Unstable Dynamics of Vector-Borne Diseases: Modeling Through Delay-Differential Equations

Vector-borne diseases provide unique challenges to public health because the epidemiology is so closely tied to external environmental factors such as climate, landscape, and population migration, as well as the complicated biology of vectortransmitted pathogens. In particular, this close link between the epidemiology, the environment, and pathogen biology means that the traditional view that many vector-borne diseases are relatively stable in numerous regions does not provide a complete picture of their complexity. In fact, several regions exist with low levels of endemicity most of the time, punctuated by severe, often explosive, epidemics. These regions are considered unstable transmission settings. Ordinary differential equation (ODE) models have thus far dominated the study of vector-borne disease and have provided considerable insight into our understanding of transmission and effective control in stable transmission settings. To address the short-comings of autonomous ODE models, we present a class of models, differential-delay equation (DDE) models, that have the potential to better describe unstable endemic settings for vector-borne disease. These models develop naturally out of the biology ∗Corresponding author.