Continuous-time random walks on networks with vertex- and time-dependent forcing

The effect mitigation measures for COVID-19 by a fractional-order SEIHRDP model with individuals migration

In this paper, the generalized SEIHRDP (susceptible-exposed-infective-hospitalized-recovered-death-insusceptible) fractional-order epidemic model is established with individual migration. Firstly, the global properties of the proposed system are studied. Particularly, the sensitivity of parameters to the basic reproduction number are analyzed both theoretically and numerically. Secondly, according to the real data in India and Brazil, it can all be concluded that the bilinear incidence rate has a better description of COVID-19 transmission. Meanwhile, multi-peak situation is considered in China, and it is shown that the proposed system can better predict the next peak. Finally, taking individual migration between Los Angeles and New York as an example, the spread of COVID-19 between cities can be effectively controlled by limiting individual movement, enhancing nucleic acid testing and reducing individual contact.

Heterogeneous continuous-time random walks

We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.

Anomalous Metapopulation Dynamics on Scale-Free Networks

We model transport of individuals across a heterogeneous scale-free network where a few weakly connected nodes exhibit heavy-tailed residence times. Using the empirical law of the axiom of cumulative inertia and fractional analysis, we show that "anomalous cumulative inertia" overpowers highly connected nodes in attracting network individuals. This fundamentally challenges the classical result that individuals tend to accumulate in high-order nodes. The derived residence time distribution has a nontrivial U shape which we encounter empirically across human residence and employment times.