By appealing to the theory of global attractors on complete metric spaces, we obtain weaker sufficient conditions for the existence of interior global attractors for uniformly persistent dynamical systems, and hence generalize the earlier results on coexistence steady states. We also provide examples to show applicability of our interior fixed point theorem in the case of convex $\kappa$-contracting maps, and to prove the existence of discrete- and continuous-time dynamical systems that admit global attractors, but no strong global attractors, which gives an affirmative answer to an open question presented by Sell and You [Dynamics of Evolutionary Equations, Springer-Verlag, New York, 2002] in the case of continuous-time semiflows.

We develop a mathematical model to provide epidemic predictions for the COVID-19 epidemic in Wuhan, China. We use reported case data up to 31 January 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model, we identify the number of unreported cases. We then use the model to project the epidemic forward with varying levels of public health interventions. The model predictions emphasize the importance of major public health interventions in controlling COVID-19 epidemics.

At the beginning of a COVID-19 infection, there is a period of time known as the exposed or latency period, before an infected person is capable of transmitting the infection to another person. We develop two differential equations models to account for this period. The first is a model that incorporates infected persons in the exposed class, before transmission is possible. The second is a model that incorporates a time delay in infected persons, before transmission is possible. We apply both models to the COVID-19 epidemic in China. We estimate the epidemiological parameters in the models, such as the transmission rate and the basic reproductive number, using data of reported cases. We thus evaluate the role of the exposed or latency period in the dynamics of a COVID-19 epidemic.

We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.