The goal of this study is to establish a general framework for predicting the so-called critical "Turning Period" in an infectious disease epidemic such as the COVID-19 outbreak in China early this year. This framework enabled a timely prediction of the turning period when applied to Wuhan COVID-19 epidemic and informed the relevant authority for taking appropriate and timely actions to control the epidemic. It is expected to provide insightful information on turning period for the world's current battle against the COVID-19 pandemic.The underlying mathematical model in our framework is the individual Susceptible-Exposed-Infective-Removed (iSEIR) model, which is a set of differential equations extending the classic SEIR model. We used the observed daily cases of COVID-19 in Wuhan from February 6 to 10, 2020 as the input to the iSEIR model and were able to generate the trajectory of COVID-19 cases dynamics for the following days at midnight of February 10 based on the updated model, from which we predicted that the turning period of CIVID-19 outbreak in Wuhan would arrive within one week after February 14. This prediction turned to be timely and accurate, providing adequate time for the government, hospitals, essential industry sectors and services to meet peak demands and to prepare aftermath planning.Our study also supports the observed effectiveness on flatting the epidemic curve by decisively imposing the "Lockdown and Isolation Control Program" in Wuhan since January 23, 2020. The Wuhan experience provides an exemplary lesson for the whole world to learn in combating COVID-19.

The goal of this study is to establish a general framework for predicting the so-called critical "Turning Period" in an infectious disease epidemic such as the COVID-19 outbreak in China early this year. This framework enabled a timely prediction of the turning period when applied to Wuhan COVID-19 epidemic and informed the relevant authority for taking appropriate and timely actions to control the epidemic. It is expected to provide insightful information on turning period for the world's current battle against the COVID-19 pandemic.The underlying mathematical model in our framework is the individual Susceptible-Exposed-Infective-Removed (iSEIR) model, which is a set of differential equations extending the classic SEIR model. We used the observed daily cases of COVID-19 in Wuhan from February 6 to 10, 2020 as the input to the iSEIR model and were able to generate the trajectory of COVID-19 cases dynamics for the following days at midnight of February 10 based on the updated model, from which we predicted that the turning period of CIVID-19 outbreak in Wuhan would arrive within one week after February 14. This prediction turned to be timely and accurate, providing adequate time for the government, hospitals, essential industry sectors and services to meet peak demands and to prepare aftermath planning.Our study also supports the observed effectiveness on flatting the epidemic curve by decisively imposing the "Lockdown and Isolation Control Program" in Wuhan since January 23, 2020. The Wuhan experience provides an exemplary lesson for the whole world to learn in combating COVID-19.

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Based on a new concept called " Turning Period", the goal of this report is to show how we can conduct the prediction for the outlook in the different stages for the battle with outbreak of COVID-19 currently in US, in particular, to identify when each of top 15 states in USA (basically on their populations) is going to enter into the stage that the outbreak of COVID-19 is under the control by the criteria such as daily change of new patients is less than 10% smoothly. Indeed, based on the data of April 10, 2020 with the numerical analysis, we are able to classify 15 states of US into the following four different categories for the Prevention and Control of Infectious Diseases Today and the main conclusion are:First, staring around April 14, 20202, three states which are Washington State, Louisiana and Indiana are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Second, staring around April 15, 20202, two states which are New Jersey, and New York are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Third, staring around April 16, 20202, seven states which are California, Florida, Georgia (GA), Illinois, Maryland, Indiana, Michigan, and Pennsylvania are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Fourth, staring around April 17, 20202, three states which are Texas, Massachusetts, and Connecticut are entering the stage that the outbreak of COVID-19 is under the control, which means daily change of new patients is less than 10% and the gamma is less than zero in general.Finally, we want to reinforce that emergency risk management is always associated with the implementation of an emergency plan. The identification of the Turning Time Period is key to emergency planning as it provides a timeline for effective actions and solutions to combat a pandemic by reducing as much unexpected risk as soon as possible.

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This paper focuses on studying and understanding of stochastic dynamics in population composition when the population is subject to rumor spreading. We undertake the study by first developing an individual Susceptible-Exposed-Infective-Removed (iSEIR) model, an extension of the SEIR model, for summarizing rumor-spreading behaviors of interacting groups in the population. With this iSEIR model, the interacting groups may be regarded as nodes in a multiplex network. Then various properties of the dynamic behaviors of the interacting groups in rumor spreading can be drawn from samples of the multiplex network. The samples are simulated based on the iSEIR model with different settings in terms of population scale, population distribution and transfer rate. Results from the simulation study show that effective control of rumor spreading in the multiplex network entails an efficient management on information flow, which may be achieved by setting appropriate immunization and spreading thresholds in individual behavior dynamics. Under the proposed iSEIR model we also have derived a steady-state result, named the "supersaturation phenomenon", when the rumor spreading process becomes equilibriumm, which may help us to make the optimal or better control of information flow in the practice.

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