A random-walk-based epidemiological model

Random walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates non-trivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The functional dependence of the basic reproductive number $$R_{0}$$ R 0 on the model’s defining parameters reveals the role of spatial fluctuations and leads to a novel expression for $$R_{0}$$ R 0 . Special attention is given to simulations of inter-regional transmission of the contagion. The scaling of the epidemic with respect to space and time scales is studied in detail in the critical region, which is shown to be compatible with the directed-percolation universality class.

Emergence of an Adaptive Movement from a Subjective Inference about Resource Distribution

Background: In animal foraging, the optimal search strategy in an unknown environment varies according to the context. When food is distributed sparsely and randomly, super-diffusive walks outperform normal-diffusive walks. However, super-diffusive walks are no longer advantageous when random walkers forage in a resource-rich environment. It is not currently clear whether a relationship exists between an agent’s use of local information to make subjective inferences about global food distribution and an optimal random walk strategy. Methods: Therefore, I investigated how flexible exploration is achieved if an agent alters its directional rule based on local resource distribution. In the proposed model, the agent, a Brownian-like walker, estimates global resource distribution using local resource patterns and makes a decision by altering its rules. Results: I showed that the agent behaved like a non-Brownian walker and the model adaptively switched between diffusive properties depending on the resource density. This led to a more effective resource-searching performance compared with that of a simple random-walk model. Conclusion: These results demonstrate a process of optimal searching dependent on context.