Outbreak minimization v.s. influence maximization: an optimization framework

Influence maximization based on threshold models in hypergraphs

Influence maximization problem has received significant attention in recent years due to its application in various domains, such as product recommendation, public opinion dissemination, and disease propagation. This paper proposes a theoretical analysis framework for collective influence in hypergraphs, focusing on identifying a set of seeds that maximize influence in threshold models. First, we extend the message passing method from pairwise networks to hypergraphs to accurately describe the activation process in threshold models. Then, we introduce the concept of hypergraph collective influence (HCI) to measure the influence of nodes. Subsequently, we design an algorithm, HCI-TM, to select the influence maximization set, taking into account both node and hyperedge activation. Numerical simulations demonstrate that HCI-TM outperforms several competing algorithms in synthetic and real-world hypergraphs. Furthermore, we find that HCI can be used as a tool to predict the occurrence of cascading phenomena. Notably, we find that the HCI-TM algorithm works better for larger average hyperdegrees in Erdös-Rényi hypergraphs and smaller power-law exponents in scale-free hypergraphs.

Hyperscaling in the Coherent Hyperspin Machine

Classical and quantum systems are used to simulate the Ising Hamiltonian, an essential component in large-scale optimization and machine learning. However, as the system size increases, devices like quantum annealers and coherent Ising machines face an exponential drop in their success rate. Here, we introduce a novel approach involving high-dimensional embeddings of the Ising Hamiltonian and a technique called "dimensional annealing" to counteract the decrease in performance. This approach leads to an exponential improvement in the success rate and other performance metrics, slowing down the decline in performance as the system size grows. A thorough examination of convergence dynamics in high-performance computing validates the new methodology. Additionally, we suggest practical implementations using technologies like coherent Ising machines, all-optical systems, and hybrid digital systems. The proposed hyperscaling heuristics can also be applied to other quantum or classical Ising devices by adjusting parameters such as nonlinear gain, loss, and nonlocal couplings.

On the firefighter problem with spreading vaccination for maximizing the number of saved nodes: the IP model and LP rounding algorithms

When an infectious disease spreads, how to quickly vaccinate with a limited budget per time step to reduce the impact of the virus is very important. Specifically, vaccination will be carried out in every time step, and vaccinated nodes will no longer be infected. Meanwhile, the protection from vaccination can spread to the neighbors of a vaccinated node. Our goal is to efficiently find optimal and approximation solutions to our problem with various algorithms. In this paper, we first design an integer linear program to solve this problem. We then propose approximation algorithms of (1) Linear programming (LP) deterministic threshold rounding, (2) LP dependent randomized rounding, and (3) LP independent randomized rounding. We prove that the LP independent randomized rounding algorithm has a high probability of finding a feasible solution that gives an approximation ratio of ( 1 - δ ) , where a small constant δ between 0 and 1 reduces the lower bound on the feasibility probability. We also provide experimental results for three different rounding algorithms to show that they perform numerically well in terms of approximation ratios. These analytical and numerical studies allow each individual to adopt the most appropriate approximation algorithm to efficiently resolve the vaccination problem when her reliance on commercial optimization solvers is costly.

Patient allocation method in major epidemics under the situation of hierarchical diagnosis and treatment

OBJECTIVES

Patients are classified according to the severity of their condition and graded according to the diagnosis and treatment capacity of medical institutions. This study aims to correctly assign patients to medical institutions for treatment and develop patient allocation and medical resource expansion schemes among hospitals in the medical network.

METHODS

Illness severity, hospital level, allocation matching benefit, distance traveled, and emergency medical resource fairness were considered. A multi-objective planning method was used to construct a patient allocation model during major epidemics. A simulation study was carried out in two scenarios to test the proposed method.

RESULTS

(1) The single-objective model obtains an unbalanced solution in contrast to the multi-objective model. The proposed model considers multi-objective problems and balances the degree of patient allocation matching, distance traveled, and fairness. (2) The non-hierarchical model has crowded resources, and the hierarchical model assigns patients to matched medical institutions. (3) In the "demand exceeds supply" situation, the patient allocation model identified additional resources needed by each hospital.

CONCLUSION

Results verify the maneuverability and effectiveness of the proposed model. It can generate schemes for specific patient allocation and medical resource amplification and can serve as a quantitative decision-making tool in the context of major epidemics.

