Epidemiological spreading processes constitute the core of a large number of disparate networks. In some, faster spread is desirable, in others containing the spread is critically important. We focus on understanding the spatio-temporal spread of epidemics over contact networks with the goal of facilitating or containing the spread as the case may be. In this study, we choose specific systems as exemplars of instances where the spread is desirable (e.g., Vehicle-to-Everything; V2X) and others where the spread is harmful (e.g., spread of infectious diseases). In transportation systems, vehicles are expected to exchange messages with each other and with bikers, pedestrians, wheelchairs (Vehicle-to-Vehicle; V2V) and with signaling infrastructure on the roadways (Infrastructure-to-Vehicle; I2V) (together, V2X). We seek to qualitatively understand and subsequently quantitatively model the impact of complex, various interdependencies between wireless communication (spread of information through evolving links) and vehicular mobility (spatial movements of nodes). Towards this end, we introduce epidemiological modeling into transportation systems, a novel concept geared towards V2X, in which the computations remain tractable even for large, complex transportation networks. We additionally accommodate arbitrary traffic synchronization patterns corresponding for example to the presence of an arbitrary number of traffic signals. Furthermore, numerical computations using our mathematical framework reveal several questions that influence the practice of V2X network design and security. Next, suppressing spread of infectious diseases is clearly of critical importance. Recently COVID-19 pandemic has wrecked havoc on lives and livelihoods worldwide. We explore the costs and benefits of a new tracing and testing concept towards containing COVID-19. We propose to preemptively identify the contact chain by testing primary, secondary, tertiary or further-off contacts of those who test positive, more specifically, the k-hop contacts for a parameter k of choice. We evaluate the costs and benefits of this novel multi-hop testing strategy for various reported disease parameters and on diverse human contact patterns, and see if the cost-benefit tradeoffs may be substantially enhanced through the deployment of the strategy. Furthermore, we propose an analytical methodology for evaluating multi-hop contact tracing strategy by combining the multi-hop contact tracing dynamics and the virus transmission mechanism in a single framework using microscopic Markov Chain approach.