Besides the inherent benefits of exchanging information and interactions between nodes on a social graph, they can also become a means for the propagation of knowledge. Social graphs have also become a veritable structure for the spread of disease outbreaks. These and its set of protocols are deployed as measures to curb its widespread effects as it has also left network experts puzzled. The recent lessons from the COVID-19 pandemic continue to reiterate that diseases will always be around. Nodal exposure, adoption/diffusion of disease(s) among interacting nodes vis-a-vis migration of nodes that cause further spread of contagion (concerning COVID-19 and other epidemics) has continued to leave experts bewildered towards rejigging set protocols. We model COVID-19 as a Markovian process with node targeting, propagation and recovery using migration-interaction as a threshold feat on a social graph. The migration-interaction design seeks to provision the graph with minimization and block of targeted diffusion of the contagion using seedset(s) nodes with a susceptible-infect policy. The study results showed that migration and interaction of nodes via the mobility approach have become an imperative factor that must be added when modeling the propagation of contagion or epidemics.