A multi-strain sequential super-infection model for dengue fever with antibody dependent enhancement

Dengue fever is a vector-borne disease that is transmitted by the aedes aegypti mosquito. The disease is caused by four different viral serotypes which are DEN-1, DEN-2, DEN-3, and DEN-4. Of these serotypes, DEN-1 and DEN-2 are the most prevalent, and their co-circulation presents complex disease dynamics due to the antibody-dependent enhancement (ADE) phenomenon as well as the cross-immunity interaction of these viral serotypes. In this study, we formulate a novel multi-strain sequential super-infection model that captures the primary and secondary infection dynamics with temporary cross immunity, asymptomatic infections, and enhancement in disease transmissibility due to antibody-dependent enhancement (ADE) upon heterologous reinfection. Our analyses revealed that significant secondary infections cause a backward bifurcation phenomena due to changes in the biting rate $ b $, which maintains disease endemicity when the basic reproduction number is below unity. The implications of this phenomena are that intervention measures would need to target a critical threshold of $ \mathcal{R}_{0} $ associated with $ b_c $, below which we are assured of disease elimination. Numerical analysis showed that the values of $ b_{c} $ are highly influenced by changes in the ADE. Thus effective control of dengue fever requires intensified and sustained control methods that drive transmission below critical thresholds. The findings of this study shed light on critical insights in the design and implementation of eradication measures in dengue fever endemic regions.