Every epidemiological model contains an assumption regarding the relationship between host contact rates and host density, where the two most common assumptions are that contact rates increase linearly with density (dependent-dependent transmission) or that contact rates are independent of density (frequency-dependent transmission). But in many systems, these two canonical functions are outperformed by nonlinear transmission functions, suggesting that nonlinear functions are under-utilized by ecologists. Ecologists might be reluctant to use nonlinear functions because the existing options are predominantly phenomenological, with parameters that do not have obvious biological interpretations. Therefore, we tested the epidemiological utility of a mechanistic contact rate function, the Holling Type II functional response, which has been used extensively in dynamic predator-prey models. In particular, we first used field transmission experiments with sentinel hosts to determine whether nonlinear transmission functions were appropriate in a system where symbiotic oligochaetes are directly-transmitted among snail hosts. We then used laboratory contact rate experiments to quantify the relationship between snail contact rates and snail density, focusing specifically on how well a Holling Type II functional response could describe the observed contact function.
Results/Conclusions
Even in this relatively simple system, transmission rates were nonlinear functions of host density in the field, and host contact rates saturated with host density in our laboratory experiment. In particular, snail contact rates saturated at high snail densities because each contact required a time investment, and snails had finite time for contacts. The observed nonlinear contact function was well-described by a Holling Type II functional response, and the best-fitting model provided a reasonable estimation of the known duration of an average snail contact (97 seconds), suggesting that this function is biologically appropriate for our snail-symbiont system. Because handling times can be independently estimated for the Holling Type II functional response, we found this nonlinear function particularly easy to use and interpret. Additionally, this simple mechanistic function might be broadly applicable to epidemiological models because host contacts in many other systems should involve handling times. Therefore, as ecologists work to increase descriptive and predictive accuracy of epidemiological models, we recommend considering the utility of the Holling Type II functional response as a transmission function.