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In this paper, we present a discrete-time networked SEIR model using population flow, its derivation, and assumptions under which this model is well defined. We identify properties of the system's equilibria, namely the healthy states. We show that the set of healthy states is asymptotically stable, and that the value of the equilibria becomes equal across all sub-populations as a result of the network flow model. Furthermore, we explore closed-loop feedback control of the system by limiting flow between sub-populations as a function of the current infected states. These results are illustrated via simulation based on flight traffic between major airports in the United States. We find that a flow restriction strategy combined with a vaccine roll-out significantly reduces the total number of infections over the course of an epidemic, given that the initial flow restriction response is not delayed. I. INTRODUCTIONGlobal interconnectivity has proven to be a key factor in the propagation of infectious diseases [1], [2]. Most recently, we have seen evidence of such connectivity through the rapid spread of the COVID-19 pandemic, which propagated from its origin in Wuhan, China to every major population center globally in a matter of weeks [3]. Given the implications of global population flow on disease spread, it becomes important to accurately model this flow, as reliable modeling is an essential step to developing effective and efficient mitigation strategies. Various infection models have been proposed based on characteristics of individual pathogens and studied in the literature, including susceptible-infected-susceptible (SIS), susceptible-infected-removed (SIR), and susceptible-infected-removed-susceptible (SIRS) [4], [5]. For this paper, we consider the recent COVID-19 pandemic as a motivating case for the model selection and construction. Due to the delay in onset of COVID-19 symptoms [6]-[9] and large asymptomatic populations estimated between 17 − 81% [10]-[13], we choose the susceptible-exposed-infected-removed (SEIR) model as the foundation of our model development. Previous work involving the incorporation of population flows in epidemic process models include analysis of a networked SIS model with flows [14] as well as using a networked SIR model with flows to predict arrival times for various epidemics using global flight data [15], where both models are developed in continuous time. This paper uses similar derivation techniques to define our discrete-time epidemic model. However, we contribute to the development of such models by including the exposed state in our model formulation, as well as provide analysis of the discrete time dynamics. While other work has considered capturing the effect of transportation on the spread of COVID-19 using the SEIR model [16], the key distinction in this work is that infection propagation over the network is modeled by the relocation of infected individuals

The study of evaporation patterns of liquid drops is a growing field of research with numerous applications in inkjet printing, controlled particle deposition, self-assembly, etc. After the liquid in a drop completely evaporates, it leaves behind the constituent particles in various patterns on the substrate. This depends on factors such as ambient temperature, substrate’s thermal conductivity, particle size, and density. Ferrofluids are known to show a variety of magnetic field dependent properties. Controllable evaporation using ferrofluids can result in desired patterns of particles on a substrate. However, before studying the evaporation of these nanofluids in the presence of magnetic field, their drying behavior under ambient conditions needs to be studied. Here, kerosene-based ferrofluid droplets were allowed to evaporate under ambient conditions. Video analysis of particle motion showed a Marangoni flow inside the drop. At the early stages of evaporation, non-interacting Marangoni instability loops were observed with equidistant empty lines between them propagating in the radial direction. These lines merged in the later stages of evaporation. The particles moved from the center toward the contact line and reversed their direction at a very close distance from the contact line, moving toward the top of the drop through the liquid–air interface. The distance of the point of reverse motion, called the stagnation point, was measured from the contact line, and it agrees with an existing theory. Moreover, the measurements of contact angle and mass evolution indicate that this evaporation follows the model of thin droplets. After drying, the ring pattern was observed on the substrate with a central accumulation of particles. The region between the central accumulation and the outer ring was seen to be empty. The size of this empty region decreased with increasing droplet size and increasing volume fraction of the nanoparticles. This study may help in understanding the drying behavior of magnetic nanofluids under ambient conditions for self-assembly and inkjet printing applications. The drying behavior in the presence of external magnetic field will be discussed in the future.