Panic Reactions and Global Disease Dynamics
We analyze spatially extended disease dynamics in a system in which individuals change their dispersal characteristics in response to the local infection level. The key question is to what extent infectious wave front dynamics and the time course of the global infection change in response to host awareness and individuals trying to avoid infection by increased dispersal. We investigate two qualitatively different responses to the local degree of infection. In one system (panic reaction) the local diffusion coefficient increases with the concentration of infecteds, in the other system (directed reaction) individuals drift proportional to infection level gradients. Also, a third, non-local system (strategic flight) is studied where individuals are repelled from areas with high infection level depending on the distance.For all systems we develop a mean field model. Although one expects that the individual rationale of avoiding an epidemic wave mitigates disease dynamics we find extended parameter regimes in which this rationale actually facilitates epidemic spread. Only the non-local population response is found to be capable of containing an epidemic in the mean field model – also, the non-local system shows some interesting complex spatio-temporal patterns. Finally, we investigate the dynamics of a fully stochastic system in which the effects prevail but which also show an increased extinction probability of the epidemic as a function of increasing dispersal response.
So far, we have investigated the dynamics on a regular lattice which serves as a convenient toy model in which the effects of the different population responses can be studied. Currently, we are extending our formalism to incorporate the modern human travel behavior's long distance jumps. Then we can test whether the (both negative and positive) effects of population responses are also visible in more realistic scenarios.
