Estimating the spectrum of the Poincaré map of delay equations with periodic development delays: models, threshold dynamics and vector-borne disease risk prediction

To better understand the effects of seasonal temperature variation and host community composition on vector-borne disease pathogen transmission and spread, we have been developing stage-structured periodic deterministic models (both vector population ecological models dynamics models, and vector–host–pathogen epidemiological models). The models integrate seasonal vector development and activity, multiple host species and complex transmission routes between vectors and hosts. These models can be parameterized by the considered geographical landscape and environmental conditions. We derive algorithms for two basic reproductive ratios relevant to the spectral radius of the Poincaré map of (integral) renewal equations with periodic coefficients, one for the vector and another for disease pathogen, and use these ratios to identify the range expansion fronts of vector populations and vector-borne disease pathogen. These generate the much needed risk prediction maps. To use these algorithms and big data from surveillance for examining the effect of climate warming and host diversity on the pathogen transmission, we call for effective computational and visualization tools in estimating the spectra radius and conducting sensitivity analysis.

The seminar is part of the series “I mercoledì del DMIF”.

Jianhong Wu