The COVID-19 pandemic has created an urgent need for mathematical models that can project epidemic trends and evaluate the effectiveness of mitigation strategies. A major challenge in forecasting the transmission of COVID-19 is the accurate assessment of the multiscale human mobility and how it impacts infection through close contacts. By combining the stochastic agent-based modeling strategy and hierarchical structures of spatial containers corresponding to the notion of geographical places, this study proposes a novel model, Mob-Cov, to study the impact of human traveling behavior and individual health conditions on the disease outbreak and the probability of zero-COVID in the population. Specifically, individuals perform power law-type local movements within a container and global transport between different-level containers. It is revealed that frequent long-distance movements inside a small-level container (e.g., a road or a county) and a small population size reduce both the local crowdedness and disease transmission. It takes only half of the time to induce global disease outbreaks when the population increases from 150 to 500 (normalized unit). When the exponent of the long-tail distribution of distance k moved in the same-level container, , increases, the outbreak time decreases rapidly from 75 to 25 (normalized unit). In contrast, travel between large-level containers (e.g., cities and nations) facilitates global spread of the disease and outbreak. When the mean traveling distance across containers increases from 0.5 to 1 (normalized unit), the outbreak occurs almost twice as fast. Moreover, dynamic infection and recovery in the population are able to drive the bifurcation of the system to a “zero-COVID” state or to a “live with COVID” state, depending on the mobility patterns, population number and health conditions. Reducing population size and restricting global travel help achieve zero-COVID-19. Specifically, when is smaller than 0.2, the ratio of people with low levels of mobility is larger than 80% and the population size is smaller than 400, zero-COVID can be achieved within fewer than 1000 time steps. In summary, the Mob-Cov model considers more realistic human mobility at a wide range of spatial scales, and has been designed with equal emphasis on performance, low simulation cost, accuracy, ease of use and flexibility. It is a useful tool for researchers and politicians to apply when investigating pandemic dynamics and when planning actions against disease. Supplementary Information The online version contains supplementary material available at 10.1007/s11071-023-08489-5.

The COVID-19 pandemic has created an urgent need for mathematical models that can project epidemic trends and evaluate the effectiveness of mitigation strategies. To forecast the transmission of COVID-19, a major challenge is the accurate assessment of the multi-scale human mobility and how they impact the infection through close contacts. By combining the stochastic agent-based modeling strategy and hierarchical structures of spatial containers corresponding to the notion of places in geography, this study proposes a novel model, Mob-Cov, to study the impact of human traveling behaviour and individual health conditions on the disease outbreak and the probability of zero COVID in the population. Specifically, individuals perform power-law type of local movements within a container and global transport between different-level containers. Frequent long movements inside a small-level container (e.g. a road or a county) and a small population size reduce the local crowdedness of people and the disease infection and transmission. In contrast, travels between large-level containers (e.g. cities and nations) facilitate global disease spread and outbreak. Moreover, dynamic infection and recovery in the population are able to drive the bifurcation of the system to a "zero-COVID" state or a "live with COVID" state, depending on the mobility patterns, population number and health conditions. Reducing total population and local people accumulation as well as restricting global travels help achieve zero-COVID. In summary, the Mob-Cov model considers more realistic human mobility in a wide range of spatial scales, and has been designed with equal emphasis on performance, low simulation cost, accuracy, ease of use and flexibility. It is a useful tool for researchers and politicians to investigate the pandemic dynamics and plan actions against the disease.

One of the primary challenges of magnetic drug targeting is to achieve efficient and accurate delivery of drug particles to the desired sites in complex physiological conditions. Though a majority of drugs are delivered through intravenous administration, until now, the kinematics and dynamics of drug particles influenced by the magnetic field, vascular topology and blood flows are still less understood. In this work, a multi-physics dynamical model which captures transient particle motions in both artificial and in vivo-like 3D vascular networks manipulated by the timevarying magnetic field is developed. Based on the model, it is found that particles which perform a random walk with correlated speed and persistence (RWSP motion) inspired by the migratory motion of immune and metastasis cells have higher mobility and navigation ability in both 2D and 3D tree-like and web-like networks. Moreover, to steer particles to perform the efficient RWSP motion, a stochastic magnetic steering strategy which uses time-varying gradient magnetic field is proposed. Parameters of the steering strategy is optimized and the capability of controlling particles to achieve fast spreading and transport in the vascular networks is demonstrated. In addition, the influence of heterogeneous flows in the vascular networks on the particle steering efficiency is discussed. Overall, the numerical model and the magnetic steering strategy can be widely used in the drug delivery systems for precise medicine research.