In this study, an epidemic model was developed to simulate and predict the disease variations of Guangdong province which was focused on the period from Jan 27 to Feb 20, 2020. To explore the impacts of the input population and quarantine strategies on the disease variations at different scenarios, four time points were assumed as Feb 6, Feb 16, Feb 24 and Mar 5 2020. The major results suggest that our model can well capture the disease variations with high accuracy. The simulated peak value of the confirmed cases is 1002 at Feb 10, 2020 which is mostly close to the reported number of 1007 at Feb 9, 2020. The disease will become extinction with peak value of 1397 at May 11, 2020. Moreover, the increased numbers of the input population can mainly shorten the disease extinction days and the increased percentages of the exposed individuals of the input population increase the number of cumulative confirmed cases at a small percentage. Increasing the input population and decreasing the quarantine strategy together around the time point of the peak value of the confirmed cases, may lead to the second outbreak.

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Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.

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