Beyond the biting - limited impact of explicit mosquito dynamics in dengue models

Mathematical models play a crucial role in assisting public health authorities in timely disease control decision-making. For vector-borne diseases, integrating host and vector dynamics into models can be highly complex, particularly due to limited data availability, making system validation challenging. In this study, two compartmental models akin to the SIR type were developed to characterize vector-borne infectious disease dynamics. Motivated by dengue fever epidemiology, the models varied in their treatment of vector dynamics, one with implicit vector dynamics and the other explicitly modeling mosquito-host contact. Both considered temporary immunity after primary infection and disease enhancement in secondary infection, analogous to the temporary cross-immunity and the Antibody-dependent enhancement biological processes observed in dengue epidemiology. Qualitative analysis using bifurcation theory and numerical experiments revealed that the immunity period and disease enhancement outweighed the impact of explicit vector dynamics. Both models demonstrated similar bifurcation structures, indicating that explicit vector dynamics are only justified when assessing the effects of vector control methods. Otherwise, the extra equations are irrelevant, as both systems display similar dynamics scenarios. The study underscores the importance of using simple models for mathematical analysis, initiating crucial discussions among the modeling community in vector-borne diseases.