  Our recent experience with the COVID-19 pandemic amply shows that spatial
effects like the mobility of agents and average interpersonal distance,
together with adaptation of agents, are very important in deciding the outcome
of epidemic dynamics. Structural and dynamical aspects of random geometric
graphs are widely employed in describing processes with a spatial dependence,
such as the spread of an airborne disease. In this work, we investigate the
interplay between spatial factors, such as agent mobility and average
interpersonal distance, and the adaptive responses of individuals to an ongoing
epidemic within the framework of random geometric graphs. We show that such
spatial factors, together with the adaptive behavior of the agents in response
to the prevailing level of global epidemic, can give rise to oscillatory
prevalence even with the classical SIR framework. We characterize in detail the
effects of social adaptation and mobility of agents on the disease dynamics and
obtain the threshold values. We also study the effects of delayed adaptive
response of agents on epidemic dynamics. We show that a delay in executing
non-pharmaceutical spatial mitigation strategies can amplify oscillatory
prevalence tendencies and have non-linear effects on peak prevalence. This
underscores the importance of early implementation of adaptive strategies
coupled with the dissemination of real-time prevalence information to manage
and control the epidemic effectively.
