A simplified SIS model is proposed and investigated to understand the impact of spatial heterogeneity of environment and advection on the persistence and eradication of an infectious disease. The ...free boundary is introduced to model the spreading front of the disease. The basic reproduction number associated with the diseases in the spatial setting is introduced. Sufficient conditions for the disease to be eradicated or to spread are given. Our result shows that if the spreading domain is high-risk at some time, the disease will continue to spread till the whole area is infected; while if the spreading domain is low-risk, the disease may be vanishing or keep spreading depending on the expanding capability and the initial number of the infective individuals. The spreading speeds are also given when spreading happens, numerical simulations are presented to illustrate the impacts of the advection and the expanding capability on the spreading fronts.
This paper deals with a predator–prey model with time delay and constant prey harvesting. We investigate the effect of the time delay on the stability of the coexistence equilibrium and demonstrate ...that time delay can induce spatial patterns. Furthermore, a Hopf bifurcation occurs when the delay increases to a critical value. By applying normal form theory and the center manifold theorem, we develop the explicit formulae that determines the stability and direction of the bifurcating periodic solutions. Finally, we show how the initial condition affects the types of spatial patterns by numerical simulations.
Spatial heterogeneity and habitat characteristic are shown to determine the asymptotic profile of the solution to a reaction–diffusion model with free boundary, which describes the moving front of ...the invasive species. A threshold value R0Fr(D,t) is introduced to determine the spreading and vanishing of the invasive species. We prove that if R0Fr(D,t0)⩾1 for some t0⩾0, the spreading must happen; while if R0Fr(D,0)<1, the spreading is also possible. Our results show that the species in the favorable habitat can establish itself if the diffusion is slow or the occupying habitat is large. In an unfavorable habitat, the species dies out if the initial value of the species is small. However, big initial number of the species is benefit for the species to survive. When the species spreads in the whole habitat, the asymptotic spreading speed is given. Some implications of these theoretical results are also discussed.
In this paper, we consider a Fisher-KPP equation with an advection term and two free boundaries, which models the behavior of an invasive species in one dimension space. When spreading happens (that ...is, the solution converges to a positive constant), we use phase plane analysis and upper/lower solutions to prove that the rightward and leftward asymptotic spreading speeds exist and both are positive constants. Moreover, one of them is bigger and the other is smaller than the spreading speed in the corresponding problem without advection term.
Network traffic classification is crucial for identifying network applications and defending against network threats. Traditional traffic classification approaches struggle to extract structural ...features and suffer from poor interpretability of feature representations. The high symmetry between network traffic classification and its interpretable feature representation is vital for network traffic analysis. To address these issues, this paper proposes a traffic classification and feature representation model named the attention mechanism autoencoder (AMAE). The AMAE model extracts the global spatial structural features of network traffic through attention mechanisms and employs an autoencoder to extract local structural features and perform dimensionality reduction. This process maps different network traffic features into one-dimensional coordinate systems in the form of spectra, termed FlowSpectrum. The spectra of different network traffic represent different intervals in the coordinate system. This paper tests the interpretability and classification performance of network traffic features of the AMAE model using the ISCX-VPN2016 dataset. Experimental results demonstrate that by analyzing the overall distribution of attention weights and local weight values of network traffic, the model effectively explains the differences in the spectral representation intervals of different types of network traffic. Furthermore, our approach achieves the highest classification accuracy of up to 100% for non-VPN-encrypted traffic and 99.69% for VPN-encrypted traffic, surpassing existing traffic classification schemes.
To explore the impact of the number of hospital beds on the prevention and control of an infectious disease, a diffusive SIS epidemic model in a heterogeneous environment is proposed and ...investigated. A nonlinear recovery rate is introduced to describe the effects of the number of hospital beds on the transmission dynamics of the disease. The basic reproduction number, which depends on the number of hospital beds and spatial heterogeneity, is defined. It is shown that a sufficient number of hospital beds is very important for disease control and eradication. The numerical simulations are presented to confirm our theoretical results.
In this paper, a reaction–diffusion system is proposed to model the spatial spreading of West Nile virus in vector mosquitoes and host birds in North America. Transmission dynamics are based on a ...simplified model involving mosquitoes and birds, and the free boundary is introduced to model and explore the expanding front of the infected region. The spatial-temporal risk index
R
0
F
(
t
)
, which involves regional characteristic and time, is defined for the simplified reaction–diffusion model with the free boundary to compare with other related threshold values, including the usual basic reproduction number
R
0
. Sufficient conditions for the virus to vanish or to spread are given. Our results suggest that the virus will be in a scenario of vanishing if
R
0
≤
1
, and will spread to the whole region if
R
0
F
(
t
0
)
≥
1
for some
t
0
≥
0
, while if
R
0
F
(
0
)
<
1
<
R
0
, the spreading or vanishing of the virus depends on the initial number of infected individuals, the area of the infected region, the diffusion rate and other factors. Moreover, some remarks on the basic reproduction numbers and the spreading speeds are presented and compared.
To discuss the impact factors on the spread of infectious diseases, we study a free boundary problem describing a SIS (susceptible-infected-susceptible) model in a heterogeneous environment. Firstly, ...the existence and uniqueness of the global solution are given. Then the basic reproduction number related to time is defined, and a spreading-vanishing dichotomy of infectious diseases is obtained. The impacts of the diffusion rate of infected individuals, expanding capability, and the scope and scale of initial infection on the spreading and vanishing of infectious disease are analyzed. Numerical simulations are given to show that the large expanding capability is unfavorable to the prevention and control of the disease.
Traffic classification is essential in network-related areas such as network management, monitoring, and security. As the proportion of encrypted internet traffic rises, the accuracy of port-based ...and DPI-based traffic classification methods has declined. The methods based on machine learning and deep learning have effectively improved the accuracy of traffic classification, but they still suffer from inadequate extraction of traffic structure features and poor feature representativeness. This article proposes a model called Semi-supervision 2-Dimensional Convolution AutoEncoder (Semi-2DCAE). The model extracts the spatial structure features in the original network traffic by 2-dimensional convolution neural network (2D-CNN) and uses the autoencoder structure to downscale the data so that different traffic features are represented as spectral lines in different intervals of a one-dimensional standard coordinate system, which we call FlowSpectrum. In this article, the PRuLe activation function is added to the model to ensure the stability of the training process. We use the ISCX-VPN2016 dataset to test the classification effect of FlowSpectrum model. The experimental results show that the proposed model can characterize the encrypted traffic features in a one-dimensional coordinate system and classify Non-VPN encrypted traffic with an accuracy of up to 99.2%, which is about 7% better than the state-of-the-art solution, and VPN encrypted traffic with an accuracy of 98.3%, which is about 2% better than the state-of-the-art solution.
This article concerns a two-species competitive model with diffusive terms in a periodically evolving domain and study the impact of the spatial periodic evolution on the dynamics of the model. The ...Lagrangian transformation approach is adopted to convert the model from a changing domain to a fixed domain with the assumption that the evolution of habitat is uniform and isotropic. The ecological reproduction indexes of the linearized model are given as thresholds to reveal the dynamic behavior of the competitive model. Our theoretical results show that a lager evolving rate benefits the persistence of competitive populations for both sides in the long run. Numerical experiments illustrate that two competitive species, one of which survive and the other vanish in a fixed domain, both survive in a domain with a large evolving rate, and both vanish in a domain with a small evolving rate.
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