scholarly journals Searching for the most cost-effective strategy for controlling epidemics spreading on regular and small-world networks

2011 ◽  
Vol 9 (66) ◽  
pp. 158-169 ◽  
Author(s):  
Adam Kleczkowski ◽  
Katarzyna Oleś ◽  
Ewa Gudowska-Nowak ◽  
Christopher A. Gilligan
Keyword(s):  
Long Range ◽  
Optimal Strategy ◽  
Small World ◽  
Cost Effective ◽  
Optimal Size ◽  
Small World Networks ◽  
Reproduction Ratio ◽  
Local Strategy ◽  
The Cost ◽  
Number Of Individuals

We present a combined epidemiological and economic model for control of diseases spreading on local and small-world networks. The disease is characterized by a pre-symptomatic infectious stage that makes detection and control of cases more difficult. The effectiveness of local (ring-vaccination or culling) and global control strategies is analysed by comparing the net present values of the combined cost of preventive treatment and illness. The optimal strategy is then selected by minimizing the total cost of the epidemic. We show that three main strategies emerge, with treating a large number of individuals (global strategy, GS), treating a small number of individuals in a well-defined neighbourhood of a detected case (local strategy) and allowing the disease to spread unchecked (null strategy, NS). The choice of the optimal strategy is governed mainly by a relative cost of palliative and preventive treatments. If the disease spreads within the well-defined neighbourhood, the local strategy is optimal unless the cost of a single vaccine is much higher than the cost associated with hospitalization. In the latter case, it is most cost-effective to refrain from prevention. Destruction of local correlations, either by long-range (small-world) links or by inclusion of many initial foci, expands the range of costs for which the NS is most cost-effective. The GS emerges for the case when the cost of prevention is much lower than the cost of treatment and there is a substantial non-local component in the disease spread. We also show that local treatment is only desirable if the disease spreads on a small-world network with sufficiently few long-range links; otherwise it is optimal to treat globally. In the mean-field case, there are only two optimal solutions, to treat all if the cost of the vaccine is low and to treat nobody if it is high. The basic reproduction ratio, R 0 , does not depend on the rate of responsive treatment in this case and the disease always invades (but might be stopped afterwards). The details of the local control strategy, and in particular the optimal size of the control neighbourhood, are determined by the epidemiology of the disease. The properties of the pathogen might not be known in advance for emerging diseases, but the broad choice of the strategy can be made based on economic analysis only.

INFLUENCE OF THE INITIAL SOURCE OF EPIDEMIC AND PREVENTIVE VACCINATION ON THE SPREADING PHENOMENA IN A TWO-DIMENSIONAL LATTICE

2004 ◽  
Vol 15 (06) ◽  
pp. 755-765 ◽  
Author(s):  
R. A. KOSIŃSKI ◽  
Ł. ADAMOWSKI
Keyword(s):  
Long Range ◽  
Probabilistic Model ◽  
Small World ◽  
Two Dimensional ◽  
Small World Networks ◽  
Spreading Process ◽  
Dimensional Lattice ◽  
Epidemic Curve ◽  
Preventive Vaccination ◽  
Initial Source

The probabilistic model of epidemic in a two-dimensional lattice with an additional random, long range connections characteristic for the small world networks is presented. Relations describing the spreading process of epidemics, like epidemic curve or range of epidemic in time, were found. The influence of the borders of the lattice and the localization of the initial source of epidemic on the epidemic curve is found analytically. The application of the preventive vaccination in the population is discussed.

Fractal aggregation on small-world networks with long-range deposition

Fractals ◽  
2020 ◽  
Author(s):  
Ren-Fei Wang ◽  
Sheng-Jun Wang ◽  
Zi-Gang Huang
Keyword(s):  
Long Range ◽  
Small World ◽  
Small World Networks

EXISTENCE, COST AND ROBUSTNESS OF SPATIAL SMALL-WORLD NETWORKS

2007 ◽  
Vol 17 (07) ◽  
pp. 2331-2342 ◽  
Author(s):  
P. DE LOS RIOS ◽  
T. PETERMANN
Keyword(s):  
Euclidean Space ◽  
Long Range ◽  
Communication Systems ◽  
Large Scale ◽  
Probability Distributions ◽  
Flow Distribution ◽  
Small World ◽  
Electronic Circuits ◽  
Small World Networks ◽  
Network Cost

Small-world networks embedded in Euclidean space represent useful cartoon models for a number of real systems such as electronic circuits, communication systems, the large-scale brain architecture and others. Since the small-world behavior relies on the presence of long-range connections that are likely to have a cost which is a growing function of the length, we explore whether it is possible to choose suitable probability distributions for the shortcut lengths so as to preserve the small-world feature and, at the same time, to minimize the network cost. The flow distribution for such networks, and their robustness, are also investigated.

scholarly journals Asymptotic Behaviour of Gossip Processes and Small-World Networks

