Global dynamics of a reaction-diffusion malaria model
This paper studies the global dynamics of a spatial Lotka-Volterra model. The model describes two interacting species in a river. These species are in competition. The paper studies global dynamics as opposed to local: the goal is to establish a ``phase diagram'' that describes the effect of different parameter regimes on the qualitative behaviour of the model. The main results of this paper are classifications of different regimes controlled by model parameters, shown in figures 1 and 2. The authors impose a symmetry on the death rates, assumption (H). After imposing this symmetry, the growth rates \(r_1\) and \(r_2\) of the two species control whether the system tends to fall into one of four asymptotic behaviors. These behaviours consist of extinction of both species, competitive exclusion, bistability, and coexistence. This paper is primarily relevant to theoretical ecologists and mathematical biologists. The approach may also be applicable to other structured population models, although this point is not mentioned by the authors.
scientific article; zbMATH DE number 7457486
scientific article