Periodic and aperiodic traveling pulses in population dynamics: an example from the occurrence of epidemic infections

SPATIAL PATTERN IN AN EPIDEMIC SYSTEM WITH CROSS-DIFFUSION OF THE SUSCEPTIBLE

In this paper, pattern formation of a spatial model with cross diffusion of the susceptible is investigated. We compute Hopf and Turing bifurcations for the model. In particular, the exact Turing domain is delineated in the parameter space. When the parameters are in that domain, a series of numerical simulations reveals that the typical dynamics of the infecteds class typically involves the formation of isolated groups, i.e., striped, spotted or labyrinthine patterns. Furthermore, spatial oscillatory and anti-phase dynamics of different spatial points were also found. These results demonstrate that cross diffusion of susceptibles may have great influence on the spread of the epidemic.

Periodic forcing in a three-level cellular automata model for a vector-transmitted disease

A periodically forced two-dimensional cellular automata model is used to reproduce and analyze the complex spatiotemporal patterns observed in the transmission of vector infectious diseases. The system, which comprises three population levels, is introduced to describe complex features of the dynamics of the vector-transmitted dengue epidemics, known to be very sensitive to seasonal variables. The three coupled levels represent the human, the adult, and immature vector populations. The dynamics includes external seasonality forcing, human and mosquito mobility, and vector control effects. The model parameters, even if bounded to well-defined intervals obtained from reported data, can be selected to reproduce specific epidemic outbursts. In the current study, explicit results are obtained by comparison with actual data retrieved from the time series of dengue epidemics in two cities in Brazil. The results show fluctuations that are not captured by mean-field models. It also reveals the qualitative behavior of the spatiotemporal patterns of the epidemics. In the extreme situation of the absence of external periodic drive, the model predicts a completely distinct long-time evolution. The model is robust in the sense that it is able to reproduce the time series of dengue epidemics of different cities, provided that the forcing term takes into account the local rainfall modulation. Finally, an analysis is provided of the effect of the dependence between epidemics threshold and vector control actions, both in the presence and absence of human mobility factor.

Epidemic spreading in complex networks

The study of epidemic spreading in complex networks is currently a hot topic and a large body of results have been achieved. In this paper, we briefly review our contributions to this field, which includes the underlying mechanism of rumor propagation, the epidemic spreading in community networks, the influence of varying topology, and the influence of mobility of agents. Also, some future directions are pointed out.

Spatial organization and evolution period of the epidemic model using cellular automata

We investigate epidemic models with spatial structure based on the cellular automata method. The construction of the cellular automata is from the study by Weimar and Boon about the reaction-diffusion equations [Phys. Rev. E 49, 1749 (1994)]. Our results show that the spatial epidemic models exhibit the spontaneous formation of irregular spiral waves at large scales within the domain of chaos. Moreover, the irregular spiral waves grow stably. The system also shows a spatial period-2 structure at one dimension outside the domain of chaos. It is interesting that the spatial period-2 structure will break and transform into a spatial synchronous configuration in the domain of chaos. Our results confirm that populations embed and disperse more stably in space than they do in nonspatial counterparts.