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Register a new userThe spatial-temporal risk index and spreading dynamics for a time-periodic diffusive WNv model
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This paper is concerned 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 $R_0^D$ and the spatial-temporal risk index $R_0^F(t)$, 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.
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In current paper, we put forward a reaction-diffusion system for West Nile virus in spatial heterogeneous and time almost periodic environment with free boundaries to investigate the influences of the habitat differences and seasonal variations on the propagation of West Nile virus. The existence, uniqueness and regularity estimates of the global solution for this disease model are given. Focused on the effects of spatial heterogeneity and time almost periodicity, we apply the principal Lyapunov exponent $lambda(t)$ with time $t$ to get the initial infected domain threshold $L^*$ to analyze the long-time dynamical behaviors of the solution for this almost periodic West Nile virus model and give the spreading-vanishing dichotomy regimes of the disease. Especially, we prove that the solution for this West Nile virus model converges to a time almost periodic function locally uniformly for $x$ in $mathbb R$ when the spreading occurs, which is driven by spatial differences and seasonal recurrence. Moreover, the initial disease infected domain and the front expanding rate have momentous impacts on the permanence and extinction of the epidemic disease. Eventually, numerical simulations identify our theoretical results.
We study the asymptotic spatial behavior of the vorticity field, $omega(x,t)$, associated to a time-periodic Navier-Stokes flow past a body, $mathscr B$, in the class of weak solutions satisfying a Serrin-like condition. We show that, outside the wake region, $mathcal R$, $omega$ decays pointwise at an exponential rate, uniformly in time. Moreover, denoting by $bar{omega}$ its time-average over a period and by $omega_P:=omega-bar{omega}$ its purely periodic component, we prove that inside $mathcal R$, $bar{omega}$ has the same algebraic decay as that known for the associated steady-state problem, whereas $omega_P$ decays even faster, uniformly in time. This implies, in particular, that sufficiently far from $mathscr B$, $omega(x,t)$ behaves like the vorticity field of the corresponding steady-state problem.
Taxi arrival time prediction is an essential part of building intelligent transportation systems. Traditional arrival time estimation methods mainly rely on traffic map feature extraction, which can not model complex situations and nonlinear spatial and temporal relationships. Therefore, we propose a Multi-View Spatial-Temporal Model (MVSTM) to capture the dependence of spatial-temporal and trajectory. Specifically, we use graph2vec to model the spatial view, dual-channel temporal module to model the trajectory view, and structural embedding to model the traffic semantics. Experiments on large-scale taxi trajectory data show that our approach is more effective than the novel method. The source code can be obtained from https://github.com/775269512/SIGSPATIAL-2021-GISCUP-4th-Solution.
In {em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby justifying stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centering condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by heat equations on the edges supplemented with Robin like boundary conditions at the vertices modeling exchanges between incident edges and the associated vertex. We describe the main properties of the system, and also derive the final total population of infected individuals. We present a semi-implicit in time numerical scheme based on finite differences in space which preserves the main properties of the continuous model such as the uniqueness and positivity of solutions and the conservation of the total population. We also illustrate our results with a selection of numerical simulations for a selection of connected graphs.
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