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In this brief, a cellular neural network (CNN) vector disease model is investigated from the point of view of its dynamics. Some vector-borne diseases such as malaria, yellow fever, and typhus, which arrive and spread in new areas, are one of the main public health problems throughout the world. The investigations of the spatial spread of newly introduced diseases are interesting and challenging for both theory and applications. Existence of traveling waves for such CNN vector disease model is proved. Simulations of the obtained CNN model are given, which confirm the obtained theoretical results. Index Terms--Cellular neural network (CNN), harmonic balance method, traveling waves, vector disease model.

Cellular neural networks are a novel class of information-processing systems which have architecture similar to neural networks. In this short paper, we consider a nonlinear cellular neural network where the nonlinearity in the feedback circuit is allowed to exhibit hysteresis. Stability analysis of the equilibrium points for such a network is made. Hopf-like bifurcations are proved for an example of a two-cell autonomous cellular neural network. Index Terms - Bifurcations, cellular neural networks, hysteresis, limit cycles.