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Pandemics often involve complex transmission dynamics in which epidemiological surveillance is essential but not sufficient for containment, as resurgence may be driven by emerging or imported variants. Rapidly evolving pathogens produce complex disease dynamics driven by emerging variants often differing in their transmissibility, immune escape, and cross-infection. These processes influence individuals’ immune life histories, producing highly dynamic immune landscapes that modulate the emergence and dominance of novel variants. We develop an integrated modeling framework that couples multivariant mean-field epidemic modeling with a mechanistic genomic dominance model and a probabilistic surveillance model. This study examines how variant emergence timing, infectiousness advantage, and cross-infection jointly shape epidemic trajectories, immune landscapes, and genomic composition. Our results demonstrate that the dominance dynamics of cocirculating variants correspond to a selective sweep characterized by a system of multilogistic equations driven by population immunity. Moreover, we show that the detection time of newly introduced variants can be accelerated or delayed depending on their emergence conditions and the prevailing variant landscape. Finally, we demonstrate that the effectiveness of response strategies depends critically on the evolving genomic composition of the outbreak, highlighting trade-offs between surveillance sensitivity and intervention timing. We validate our framework by jointly fitting epidemiological and genomic data from the spread of the Ancestral, Alpha, Gamma, and Delta variants in the United States, Denmark, the United Kingdom, and Canada. The results provide a quantitative foundation for linking epidemic dynamics, genomic surveillance, and immune life histories, advancing the development of genomic epidemiology for multivariant outbreaks. 

Abstract Allocating students to schools or universities, people to teams or groups, people to urban housing, and matching users on social platforms are prominent examples of allocating limited goods, spaces, or positions to optimize social welfare. We study a welfare maximization problem that arises when such resource allocation scenarios involve peer effects, where people have preferences over the others who are nearby (e.g. their classmates, teammates, neighbors, or partners). We first develop a unified mathematical framework for this “position allocation problem,” which assigns people to positions in a given network, with people caring about both their positions and their neighbors’ attributes. We show that welfare maximization for the corresponding position allocation problem is computationally intractable, even when people have preferences that depend only on who is allocated to nearby positions, and those preferences satisfy simple constraints that arise naturally in urban and other real-world systems. In contrast to this computational lower bound, we show that if people can be classified into a fixed number of (demographic) groups and the network satisfies certain realistic spatial conditions, then efficiently computable allocations can be obtained for many natural scenarios. Importantly, the achieved social welfare is either optimal or arbitrarily close to optimal for natural forms of preferences. Our methods provide a foundation for position allocation with peer effects, and guide the design of optimal allocation strategies when people can be classified into a fixed number of groups in which members share similar preferences. 

The Russian invasion of Ukraine in February 2022 has led to the largest forced migration crisis in Europe since World War II, with millions displaced both internally and internationally. Among the displaced, approximately 4.2 million individuals have returned, highlighting the significance of return migration as a critical phase in the migration continuum. Existing studies on return migration are limited in scope, relying on survey-based approaches that suffer from demographic bias, lack of validation against ground truth, and inability to account for uncertainty. We propose a novel computational framework for modeling the return of conflict-induced migrants, using agent-based models (ABMs) and their surrogates. These models are grounded in hazard functions and account for sociopolitical contexts. Our proposed ABMs outperform baseline methods in estimating return migration from Poland to Ukraine by at least 42% and by as much as 57% in terms of normalized root mean squared error (NRMSE). Further, to illustrate the utility of such models for policymakers, we conduct two case studies that estimate the duration of displacement and characterize the demographic breakdown among the returnees. 

Discrete dynamical systems serve as useful formal models to study diffusion phenomena in social networks. Several recent articles have studied the algorithmic and complexity aspects of some decision problems on synchronous Boolean networks, which are discrete dynamical systems whose underlying graphs are directed, and may contain directed cycles. Such problems can be regarded as reachability problems in the phase space of the corresponding dynamical system. Previous work has shown that some of these decision problems become efficiently solvable for systems on directed acyclic graphs (DAGs). Motivated by this line of work, we investigate a number of decision problems for dynamical systems whose underlying graphs are DAGs. We show that computational intractability (i.e.,PSPACE-completeness) results for reachability problems hold even for dynamical systems on DAGs. We also identify some restricted versions of dynamical systems on DAGs for which reachability problem can be solved efficiently. In addition, we show that a decision problem (namely, Convergence), which is efficiently solvable for dynamical systems on DAGs, becomesPSPACE-complete for Quasi-DAGs (i.e., graphs that become DAGs by the removal of asingleedge). In the process of establishing the above results, we also develop several structural properties of the phase spaces of dynamical systems on DAGs. 

