Self-organized patchiness in malaria: a deterministic signal in an ocean of noise
Considerable attention has been given in ecology to critical transitions in a number of ecosystems where coexisting, alternative steady states, lead to the occurrence of tipping points with a slowly varying parameter in time. Only recently, the possibility of similar bifurcations have been found in models for the population of an infectious disease, malaria, in the presence of re-infection or super-infection. The consequences of such alternative steady states for the spatio-temporal dynamics of the disease remain unexplored.
With a reaction-diffusion system for the coupled dynamics of transmission between mosquitoes and humans, we investigate the spatio-temporal patterns arising in the absence of any underlying spatial heterogeneity. In particular, we determine conditions leading to self-organized Turin structures, and to the formation of emergent disease hotspots in homogeneous environments. We show that these conditions are related to those allowing for bi-stability of equilibria. Consideration of more realistic representations for human and mosquito movement enhance the feasibility of these patterns.
Thus super-infection (and re-infection), important processes in the transmission dynamics of malaria, can lead to ‘intrinsic’ spatial patterns in the absence of environmental variability. Ways to detect the existence of alternative steady-states and associated spatial patterns are under investigation for the disease.