Dynamical Effects of Homologous Reinfections in a Multi-Strain Dengue Model

Dengue transmission is shaped by multiple viral serotypes, temporary cross-immunity (TCI), antibody-dependent enhancement (ADE), and repeated exposure in endemic populations. Classical multi-strain models usually assume lifelong protection against reinfection with the same serotype. However, recent evidence suggests that homologous dengue reinfections, although rare, can occur. Their population-level consequences remain poorly understood. We extend a two-infection, two-strain dengue model with TCI and ADE-mediated transmission differences to include homologous reinfections. Homologous reinfection is represented by two exploratory parameters: relative susceptibility to reinfection with the same serotype and relative infectiousness during homologous reinfection. Using equilibrium analysis, bifurcation diagrams, simulations, and phase-space projections, we examine how these parameters affect dengue dynamics and interact with TCI duration and seasonal forcing under intermediate and long TCI durations, with and without seasonality. The extended model shows that qualitative dynamics characteristic of endemic dengue transmission are reproduced mainly when susceptibility to homologous reinfection is low, so that homologous reinfections remain rare but dynamically influential. Longer TCI broadens regions of complex oscillatory dynamics, while seasonality shifts the bifurcation structure and makes torus bifurcations a central route to complex behavior. Although backward bifurcation can occur when homologous susceptibility exceeds the biologically meaningful range, this result should be interpreted as a mathematical mechanism rather than a realistic dengue scenario. These results indicate that rare homologous reinfection pathways can influence long-term dengue dynamics when interacting with immune history, TCI, ADE-mediated transmission differences, and seasonal variation. Incorporating such pathways may improve understanding of recurrent outbreaks and irregular incidence patterns in highly exposed populations.