Spatial Dynamics of an Imprecise Epidemic Model With Beddington–DeAngelis Incidence Rate

Due to the incomplete information caused by measurements, data collection, and initial value determination processes, imprecise parameters in epidemic modeling should be taken into account. This paper studies spatial dynamics of an imprecise epidemic model with the Beddington–DeAngelis incidence rate by presenting imprecise parameters as a form of interval parameters. First, Turing instability is analyzed via bifurcation analysis and an interval-valued function. Then, the effects of interval parameters on pattern selection are discussed via multiple scale analysis. We find that an interval parameter does not change the type of patterns on the condition that the value of the interval number of the control parameter lies in the corresponding pattern selection domain. Moreover, we discover that when the incidence rate and diffusion rate are selected as interval numbers, respectively, the type of pattern or the spot pattern either transits orderly or becomes sparse; meanwhile, the spatial density of the infected decreases as the interval variable increases. Moreover, our results show that the effects of both different interval parameters and the same interval parameter with different interval value on the system are different. This paper provides a new perspective to study a spatial epidemic model.