A new population model for urban infestations

Abstract

The spread of rodents and insects in cities, in particular in summer periods, poses significant health, economic, social and environmental threats. The analysis of incidence and identification of seasonal and weather determinants are crucial for addressing intervention strategies. In this context, we investigate the occurrence of rats and cockroaches infestations in the city of Madrid, Spain, with differential equation models. Birth–death fluxes, sine–cosine waves and temperature conform the mechanistic nature of the models. Available data on citizen-reported sightings from 2010 until 2013 are fitted by parameter calibration and uncertain-error measurement. Numerical simulations show that the time series are adequately explained by the proposed models. This strongly suggests that the models can be used to predict future infestation dynamics, which can guide health policy measures.