Models have been developed to assess the effectiveness of culling as a tool to eradicate mosquito-borne diseases such as malaria, dengue fever and West Nile virus. Mosquitoes can be culled either at the larval stage using larvicides, or as adults using adulticides sprayed into the atmosphere as fine droplets. Conditions have been found which ensure eradication of the disease, and enable comparisons between the effectiveness of larvicides and adulticides.

Birds, especially crows, play an important role in the spread of West Nile virus. The age structure of birds is important because fledgling birds are more vulnerable to attack by mosquitoes, and models which incorporate this age structure have been developed. The theoretical models can be used to estimate the speed of spread through space of a disease such as West Nile virus. International trade, travel and climate change increase the risk of insect infestations by exotic species. For example the Asian Longhorned Beetle has found its way into the USA and Canada via packing cases used for imports.

Work has been proceeding on the development of mathematical models to help understand the likely temporal and spatial spread of an exotic species. Modelling of invasive species is challenging because the species is outside of its natural environment and existing models for it need not apply or be sufficiently accurate.