Spatial behavior of an epidemic model with migration

Abstract

It was reported that there are traveling patterns in the spatiotemporal data of epidemics (Cummings et al., Nature 427:344, 2004; Grenfell et al., Nature 414:716, 2001). To well understand the mechanism, we present a spatial epidemic model with migration, which means that the individuals exhibit a correlated motion toward certain direction, and obtain traveling pattern. Our results may be helpful to understand the mechanism of the spatiotemporal epidemics and have potential application of control of the epidemics.

Coupling dynamics of epidemic spreading and information diffusion on complex networks

“…In addition, in this work, we only consider the general preventive behavioral response of crowd. However, the dynamics of an epidemic may be very different due to the behavioral responses of people, such as adaptive process [44] , migration [61] , vaccination [39] , and immunity [62] . This work just provides a starting point to understand the coupling effect between the two spreading processes, a more comprehensive and in-depth study of personalized preventive behavioral responses shall need further effort s to discover.…”

Traveling Wave Solutions for a Delayed SIRS Infectious Disease Model with Nonlocal Diffusion and Nonlinear Incidence

“…R 0 is called the basic reproduction ratio of system (3), which describes the average number of newly infected cells generated from one infected cell at the beginning of the infectious process. This quantity determines the thresholds for disease transmissions.…”

“…In [1], by constructing a pair of upper-lower solutions, the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state was given. In recent years, there has been a fair amount of work on epidemiological models with spatial diffusion (see, e.g., [2][3][4][5][6]).…”

“…In the biological context, it is important to analyse the epidemic waves which are described by traveling wave solutions propagating with a certain speed. In this paper, our focus is on the existence of traveling wave solutions to the SIRS infectious disease model (3).…”

Analysis of COVID-19 based on SEIR epidemic models in a multi-patch environment

“…Driessche and Arino [18] established an epidemic patch model for n cities and analyzed the impact of population mobility on spatial distribution. Cui et al [19] proposed a spatial infectious disease model with migration which has the potential value for disease control. Li [20] showed that pattern transition from stationary pattern to patch invasion appears to be possible in a fully deterministic parasite-host model.…”