Serious role of non-quarantined COVID-19 patients for random walk simulations

An application of small-world network on predicting the behavior of infectious disease on campus

Networks haven been widely used to understand the spread of infectious disease. This study examines the properties of small-world networks in modeling infectious disease on campus. Two different small-world models are developed and the behaviors of infectious disease in the models are observed through numerical simulations. The results show that the behavior pattern of infectious disease in a small-world network is different from those in a regular network or a random network. The spread of the infectious disease increases as the proportion of long-distance connections p increasing, which indicates that reducing the contact among people is an effective measure to control the spread of infectious disease. The probability of node position exchange in a network (p2) had no significant effect on the spreading speed, which suggests that reducing human mobility in closed environments does not help control infectious disease. However, the spreading speed is proportional to the number of shared nodes (s), which means reducing connections between different groups and dividing students into separate sections will help to control infectious disease. In the end, the simulating speed of the small-world network is tested and the quadratic relationship between simulation time and the number of nodes may limit the application of the SW network in areas with large populations.

Population persistence under two conservation measures: Paradox of habitat protection in a patchy environment

Anthropogenic modification of natural habitats is a growing threat to biodiversity and ecosystem services. The protection of biospecies has become increasingly important. Here, we pay attention to a single species as a conservation target. The species has three processes: reproduction, death and movement. Two different measures of habitat protection are introduced. One is partial protection in a single habitat (patch); the mortality rate of the species is reduced inside a rectangular area. The other is patch protection in a two-patch system, where only the mortality rate in a particular patch is reduced. For the one-patch system, we carry out computer simulations of a stochastic cellular automaton for a "contact process". Individual movements follow random walking. For the two-patch system, we assume an individual migrates into the empty cell in the destination patch. The reaction-diffusion equation (RDE) is derived, whereby the recently developed "swapping migration" is used. It is found that both measures are mostly effective for population persistence. However, comparing the results of the two measures revealed different behaviors. ⅰ) In the case of the one-patch system, the steady-state densities in protected areas are always higher than those in wild areas. However, in the two-patch system, we have found a paradox: the densities in protected areas can be lower than those in wild areas. ⅱ) In the two-patch system, we have found another paradox: the total density in both patches can be lower, even though the proportion of the protected area is larger. Both paradoxes clearly occur for the RDE with swapping migration.