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Extraction of the underlying dynamics of large biological systems is a crucial step to understanding their mechanisms and predicting their future behaviors. Some of the techniques developed in physics to analyze chaotical phenomena should be applied with caution when the data are short and noisy.
In this paper, we compared the Eckmann-Ruelle Linearization (ERL) local prediction method, and Neural Network (NN), fitting of a global nonlinear function, in the context of population dynamics. Data were generated by a discrete model and subjected to measurement noise. Prediction errors were analyzed according to noise level and length of the observations, using the above two methods
Where the noise level is high, ERL is more effective for prediction than NN. On the basis of these results, we proposed for short series of available observations, that additional data be generated by the Eckmann—Ruelle linearization method and these data be used as input for Neural Nets in order to obtain a global function for the observed dynamics. This gave more reliable results than when we apply the NN method directly .
Two examples are given, in ecology and epidemiology.
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Analyzes has been carried out for the two-dimensional whooping cough model. The solution of the arising nonlinear initial/boundary value problem is computed by a homotopy analysis method (HAM). Convergence of the derived solution is highlighted. The plotted graphs show great confidence into the used methodology of solution.
The pertussis resurgence has currently become a global public health concern. The widespread vaccination of pertussis vaccine will inevitably lead to changes in the transmission pattern, epidemiological characteristics, and clinical manifestations of pertussis while reducing the overall incidence level. At present, there is no unified pertussis surveillance program across countries, and different surveillance and monitoring approaches are used in different regions, and the reported incidence levels and epidemiological characteristics vary greatly. The integration of emergency management and epidemiological research is essential in the combating of pertussis. Emergency management provides the rapid response necessary to mitigate the impact of an outbreak, while epidemiological research provides the knowledge and understanding to guide effective control strategies. Researchers should take a consideration and discussion about the role of traditional Chinese medicine in this epidemic, as well as the treatment and prevention in the whole course of the disease. Besides, a model of emergency management and epidemiological surveillance system should be established and continuously improved in clinical to combat the pertussis outbreak. This paper aims to provide an epidemic control model of the emergency management procedure in hospital for references, so that the clinical practitioners and healthcare workers may be better prepared and well-respond to a next epidemic.