The 2019 novel coronavirus disease (COVID-19) outbreak has become a worldwide problem. Due to globalization and the proliferation of international travel, many countries are now facing local epidemics. The existence of asymptomatic and pre-symptomatic transmissions makes it more difficult to control disease transmission by isolating infectious individuals. To accurately describe and represent the spread of COVID-19, we suggest a susceptible-exposed-infected-hospitalized-removed (SEIHR) model with human migrations, where the “exposed” (asymptomatic) individuals are contagious. From this model, we derive the basic reproduction number of the disease and its relationship with the model parameters. We find that, for highly contagious diseases like COVID-19, when the adjacent region’s epidemic is not severe, a large migration rate can reduce the speed of local epidemic spreading at the price of infecting the neighboring regions. In addition, since “infected” (symptomatic) patients are isolated almost immediately, the transmission rate of the epidemic is more sensitive to that of the “exposed” (asymptomatic) individuals. Furthermore, we investigate the impact of various interventions, e.g. isolation and border control, on the speed of disease propagation and the resultant demand on medical facilities, and find that a strict intervention measure can be more effective than closing the borders. Finally, we use some real historical data of COVID-19 caseloads from different regions, including Hong Kong, to validate the modified SEIHR model, and make an accurate prediction for the third wave of the outbreak in Hong Kong.

Vaccination is an important means to fight against the spread of the SARS-CoV-2 virus and its variants. In this work, we propose a general susceptible-vaccinated-exposed-infected-hospitalized-removed (SVEIHR) model and derive its basic and effective reproduction numbers. We set Hong Kong as an example and calculate conditions of herd immunity for multiple vaccines and disease variants. The model shows how the number of confirmed COVID-19 cases in Hong Kong during the second and third waves of the COVID-19 pandemic would have been reduced if vaccination were available then. We then investigate the relationships between various model parameters and the cumulative number of hospitalized COVID-19 cases in Hong Kong for the ancestral, Delta, and Omicron strains. Numerical results demonstrate that the static herd immunity threshold corresponds to one percent of the population requiring hospitalization or isolation at some point in time. We also demonstrate that when the vaccination rate is high, the initial proportion of vaccinated individuals can be lowered while still maintaining the same proportion of cumulative hospitalized/isolated individuals.

Energy efficiency and Quality of Service (QoS) are two important considerations for the design and planning of cellular networks. One effective approach to handle the tradeoff between power consumption and QoS is to switch some of the Base Stations (BSs) to sleep mode when traffic load is low. In this paper, we model each BS as a processor-sharing queue with vacations, and investigate the performance of three BS sleeping schemes, namely the isolated scheme in which each BS switches mode based on its own load, the cooperative scheme in which traffic is allowed to overflow from sleeping BSs to neighboring active BSs, and a combination of both schemes. We propose a robust, scalable and computationally efficient analytical method to evaluate QoS metrics (including mean delay and blocking probability) and power consumption for each scheme and validate their accuracy by simulations. We also demonstrate the power consumption and QoS trade-off by extensive and statistically reliable experiments, and compare the performance of the three schemes under different network conditions.