schemes relevant for the dengue vaccine design and development.