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

Jianhong Wu

Università di York

Abstract
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.

Jianhong Wuwu

Jianhong Wu is a Canadian applied mathematician and the founding Director of the Laboratory for Industrial and Applied Mathematics at York University. He holds the lifetime title of University Distinguished Research Professor, and has been a senior Canada Research Chair in Industrial and Applied Mathematics at York University since 2001.

He received his PhD degree from Hunan University in 1987 at age 23, making him the university’s youngest PhD recipient up to that point. He was the recipient of several important awards, among which the NSERC/Sanofi Industrial Research Chair in Vaccine Mathematics, Modelling and Manufacturing and the Canadian Applied and Industrial Mathematical Society’s Research Prize. He also received the Queen Elizabeth II Diamond Jubilee Medal from the Government of Canada in 2012 and was awarded an honorary doctorate by the University of Szeged in 2016. He is a Fields Institute Fellow.

He is recognized for his expertise and contribution in nonlinear dynamics and delay differential equations, neural networks and pattern recognition, mathematical ecology and epidemiology, and big data analytics. He serves or has served as either editor-in-chief or associate editor of various international journals, including Infectious Disease Modelling, Big Data and Information Analytics, SIAM Journal on Applied Mathematics, IEEE Transactions on Pattern Analysis and Machine Intelligence, Journal of Mathematical Biology, and Theoretical Biology and Medical Modelling.