Schedule of the mini-symposium

13:30-13:40 Opening remarks

13:40-14:10 Qi Li, Qualitative Study on The Multistable Reaction-Diffffusion Equation

14:10-14:40 Mengyun Zhang, The diffusion dynamics of Aedes aegypti mosquito in a heterogeneous environment

15:00-15:30 Jing Ge, The spatial-temporal risk index and spreading dynamics for a time-periodic diﬀusive West Nile virus model

15:30-16:00 Wenze Li, Temporal and Spatial Predictive Modelling of Mosquito Abundance and risk of human infection of West Nile virus in GTA

16:00-16:30 Goutam Saha, Environmental Effects on the Movement of Aedes Mosquitoes Affecting Dengue Prevalence

16:30-17:00 Huaiping Zhu, Some notes on modeling of spatial dispersion of single species and spreading of infectious diseases

Titles and abstracts:

Title: Qualitative Study on The Multistable Reaction-Diffffusion Equation

Speaker: Qi Li

School of Science, Shanghai Normal University, China

Abstract: In this talk, we consider the Cauchy problem of reaction diffusion equation with multistable nonlinearity in one dimensional case. First, we use the phase plane method to draw seventeen phase diagrams, which fully depict the equilibrium solution and traveling wave solution of the correlation equation. Then for this problem, we discuss the asymptotic behavior of non-negative bounded solutions and prove that they converge to a specific equilibrium solution. It is a joint work with Pengchao Lai and Bendong Lou.

Title: The diffusion dynamics of Aedes aegypti mosquito in a heterogeneous environment

Speaker: Mengyun Zhang

School of Mathematical Science, Yangzhou University, China

Abstract: A reaction-diffusion-advection model is proposed and investigated to understand the diffusion dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the mosquitoes in a heterogeneous environment. The threshold $R^D_0$ for the model with Dirichlet boundary condition is defined and the threshold $R^F_0(t)$ for the free boundary problem is introduced, with the long-time behavior of positive solutions to the reaction-diffusion-advection system discussed. Sufficient conditions for the mosquitoes to be eradicated or to spread are given. We show that, if $R^F_0(\infty)\leq 1$, the mosquitoes vanish eventually, and if $R^F_0(t_0)\geq 1$ for some $t_0\geq 0$, the mosquitoes must spread, while if $R^F_0(0)<1<R^F_0(\infty)$, the spreading or vanishing of the mosquitoes depends on the initial number of mosquitoes, or mosquitoes' expanding ability on the free boundary. Moreover, numerical simulations indicate that the advection and the expanding capability affect the mosquitoes' diffusion fronts.

Title: The spatial-temporal risk index and spreading dynamics for a time-periodic diﬀusive West Nile virus model

Speaker: Jing Ge

School of Mathematics and Statistics, Huaiyin Normal University, China

Abstract: In this talk, we will concern with a simpliﬁed epidemic model for West Nile virus in a heterogeneous time-periodic environment. By means of the model, we will explore the impact of spatial heterogeneity of environment and temporal periodicity on the persistence and eradication of West Nile virus. The free boundary is employed to represent the moving front of the infected region. The basic reproduction number R0D and the spatial-temporal risk index R0F(t), which depend on spatial heterogeneity, temporal periodicity and spatial diﬀusion, are deﬁned by considering the associated linearized eigenvalue problem. Suﬃcient conditions for the spreading and vanishing of West Nile virus are presented for the spatial dynamics of the virus. This is joint work with Prof. Zhigui Lin and Prof. Huaiping Zhu.

Title: Temporal and Spatial Predictive Modelling of Mosquito Abundance and risk of human infection of West Nile virus in GTA

Speaker: Wenzhe Li

LAMPS, Department of Mathematics and Statistics, York University, Canada

Abstract: Emerging and re-emerging mosquito-borne infectious diseases have drawn greater attention in recent years worldwide, e.g. West Nile virus (WNV), dengue fever and Zika virus. We focus on WNV in Greater Toronto Area (GTA). As vectors for WNV, the culex mosquitoes and their abundance are sensitive to both weather conditions and landscape. In this study, we establish predictive models for mosquito abundance and risk of WNV with all of these factors. Using the surveillance data from 5 regions of GTA, we first define local modeling regions with the census tracts as units for each region, then the predictive models are built on these modeling units for the forecasting of culex mosquito abundance and risk of human infection of WNV in GTA