Multidimensional hyperspin machine

From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and show that the hyperspin machine finds to a very good approximation the ground state of complex graphs. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call "dimensional annealing". When interpolating between the XY and the Ising model, the dimensional annealing substantially increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.

An iterative algorithm for optimizing COVID-19 vaccination strategies considering unknown supply

BACKGROUND AND OBJECTIVE

The distribution of the newly developed vaccines presents a great challenge in the ongoing SARS-CoV-2 pandemic. Policy makers must decide which subgroups should be vaccinated first to minimize the negative consequences of the pandemic. These decisions must be made upfront and under uncertainty regarding the amount of vaccine doses available at a given time. The objective of the present work was to develop an iterative optimization algorithm, which provides a prioritization order of predefined subgroups. The results of this algorithm should be optimal but also robust with respect to potentially limited vaccine supply.

METHODS

We present an optimization meta-heuristic which can be used in a classic simulation-optimization setting with a simulation model in a feedback loop. The meta-heuristic can be applied in combination with any epidemiological simulation model capable of depicting the effects of vaccine distribution to the modeled population, accepts a vaccine prioritization plan in a certain notation as input, and generates decision making relevant variables such as COVID-19 caused deaths or hospitalizations as output. We finally demonstrate the mechanics of the algorithm presenting the results of a case study performed with an epidemiological agent-based model.

RESULTS

We show that the developed method generates a highly robust vaccination prioritization plan which is proven to fulfill an elegant supremacy criterion: the plan is equally optimal for any quantity of vaccine doses available. The algorithm was tested on a case study in the Austrian context and it generated a vaccination plan prioritization favoring individuals age 65+, followed by vulnerable groups, to minimize COVID-19 related burden.

DISCUSSION

The results of the case study coincide with the international policy recommendations which strengthen the applicability of the approach. We conclude that the path-dependent optimum optimum provided by the algorithm is well suited for real world applications, in which decision makers need to develop strategies upfront under high levels of uncertainty.

Optimization in the Context of COVID-19 Prediction and Control: A Literature Review

This paper presents an overview of some key results from a body of optimization studies that are specifically related to COVID-19, as reported in the literature during 2020-2021. As shown in this paper, optimization studies in the context of COVID-19 have been used for many aspects of the pandemic. From these studies, it is observed that since COVID-19 is a multifaceted problem, it cannot be studied from a single perspective or framework, and neither can the related optimization models. Four new and different frameworks are proposed that capture the essence of analyzing COVID-19 (or any pandemic for that matter) and the relevant optimization models. These are: (i) microscale vs. macroscale perspective; (ii) early stages vs. later stages perspective; (iii) aspects with direct vs. indirect relationship to COVID-19; and (iv) compartmentalized perspective. To limit the scope of the review, only optimization studies related to the prediction and control of COVID-19 are considered (public health focused), and which utilize formal optimization techniques or machine learning approaches. In this context and to the best of our knowledge, this survey paper is the first in the literature with a focus on the prediction and control related optimization studies. These studies include optimization of screening testing strategies, prediction, prevention and control, resource management, vaccination prioritization, and decision support tools. Upon reviewing the literature, this paper identifies current gaps and major challenges that hinder the closure of these gaps and provides some insights into future research directions.

TLQP: Early-stage transportation lock-down and quarantine problem

The advent of COVID-19 is a sensible reminder of the vulnerability of our society to pandemics. We need to be better prepared for finding ways to stem such outbreaks. Except from social distancing and wearing face masks, restricting the movement of people is one important measure necessary to control the spread. Such decisions on the lock-down/reduction of movement should be made in an informed way and, accordingly, modeled as an optimization problem. We propose the Early-stage Transportation Lock-down and Quarantine Problem (TLQP), which can help to decide which parts of the transportation infrastructure of a country should be restricted in early stages. On top of the network-based Susceptible-Exposed-Infectious-Recovered (SEIR) model, we establish a decision recommendation framework, which considers the lock-down of cross-border traffic, internal traffic, and movement inside individual populations. The combinatorial optimization problem aims to find the best set of actions which minimize the social cost of a lock-down. Given the inherent intractability of this problem, we develop a highly-efficient heuristic based on the Effective Distance (ED) path and the Cost-Effective Lazy Forward (CELF) algorithm. We perform and report experiments on the global spread of COVID-19 and show how individual countries may protect their population by taking appropriate measures against the threatening pandemic. We believe that our study contributes to the orchestration of measures for dealing with current and future epidemic outbreaks.