In this paper, a SEIR epidemic model for the COVID-19 is built according to some general control strategies, such as hospital, quarantine and external input. Based on the data of Hubei province, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of the system. We found that the parameters of the proposed SEIR model are different for different scenarios. Then, the model is employed to show the evolution of the epidemic in Hubei province, which shows that it can be used to forecast COVID-19 epidemic situation. Moreover, by introducing the seasonality and stochastic infection the parameters, nonlinear dynamics including chaos are found in the system. Finally, we discussed the control strategies of the COVID-19 based on the structure and parameters of the proposed model.

Abstract:The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM). Lyapunov Characteristic Exponents (LCEs) of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system has rich dynamical behaviors. Chaos and hyperchaos can be generated by decreasing fractional order q in this system. It also shows that the system is more complex when q takes smaller values. SE and C 0 complexity algorithms provide a parameter choice criteria for practice applications of fractional-order chaotic systems. The fractional-order system is implemented by digital signal processor (DSP), and a pseudo-random bit generator is designed based on the implemented system, which passes the NIST test successfully.

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