Infection age is often an important factor in epidemic dynamics. In order to realistically analyze the spreading mechanism and dynamical behavior of epidemic diseases, in this paper, a generalized disease transmission model of SIS type with age-dependent infection and birth and death on a heterogeneous network is discussed. The model allows the infection and recovery rates to vary and depend on the age of infection, the time since an individual becomes infected. We address uniform persistence and find that the model has the sharp threshold property, that is, for the basic reproduction number less than one, the disease-free equilibrium is globally asymptotically stable, while for the basic reproduction number is above one, a Lyapunov functional is used to show that the endemic equilibrium is globally stable. Finally, some numerical simulations are carried out to illustrate and complement the main results. The disease dynamics rely not only on the network structure, but also on an age-dependent factor (for some key functions concerned in the model).

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SUMMARYThis paper presents a continuum dynamic traffic assignment model for a city in which the total cost of the traffic system is minimized: the travelers in the system are organized to choose the route to their destinations that minimizes the total cost of the system. Combined with the objective function, which defines the total cost and constraints such as certain physical and boundary conditions, a continuum model can be formulated as an optimization scheme with a feasible region in the function space. To obtain an admissible locally optimal solution to this problem, we first reformulate the optimization in discrete form and then introduce a heuristic method to solve it. This method converges rapidly with attractive computational cost. Numerical examples are used to demonstrate the effectiveness of the method.

In this paper we present a modified real-coded lattice gas (RLG) model in which the floor field is introduced. The floor field is calculated on finer lattices in order to determine the pedestrians' direction accurately. Thus, the pedestrian's motion has many more degrees of freedom compared with existing discrete models. Furthermore, the walking speed is determined by the available space ahead of the pedestrians in a multi-step way. Therefore, the model can precisely describe the pedestrians' motion. Then, we calibrate model parameters by comparing with the existing measured data. Finally, we employ this model to investigate normal evacuation from a room. The conclusions are as follows: 1) In the single-exit room, for a given exit width larger than 0.6 m, the average specific flow increases with the initial number of pedestrians. For a given initial number of pedestrians, the specific flow increases first and then decreases when the width of the exit increases. 2) The evacuation time of the two-exit room is less than that of the single-exit room only when the total width is greater than 1.6 m.

To better explore asymmetrical interaction between epidemic spreading and awareness diffusion in multiplex networks, we distinguish susceptibility and infectivity between aware and unaware individuals, relax the degree of immunization, and take into account three types of generation mechanisms of individual awareness. We use the probability trees to depict the transitions between distinct states for nodes and then write the evolution equation of each state by means of the microscopic Markovian chain approach (MMCA). Based on the MMCA, we theoretically analyze the possible steady states and calculate the critical threshold of epidemics, related to the structure of epidemic networks, the awareness diffusion, and their coupling configuration. The achieved analytical results of the mean-field approach are consistent with those of the numerical Monte Carlo simulations. Through the theoretical analysis and numerical simulations, we find that global awareness can reduce the final scale of infection when the regulatory factor of the global awareness ratio is less than the average degree of the epidemic network but it cannot alter the onset of epidemics. Furthermore, the introduction of self-awareness originating from infected individuals not only reduces the epidemic prevalence but also raises the epidemic threshold, which tells us that it is crucial to enhance the early warning of symptomatic individuals during pandemic outbreaks. These results give us a more comprehensive and deep understanding of the complicated interaction between epidemic transmission and awareness diffusion and also provide some practical and effective recommendations for the prevention and control of epidemics.