Spreading speeds and traveling wave solutions of diffusive vector-borne disease models without monotonicity

Vector-borne diseases, such as chikungunya, dengue, malaria, West Nile virus, yellow fever and Zika, pose a major global public health problem worldwide. In this paper we investigate the propagation dynamics of diffusive vector-borne disease models in the whole space, which characterize the spatial expansion of the infected hosts and infected vectors. Due to the lack of monotonicity, the comparison principle cannot be applied directly to this system. We determine the spreading speed and minimal wave speed when the basic reproduction number of the corresponding kinetic system is larger than one. The spreading speed is mainly estimated by the uniform persistence argument and generalized principal eigenvalue. We also show that solutions converge locally uniformly to the positive equilibrium by employing two auxiliary monotone systems. Moreover, it is proven that the spreading speed is the minimal wave speed of travelling wave solutions. In particular, the uniqueness and monotonicity of travelling waves are obtained. When the basic reproduction number of the corresponding kinetic system is not larger than one, it is shown that solutions approach to the disease-free equilibrium uniformly and there is no travelling wave solutions. Finally, numerical simulations are presented to illustrate the analytical results.

Asymptotic propagations of a nonlocal dispersal population model with shifting habitats

This paper is concerned with the asymptotic propagations for a nonlocal dispersal population model with shifting habitats. In particular, we verify that the invading speed of the species is determined by the speed c of the shifting habitat edge and the behaviours near infinity of the species’ growth rate which is nondecreasing along the positive spatial direction. In the case where the species declines near the negative infinity, we conclude that extinction occurs if c > c*(∞), while c < c*(∞), spreading happens with a leftward speed min{−c, c*(∞)} and a rightward speed c*(∞), where c*(∞) is the minimum KPP travelling wave speed associated with the species’ growth rate at the positive infinity. The same scenario will play out for the case where the species’ growth rate is zero at negative infinity. In the case where the species still grows near negative infinity, we show that the species always survives ‘by moving’ with the rightward spreading speed being either c*(∞) or c*(−∞) and the leftward spreading speed being one of c*(∞), c*(−∞) and −c, where c*(−∞) is the minimum KPP travelling wave speed corresponding to the growth rate at the negative infinity. Finally, we give some numeric simulations and discussions to present and explain the theoretical results. Our results indicate that there may exists a solution like a two-layer wave with the propagation speeds analytically determined for such type of nonlocal dispersal equations.

Application of Facebook’s Prophet Model for Forecasting Meteorological Data

The wildfire risk index was calculated based on current meteorological information, for example, temperature, humidity, and wind speed. Thus, meteorological data forecasting could help estimate the probability of fire occurrence or spreading speed to prevent large wildfires. This study predicts meteorological data (e.g., temperature, humidity, and wind speed) using Facebook's Prophet library. We trained the Prophet model using meteorological data between 2016 and 2018 in Goseong, Gangwon-do (where the wildfire occurred in 2019) and predicted meteorological data for the first four months in 2019. We obtained that Facebook's Prophet model was effective in computing speed and predicting the overall trend. However, it could not predict sudden irregular changes satisfactorily. Considering its rapidity, these results could play an important role in future research, especially as a basic research for time-series forecasting.

Effects of Covid-19 Pandemy Over Maritime Transport: An Evaluation of Supply-demand Balance

This research aims to examine the covid-19 pandemic measurements taken in maritime transport and their possible effects on the supply-demand equilibrium and consequently on the freight market. Covid-19 virus which infected quite large geographic area and people within very short time affects negatively not only every part of our life but also the production and service sector within the globalised world. This is mainly because the future tendency and further effects of this virus are unpredictable. Because of that, most countries are focused firstly on measurements to be taken to reduce the spreading speed of the virus. Although measurements and restrictions seem reduced spreading speed in some countries in short term, those measurements increase the operating costs of production and service companies. On the one hand reduction on cargo movements due to low demand and increasing operation cost due to measurements, have effected the supply-demand equilibrium of maritime transportation. This research examined the effects of already taken and could be revised measurements due to the present situation and possible future tendency of covid-19, and its consequential results on the freight market.

Spreadability Testing of Powder for Additive Manufacturing

The spreading of powders into thin layers is a critical step in powder bed additive manufacturing, but there is no accepted technique to test it. There is not even a metric that can be used to describe spreading behaviour. A robust, image-based measurement procedure has been developed and can be implemented at modest cost and with minimal training. The analysis is automated to derive quantitative information about the characteristics of the spread layer. The technique has been demonstrated for three powders to quantify their spreading behaviour as a function of layer thickness and spreading speed.