Our recent experience with COVID19 amply shows that spatial effects like mobility and average interpersonal distance are very important in deciding the outcome of an epidemic dynamics. Spatial connectivity structure of a population is usually modelled via Random Geometric Graphs which are networks generated from spatially distributed components where connections between components are made based on a distance-dependent probability measure. Structural and dynamical aspects of such graphs are important in describing processes with a spatial dependence such as the spread of an airborne disease. In this work, using a simple computational model of an epidemic, we investigate how spatial factors like average separation between individuals and their mobility affect the spread of a disease. We show that such spatial factors can give rise to oscillatory prevalence in a society of adaptive individuals. We also show that delays in executing non-pharmaceutical spatial mitigation strategies can accentuate oscillatory prevalence and can have non-monotonic effects on the peak prevalence. In both cases, we characterize the effects of different parameters on the prevalence of the disease and peak infection and obtain threshold values.
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