In this paper, considering the impact of stochastic environment noise on infection rate, a stochastic SIS epidemic model with nonlinear incidence rate is proposed and analyzed. Firstly, for the corresponding deterministic system, the threshold which determines the extinction or permanence of the disease is obtained by analyzing the stability of the equilibria. Then, for the stochastic system, the global dynamics is investigated by using the theory of stochastic differential equations; especially the threshold dynamics is explored when the stochastic environment noise is small. The results show that the condition for the epidemic disease to go to extinction in the stochastic system is weaker than that of the deterministic system, which implies that stochastic noise has a significant impact on the spread of infectious diseases and the larger stochastic noise is conducive to controlling the epidemic diseases. To illustrate this phenomenon, we give some computer simulations with different intensities of the stochastic noise.
Recently, Finite Control Set Model Predictive Control (FCS-MPC) has been successfully applied in the grid-tied inverter with LCL filter. However, to achieve active damping and grid synchronization, many sensors are required, increasing cost and complexity. In addition, a considerable computational delay should be addressed when it is experimentally implemented, which may degrade the performance of overall system. In order to reduce the number of sensors, eliminate the computational delay, and enhance the control reliability of system, a novel FCS-MPC strategy with merely grid-injected current sensors is proposed, which contains four compositions: virtual flux observer, state observer, delay compensation and FCS-MPC algorithm based on estimations. A 3-kW/3-phase/110V experimental platform is established to validate that utilizing the proposed observations-based control method with only grid-injected current sensors is capable to obtain satisfactory performance of grid synchronization and high quality grid-injected current both under balanced and unbalanced grid voltage condition.
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