Once bitten, twice shy: A modeling framework for incorporating heterogeneous mosquito biting into transmission models

The risk of mosquito-borne disease outbreaks is tightly linked to the frequency at which mosquitoes feed on blood, also known as the biting rate. However, standard models of mosquito-borne disease transmission inherently assume that mosquitoes bite only once per reproductive cycle -- an assumption commonly violated in nature. Drivers of multiple biting also affect the mosquito gonotrophic cycle duration (GCD), the quantity customarily used to estimate biting rates. Here, we present a novel framework for incorporating more complex mosquito biting behaviors into transmission models, accounting for heterogeneity and linkages between mosquito biting rates and multiple biting. We provide general formulas for the basic offspring number, $\mathcal{N}_0$, and basic reproduction number, $\mathcal{R}_0$, threshold measures for mosquito population and pathogen transmission persistence, respectively. To exhibit its flexibility, we expand on specific models derived from the framework that arise from empirical, phenomenological, or mechanistic modeling perspectives. Using the gonotrophic cycle duration as a standard quantity to make comparisons among the models, we show that assumptions about the biting process strongly affect the relationship between GCD and $\mathcal{R}_0$. While under the standard assumption of one bite per reproductive cycle, $\mathcal{R}_0$ is an increasing linear function of the inverse of the GCD, alternative models of the biting process can exhibit saturating or concave relationships. Critically, from a mechanistic perspective, decreases in the GCD can lead to substantial decreases in $\mathcal{R}_0$. This work highlights the importance of incorporating the behavioral dynamics of mosquitoes into transmission models and provides a method for evaluating how individual-level interventions against mosquito biting scale up to determine population-level mosquito-borne disease risk.