Public health services are constantly searching for ways to reduce the spread of infectious diseases, such as public vaccination of asymptomatic individuals, quarantine and treatment of symptomatic individuals. In this paper, we introduce epidemic models including variable population size, degree-related imperfect vaccination and quarantine on scale-free networks. More specifically, the models are formulated both on the population with and without permanent natural immunity to infection, which corresponds respectively to the susceptible-vaccinated-infected-quarantined-recovered (SVIQR) model and the susceptible-vaccinated-infected-quarantined (SVIQS) model. We develop different mathematical methods to study the dynamics of two models, including the basic reproduction number, the global stability of disease-free and endemic equilibria. For the SVIQR model, we show that the system exhibits a forward bifurcation. Meanwhile, the disease-free and unique endemic equilibria are shown to be globally asymptotically stable by constructing suitable Lyapunov functions. For the SVIQS model, conditions ensuring the occurrence of multiple endemic equilibria are derived. Under certain conditions, this system cannot undergo a backward bifurcation. The global asymptotical stability of disease-free equilibrium, and the persistence of the disease are proved. The endemic equilibrium is shown to be globally attractive by using monotone iterative technique. Finally, stochastic network simulations yield quantitative agreement with the deterministic mean-field approach.

In the real world, pathogens do not exist in isolation. The transmission of one pathogen may be affected by the presence of other pathogens, and certain pathogens generate multiple strains with different spreading features. Hence, the behavior of multi-pathogen transmission has attracted much attention in epidemiological research. In this paper, we use the pairwise approximation method to formulate two-pathogen models capturing cross-immunity, super-infection, and co-infection phenomena, in which each pathogen follows a susceptible-infected-susceptible (SIS) mechanism. For each model, we calculate the basic reproduction number and analyze the stability of equilibria, and discuss the differences from the mean-field approach. We demonstrate that simulations are in good agreement with the analytical results.

Multicast is an efficient tool to transfer the same data from a publisher to multiple subscribers, and its performance relies critically on the resiliency. Compared with traditional networks, the centralized control and flexible programmability of the Software Defined Network (SDN) is more beneficial for solving the failure recovery problem. This paper presents a design of an OpenFlow controller which can recover and reconstruct a multicast tree rapidly, while reducing the Ternary Content Addressable Memory (TCAM) consumption simultaneously. We choose the protection mechanism, and calculate all the backup paths after the topology information is mastered by the controller. When a failure occurs, affected switches can enable the use of backup paths to continue forwarding multicast packets. As duplicate packets may exist after the failure recovery, the reconstruction of a tree is required by modifying only a small fraction of forwarding rules. The performance evaluations demonstrate that our proposed method recovers a multicast tree with a high speed and low cost. On one hand, the maximum failure recovery time of two protection-based methods including our proposed method is less than 11 ms, while that of two restoration-based methods is 44 ms and 30 ms, respectively. On the other hand, the amount of backup forwarding entries required by another protection-based method exceed our proposed method as long as 3 or more multicast groups exist in the network. Moreover, when our proposed method is adopted, the amount of backup forwarding entries per switch is less than 30, which can be ignored when compared with the capacity of SDN switches (a switch can support a few thousand forwarding rules).

Complex network theory involves network structure and dynamics; dynamics on networks and interactions between networks; and dynamics developed over a network. As a typical application of complex networks, the dynamics of disease spreading and control strategies on networks have attracted widespread attention from researchers. We investigate the dynamics and optimal control for an epidemic model with demographics and heterogeneous asymmetric control strategies (immunization and quarantine) on complex networks. We derive the epidemic threshold and study the global stability of disease-free and endemic equilibria based on different methods. The results show that the disease-free equilibrium cannot undergo a Hopf bifurcation. We further study the optimal control strategy for the complex system and obtain its existence and uniqueness. Numerical simulations are conducted on scale-free networks to validate and supplement the theoretical results. The numerical results indicate that the asymmetric control strategies regarding time and degree of node for populations are superior to symmetric control strategies when considering control cost and the effectiveness of controlling infectious diseases. Meanwhile, the advantages of the optimal control strategy through comparisons with various baseline immunization and quarantine schemes are also shown.