Free boundary models for mosquito range movement driven by climate warming

Abstract

As vectors, mosquitoes transmit numerous mosquito-borne diseases. Among the many factors affecting the distribution and density of mosquitoes, climate change and warming have been increasingly recognized as major ones. In this paper, we make use of three diffusive logistic models with free boundary in one space dimension to explore the impact of climate warming on the movement of mosquito range. First, a general model incorporating temperature change with location and time is introduced. In order to gain insights of the model, a simplified version of the model with the change of temperature depending only on location is analyzed theoretically, for which the dynamical behavior is completely determined and presented. The general model can be modified into a more realistic one of seasonal succession type, to take into account of the seasonal changes of mosquito movements during each year, where the general model applies only for the time period of the warm seasons of the year, and during the cold season, the mosquito range is fixed and the population is assumed to be in a hibernating status. For both the general model and the seasonal succession model, our numerical simulations indicate that the long-time dynamical behavior is qualitatively similar to the simplified model, and the effect of climate warming on the movement of mosquitoes can be easily captured. Moreover, our analysis reveals that hibernating enhances the chances of survival and successful spreading of the mosquitoes, but it slows down the spreading speed.

Semi-infinite travelling waves arising in a general reaction–diffusion Stefan model

“…One particular reaction-diffusion modelling framework giving rise to semi-infinite travelling waves over a range of wavespeeds is via the incorporation of a moving boundary [8][9][10][11]24], whereby x ∈ (−∞, L(t)] and L(t) evolves based on a Stefan-like condition at the edge of travelling wave. For particular choices of linear [8][9][10]24] and degenerate diffusivities [11], D(u), semi-infinite travelling waves exist for all wavespeeds c ∈ [0, c * ], where the value of the critical wavespeed c * depends on D(u). However, generalisations of the models presented in [10,11] for a broader class of reaction functions, R(u) and nonlinear diffusivities, D (u), has yet to be considered.…”

Spatial‐temporal basic reproduction number and dynamics for a dengue disease diffusion model

“…Lin and Zhu applied a free boundary problem to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America and showed the spreading or vanishing of the boundary depends on the basic reproduction number. Bao et al made use of diffusive logistic models with free boundary to explore the impact of climate warming on the movement of mosquito range. In studies, researchers gave conditions for the spreading front expanding or vanishing in various advection‐reaction‐diffusion models.…”

Traveling waves, blow‐up, and extinction in the Fisher–Stefan model

“…Since that time, much attention has been devoted to various generalizations, many of which are reviewed by Du 31 . In very recent times, a variety of extensions have been documented, including a rigorous results for different boundary conditions, nonlinear or nonlocal diffusion, generalized reaction terms, with one or two phases, as well as motivation in terms of applications in ecology 32–45 . Formal results and numerical simulations have been described by us 27,46–49 and others 50 …”