With the recent surge in arboviruses throughout North America, mosquitoes have become more than a nuisance; they have become a serious health risk. Understanding the population biology of these disease vectors at both small and large scales (single and multiple populations) will be crucial to effectively assessing the risk of outbreak for diseases such as West Nile virus, Dengue Fever, Eastern Equine Encephalitis, Saint Louis Encephalitis, and Yellow Fever. Current mathematical models of mosquito population dynamics are only applicable at the scale for which they were built because environmental feedback factors driving processes at one scale may be of little importance at another. Furthermore, nonlinear processes and spatial variation within and among local populations prevent simple proportional scaling. Scale transition is a developing ecological theory that attempts to link small-scale and large-scale processes by incorporating environmental feedback mechanisms at multiple scales, and by providing a mathematical framework to account for nonlinear processes. This investigation expands the mathematical framework for traditional scale transition theory to the multivariate realm and applies it to a model of mosquito population dynamics.
Results/Conclusions
We have derived a multivariate scale transition term using a multivariate Taylor expansion to predict average future regional population density as a function of current local population densities and temperatures. We then incorporated this scale transition term into a mosquito population model where the larval stage population growth is density dependent. We solve previous problems associated with continuous approximation of stiff functions (using Euler’s method) by calculating changes in population density over short time intervals (0.05 days). Future work will involve testing the model against mosquito population data gathered by the Missouri Department of Health and Senior Services and discussing how these findings might influence current mosquito control strategies. A better understanding of scale transition will potentially allow health managers to better assess regional risk of arboviral disease transmission from local dynamics, and to coordinate management strategies among local agencies accordingly. Furthermore, multivariate scale transition should have broader applications to many other population questions with similar scaling challenges.