2013 ◽  
Vol 45 (4) ◽  
pp. 981-1010 ◽  
Author(s):  
A. D. Barbour ◽  
G. Reinert
Keyword(s):  
Long Range ◽  
Branching Process ◽  
Small World ◽  
Random Variable ◽  
Random Networks ◽  
Small World Networks ◽  
Transmission Of Information ◽  
Characteristic Behaviour ◽  
Typical Distances ◽  
Common Behaviour

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.

scholarly journals Asymptotic Behaviour of Gossip Processes and Small-World Networks

2013 ◽  
Vol 45 (04) ◽  
pp. 981-1010 ◽  
Author(s):  
A. D. Barbour ◽  
G. Reinert
Keyword(s):  
Long Range ◽  
Branching Process ◽  
Small World ◽  
Random Variable ◽  
Random Networks ◽  
Small World Networks ◽  
Transmission Of Information ◽  
Characteristic Behaviour ◽  
Typical Distances ◽  
Common Behaviour

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.

Is Verifying Frequently an Optimal Strategy? A Belief-Based Model of Verification

2020 ◽  
Author(s):  
Aditya U. Kulkarni ◽  
Alejandro Salado ◽  
Christian Wernz ◽  
Peng Xu
Keyword(s):  
System Design ◽  
Optimal Strategy ◽  
Theoretical Foundation ◽  
Cost Effective ◽  
Single System ◽  
System Requirement ◽  
System Requirements ◽  
The Cost ◽  
Verification Strategy ◽  
Stakeholder Needs

Abstract Verification activities increase an engineering team’s confidence in its system design meeting system requirements, which in turn are derived from stakeholder needs. Conventional wisdom suggests that the system design should be verified frequently to minimize the cost of rework as the system design matures. However, this strategy is based more on experience of engineers than on a theoretical foundation. In this paper, we develop a belief-based model of verification of system design, using a single system requirement as an abstraction, to determine the conditions under which it is cost effective for an organization to verify frequently. We study the model for a broad set of growth rates in verification setup and rework costs. Our results show that verifying a system design frequently is not always an optimal verification strategy. Instead, it is only an optimal strategy when the costs of reworking a faulty design increase at a certain rate as the design matures.

scholarly journals Kleinberg Navigation on Anisotropic Lattices

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
J. M. Campuzano ◽  
J. P. Bagrow ◽  
D. ben-Avraham
Keyword(s):  
Long Range ◽  
Power Law ◽  
Finite Size ◽  
Small World ◽  
Small World Networks ◽  
Infinite Lattice ◽  
Preferred Direction ◽  
Lattice Size ◽  
Anisotropic Lattices ◽  
Anisotropy Strength

We study the Kleinberg problem of navigation in small-world networks when the underlying lattice is stretched along a preferred direction. Extensive simulations confirm that maximally efficient navigation is attained when the length r of long-range links is taken from the distribution P(r)∼r−α, when the exponent α is equal to 2, the dimension of the underlying lattice, regardless of the amount of anisotropy, but only in the limit of infinite lattice size, L→∞. For finite size lattices we find an optimal α(L) that depends strongly on L. The convergence to α=2 as L→∞ shows interesting power-law dependence on the anisotropy strength.

scholarly journals Cost-effectiveness analysis on measles transmission with vaccination and treatment intervention

2021 ◽  
Vol 6 (11) ◽  
pp. 12491-12527
Author(s):  
Shinta A. Rahmayani ◽  
◽  
Dipo Aldila ◽  
Bevina D. Handari
Keyword(s):  
Medical Treatment ◽  
Optimal Strategy ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Cost Effective ◽  
Qualitative Behaviour ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Effective Analysis

<abstract><p>A deterministic model which describes measles' dynamic using newborns and adults first and second dose of vaccination and medical treatment is constructed in this paper. Mathematical analysis about existence of equilibrium points, basic reproduction number, and bifurcation analysis conducted to understand qualitative behaviour of the model. For numerical purposes, we estimated the parameters' values of the model using monthly measles data from Jakarta, Indonesia. Optimal control theory was applied to investigate the optimal strategy in handling measles spread. The results show that all controls succeeded in reducing the number of infected individuals. The cost-effective analysis was conducted to determine the best strategy to reduce number of infected individuals with the lowest cost of intervention. Our result indicates that the use of the first dose measles vaccine with medical treatment is the most optimal strategy to control measles transmission.</p></abstract>

scholarly journals AN ATTEMPT TO INTRODUCE LONG-RANGE INTERACTIONS INTO SMALL-WORLD NETWORKS

2010 ◽  
Vol 24 (07) ◽  
pp. 671-679 ◽  
Author(s):  
CHUN-YANG WANG ◽  
XIANG-MU KONG
Keyword(s):  
Critical Temperature ◽  
Long Range ◽  
Gaussian Model ◽  
Small World ◽  
Classical Case ◽  
Critical Properties ◽  
Small World Networks ◽  
Lattice Systems ◽  
Spin Lattice ◽  
Long Range Interactions

Distinguishing the long-range bonds with the regular ones, the critical temperature of the spin-lattice Gaussian model built on two typical small-world networks is studied. The results show much difference from the classical case, and thus may induce some more accurate discussion on the critical properties of the spin-lattice systems combined with the small-world networks.

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