Abstract This paper describes Epihiper, a state-of-the-art, high performance computational modeling framework for epidemic science. The Epihiper modeling framework supports custom disease models, and can simulate epidemics over dynamic, large-scale networks while supporting modulation of the epidemic evolution through a set of user-programmable interventions. The nodes and edges of the social-contact network have customizable sets of static and dynamic attributes which allow the user to specify intervention target sets at a very fine-grained level; these also permit the network to be updated in response to nonpharmaceutical interventions, such as school closures. The execution of interventions is governed by trigger conditions, which are Boolean expressions formed using any of Epihiper’s primitives (e.g. the current time, transmissibility) and user-defined sets (e.g. people with work activities). Rich expressiveness, extensibility, and high-performance computing responsiveness were central design goals to ensure that the framework could effectively target realistic scenarios at the scale and detail required to support the large computational designs needed by state and federal public health policymakers in their efforts to plan and respond in the event of epidemics. The modeling framework has been used to support the CDC Scenario Modeling Hub for COVID-19 response, and was a part of a hybrid high-performance cloud system that was nominated as a finalist for the 2021 ACM Gordon Bell Special Prize for high performance computing-based COVID-19 Research. 

Networks allow us to describe a wide range of interaction phenomena that occur in complex systems arising in such diverse fields of knowledge as neuroscience, engineering, ecology, finance, and social sciences. Until very recently, the primary focus of network models and tools has been on describing the pairwise relationships between system entities. However, increasingly more studies indicate that polyadic or higher-order group relationships among multiple network entities may be the key toward better understanding of the intrinsic mechanisms behind the functionality of complex systems. Such group interactions can be, in turn, described in a holistic manner by simplicial complexes of graphs. Inspired by these recently emerging results on the utility of the simplicial geometry of complex networks for contagion propagation and armed with a large-scale synthetic social contact network (also known as a digital twin) of the population in the U.S. state of Virginia, in this paper, we aim to glean insights into the role of higher-order social interactions and the associated varying social group determinants on COVID-19 propagation and mitigation measures. 

Discrete dynamical systems are commonly used to model the spread of contagions on real-world networks. Under the PAC framework, existing research has studied the problem of learning the behavior of a system, assuming that the underlying network is known. In this work, we focus on a more challenging setting: to learn both the behavior and the underlying topology of a black-box system. We show that, in general, this learning problem is computationally intractable. On the positive side, we present efficient learning methods under the PAC model when the underlying graph of the dynamical system belongs to certain classes. Further, we examine a relaxed setting where the topology of an unknown system is partially observed. For this case, we develop an efficient PAC learner to infer the system and establish the sample complexity. Lastly, we present a formal analysis of the expressive power of the hypothesis class of dynamical systems where both the topology and behavior are unknown, using the well-known Natarajan dimension formalism. Our results provide a theoretical foundation for learning both the topology and behavior of discrete dynamical systems. 

The SARS-CoV-2 pandemic has generated a considerable number of infections and associated morbidity and mortality across the world. Recovery from these infections, combined with the onset of large-scale vaccination, have led to rapidly-changing population-level immunological landscapes. In turn, these complexities have highlighted a number of important unknowns related to the breadth and strength of immunity following recovery or vaccination. Using simple mathematical models, we investigate the medium-term impacts of waning immunity against severe disease on immuno-epidemiological dynamics. We find that uncertainties in the duration of severity-blocking immunity (imparted by either infection or vaccination) can lead to a large range of medium-term population-level outcomes (i.e. infection characteristics and immune landscapes). Furthermore, we show that epidemiological dynamics are sensitive to the strength and duration of underlying host immune responses; this implies that determining infection levels from hospitalizations requires accurate estimates of these immune parameters. More durable vaccines both reduce these uncertainties and alleviate the burden of SARS-CoV-2 in pessimistic outcomes. However, heterogeneity in vaccine uptake drastically changes immune landscapes toward larger fractions of individuals with waned severity-blocking immunity. In particular, if hesitancy is substantial, more robust vaccines have almost no effects on population-level immuno-epidemiology, even if vaccination rates are compensatorily high among vaccine-adopters. This pessimistic scenario for vaccination heterogeneity arises because those few individuals that are vaccine-adopters are so readily re-vaccinated that the duration of vaccinal immunity has no appreciable consequences on their immune status. Furthermore, we find that this effect is heightened if vaccine-hesitants have increased transmissibility (e.g. due to riskier behavior). Overall, our results illustrate the necessity to characterize both transmission-blocking and severity-blocking immune time scales. Our findings also underline the importance of developing robust next-generation vaccines with equitable mass vaccine deployment.