Could you please be share more details about what you are looking for exactly? May be you need to build a model/tool using ArcGIS model builder or ArcPy, since there is no such tool readily available (Since you are looking for forecasting/prediction).
These tools might be of use (How ever, I need to know more details about your objective for better help).
1) A optical remote sensing imagery (with Green, Red, NIR, SWIR or TIR bands)
2) Create several vegetation Indices viz, NDVI, NDWI, etc.,
3) create a location file of pest effected areas (point file) with field observation along with dependent variable.
4) Regression (depends on what type of data you have binary or continuous). You need to check about spatial auto-correlation and other details before using the regression equation.
5) And use the equation to identify other locations in the image.
About forecasting you need to be very sure about limitations of regression and details the pest under study.
If you already have past data for insect population for at least 2 or more years one can use Geographically Weighted Regression method in ARCGIS to predict future pest population.
Thank you for the informative answer. The data we plan to use is a point files of previous and current pest and disease incidence together with various meteorological data (Temp, Relative Humidity, Rainfall) which is crucial for the progression of pest and diseases.