AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.

How to model the 2019 CoronaVirus (2019-nCov) spread in China is one of the most urgent and interesting problems in applied mathematics. In this paper, we propose a novel time delay dynamic system with external source to describe the trend of local outbreak for the 2019-nCoV. The external source is introduced in the newly proposed dynamic system, which can be considered as the suspected people travel to different areas. The numerical simulations exhibit the dynamic system with the external source is more reliable than the one without it, and the rate of isolation is extremely important for controlling the increase of cumulative confirmed people of 2019-nCoV. Based on our numerical simulation results with the public data, we suggest that the local government should have some more strict measures to maintain the rate of isolation. Otherwise the local cumulative confirmed people of 2019-nCoV might be out of control.

In this work, we are concerned with the diffusive optical tomography (DOT) problem in the case when only one or two pairs of Cauchy data is available. We propose a simple and efficient direct sampling method (DSM) to locate inhomogeneities inside a homogeneous background and solve the DOT problem in both full and limited aperture cases. This new method is easy to implement and less expensive computationally. Numerical experiments demonstrate its effectiveness and robustness against noise in the data. This provides a new promising numerical strategy for the DOT problem.Mathematics Subject Classification (MSC2000): 35J67, 35R30, 65N21, 78A70, 78M25.

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In this paper, we are concerned with a shape design problem, in which our target is to design, up to rigid transformations and scaling, the shape of an object given either its polarization tensor at multiple contrasts or the partial eigenvalues of its Neumann-Poincaré operator, which are known as the Fredholm eigenvalues. We begin by proposing to recover the eigenvalues of the Neumann-Poincaré operator from the polarization tensor by means of the holomorphic functional calculus. Then we develop a regularized Gauss-Newton optimization method for the shape reconstruction process. We present numerical results to demonstrate the effectiveness of the proposed methods and to illustrate important properties of the Fredholm eigenvalues and their associated eigenfunctions. Our results are expected to have important applications in the design of plasmon resonances in nanoparticles as well as in the multifrequency or pulsed imaging of small anomalies. (MSC 2000): 49J20, 47A75, 35R30, 35B30. Mathematics Subject Classification