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Efficient control of epidemics spreading on networks: balance between treatment and recovery.

Oleś K, Gudowska-Nowak E, Kleczkowski A - PLoS ONE (2013)

Bottom Line: The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease.However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results.Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.

View Article: PubMed Central - PubMed

Affiliation: M. Kac Complex Systems Research Center and M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland. kas@cs.stir.ac.uk

ABSTRACT
We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.

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Related in: MedlinePlus

(a) Definition of the von Neumann neighborhood of different values of order , as used in the simulations and analysis.(b) Illustration of spread of a disease (model 1) on a regular network with additional randomly chosen long-range links represented by curved lines (approximation of a small-world network). The applied control of radius  is centered on node D (yellow shaded area). Note that in model 1 the R individuals are excluded from the control and thus non-treated. (c) Representation of model 2: All individuals contained in the control neighbourhood of order  are preventively treated and moved to V class. In both models treatment does not take into account individuals connected by additional long-range links. S, I, D, R symbols stand for Susceptible, Pre-symptomatic, Symptomatic and Recovered, respectively. The order  of infection neighbourhood equals  in (b) and (c).
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pone-0063813-g001: (a) Definition of the von Neumann neighborhood of different values of order , as used in the simulations and analysis.(b) Illustration of spread of a disease (model 1) on a regular network with additional randomly chosen long-range links represented by curved lines (approximation of a small-world network). The applied control of radius is centered on node D (yellow shaded area). Note that in model 1 the R individuals are excluded from the control and thus non-treated. (c) Representation of model 2: All individuals contained in the control neighbourhood of order are preventively treated and moved to V class. In both models treatment does not take into account individuals connected by additional long-range links. S, I, D, R symbols stand for Susceptible, Pre-symptomatic, Symptomatic and Recovered, respectively. The order of infection neighbourhood equals in (b) and (c).

Mentions: We assume that individuals are located at nodes of a square lattice that represents geographical distribution of hosts, see fig. 1. On this lattice, we define a local infection neighbourhood of order as a von Neumann neighbourhood. In that neighbourhood individuals are included, involving the central one. We additionally define as corresponding to this central individual, which means that this individual is not in contact with anyone, while corresponds to the whole population, see fig. 1. To increase realism of our analysis, we also consider the small-world model [24], [25] which adds a certain number of links among randomly chosen nodes, thus adding some long-range connections to the regular lattice ones [24]. Although the disease can spread along these long-range links, we assume that they are so difficult to identify that they are not included in any treatment strategy (see below).


Efficient control of epidemics spreading on networks: balance between treatment and recovery.

Oleś K, Gudowska-Nowak E, Kleczkowski A - PLoS ONE (2013)

(a) Definition of the von Neumann neighborhood of different values of order , as used in the simulations and analysis.(b) Illustration of spread of a disease (model 1) on a regular network with additional randomly chosen long-range links represented by curved lines (approximation of a small-world network). The applied control of radius  is centered on node D (yellow shaded area). Note that in model 1 the R individuals are excluded from the control and thus non-treated. (c) Representation of model 2: All individuals contained in the control neighbourhood of order  are preventively treated and moved to V class. In both models treatment does not take into account individuals connected by additional long-range links. S, I, D, R symbols stand for Susceptible, Pre-symptomatic, Symptomatic and Recovered, respectively. The order  of infection neighbourhood equals  in (b) and (c).
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3672130&req=5

pone-0063813-g001: (a) Definition of the von Neumann neighborhood of different values of order , as used in the simulations and analysis.(b) Illustration of spread of a disease (model 1) on a regular network with additional randomly chosen long-range links represented by curved lines (approximation of a small-world network). The applied control of radius is centered on node D (yellow shaded area). Note that in model 1 the R individuals are excluded from the control and thus non-treated. (c) Representation of model 2: All individuals contained in the control neighbourhood of order are preventively treated and moved to V class. In both models treatment does not take into account individuals connected by additional long-range links. S, I, D, R symbols stand for Susceptible, Pre-symptomatic, Symptomatic and Recovered, respectively. The order of infection neighbourhood equals in (b) and (c).
Mentions: We assume that individuals are located at nodes of a square lattice that represents geographical distribution of hosts, see fig. 1. On this lattice, we define a local infection neighbourhood of order as a von Neumann neighbourhood. In that neighbourhood individuals are included, involving the central one. We additionally define as corresponding to this central individual, which means that this individual is not in contact with anyone, while corresponds to the whole population, see fig. 1. To increase realism of our analysis, we also consider the small-world model [24], [25] which adds a certain number of links among randomly chosen nodes, thus adding some long-range connections to the regular lattice ones [24]. Although the disease can spread along these long-range links, we assume that they are so difficult to identify that they are not included in any treatment strategy (see below).

Bottom Line: The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease.However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results.Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.

View Article: PubMed Central - PubMed

Affiliation: M. Kac Complex Systems Research Center and M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland. kas@cs.stir.ac.uk

ABSTRACT
We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.

Show MeSH
Related in: MedlinePlus