Optimal curing policy for epidemic spreading over a community network with heterogeneous population

Ottaviano, Stefania; Pellegrini, Francesco De; Bonaccorsi, Stefano; Mieghem, Piet Van

doi:10.1093/comnet/cnx060

Cited by 22 publications

(20 citation statements)

References 56 publications

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“…Even though the objective function is a spectral radius, which in general is non-convex, under reasonable assumptions on the cost function, tools from geometric programming and convex optimization can be leveraged to tackle the problem. Solutions have been proposed in a centralized fashion [101][102][103][104], and through distributed approaches [105][106][107][108][109]. Some of these works deal with a more general problem, in which, besides increasing the recovery rate, the controller can also reduce the infection rates λ i modeling, for instance, the distribution of personal protective equipment.…”

Section: Control Of Deterministic Epidemics On Static Networkmentioning

confidence: 99%

Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

Zino,

Cao

2021

Preprint

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During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention policies should be implemented. The study of these models -grounded in the systems theory and often analyzed using control-theoretic tools -is an extremely important research area for many researchers from different fields, including epidemiology, engineering, physics, mathematics, computer science, sociology, economics, and management. In this survey, we review the history and present the state of the art in the modeling, analysis, and control of epidemic dynamics. We discuss different approaches to epidemic modeling, either deterministic or stochastic, ranging from the first implementations of scalar systems of differential equations to describing the epidemic spreading at the population level, and to more recent models on dynamic networks, which capture the spatial spread and the time-varying nature of human interactions. Brief History of 260 years of Mathematical Models of EpidemicsSince the beginning of human history, pandemics have posed deadly threats, which often decimated our species. Hence, it was not surprising that, in parallel with the theoretical development of calculus, mathematicians started to apply their theoretical paradigms to describe, study, and unveil the mechanisms of spreading of infectious diseases. In this vein, the first milestone can be found in the work on smallpox by Daniel Bernoulli [1], published in 1760. In the 18th century, there was an ongoing public debate about variolation, i.e., inoculation of infectious material from smallpox cases to induce a mild infection and lifelong immunity. In Bernoulli's work, the Dutch-born Swiss mathematician built a mathematical

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Section: Control Of Deterministic Epidemics On Static Networkmentioning

confidence: 99%

Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

Zino,

Cao

2021

Preprint

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“…The advantage with resource allocation optimization models include the compartmentalization of the population into various heterogeneous segments and the ability to expand the set of alternative allocations, often in a finite time, not just in a long term horizon as in the case of equilibrium models discussed in the second sub-section of the third section. They can also be formulated to account for nonlinearities and as a linear programming problem, as done in (ReVelle et al, 1969), or semidefinite programming by making use of the spectral properties of the network (Ottaviano et al, 2018). Also, different health interventions can be applied to different compartments or independent populations with differential infection rates (Brandeau, 2003).…”

Section: Approaches To Resource Allocationmentioning

confidence: 99%

Epidemic Control and Resource Allocation: Approaches and Implications for the Management of COVID-19

Nyiwul

2021

Studies in Microeconomics

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The experience with COVID-19 underscores a classic public policy choice problem: how should policymakers determine how to allocate constrained budgets, limited equipment, under-resourced hospitals and stretched personnel to limit the spread of the virus. This article presents an overview of the general literature on resource allocation in epidemics and assess how it informs our understanding of COVID-19. We highlight the peculiarities of the pandemic that call for a rethinking of existing approaches to resource allocation. In particular, we analyse how the experience of COVID-19 informs our understanding and modelling of the optimal resource allocation problem in epidemics. Our delineation of the literature focuses on resource constraint as the key variable. A qualitative appraisal indicates that the current suit of models for understanding the resource allocation problem requires adaptations to advance our management of COVID-19 or similar future epidemics. Particularly under-studied areas include issues of uncertainty, potential for co-epidemics, the role of global connectivity, and resource constrained problems arising from depressed economic activity. Incorporating various global dimensions of COVID-19 into resource allocation modelling such a centralized versus decentralized resource control and the role of geostrategic interests could yield crucial insights. This will require multi-disciplinary approaches to the resource allocation problem. JEL Classifications: I14, I18, E61, D60, H4, H12

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“…Here, the cells N 1 , ..., N r are disjoint subsets of the node set N , such that N = N 1 ∪ ... ∪ N r . We adapt the definition of equitable partitions in [21,25] as:…”

Section: Related Workmentioning

confidence: 99%

Clustering for epidemics on networks: a geometric approach

Prasse,

Devriendt,

Van Mieghem

2021

Preprint

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Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is a tremendous challenge to analysing and controlling an epidemic outbreak. For some contact networks, it is possible to group individuals into clusters. A high-level description of the epidemic between a few clusters is considerably simpler than on an individual level. However, to cluster individuals, most studies rely on equitable partitions, a rather restrictive structural property of the contact network. In this work, we focus on Susceptible-Infected-Susceptible (SIS) epidemics, and our contribution is threefold. First, we propose a geometric approach to specify all networks for which an epidemic outbreak simplifies to the interaction of only a few clusters. Second, for the complete graph and any initial viral state vectors, we derive the closed-form solution of the nonlinear differential equations of the N -Intertwined Mean-Field Approximation (NIMFA) of the SIS process. Third, by relaxing the notion of equitable partitions, we derive low-complexity approximations and bounds for epidemics on arbitrary contact networks. Our results are an important step towards understanding and controlling epidemics on large networks.

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Optimal curing policy for epidemic spreading over a community network with heterogeneous population

Cited by 22 publications

References 56 publications

Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

Epidemic Control and Resource Allocation: Approaches and Implications for the Management of COVID-19

Clustering for epidemics on networks: a geometric approach

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