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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

Total cost of epidemic at optimum, , as a function of the treatment cost  ((a) and (b)) and as a function of both infectiousnes, , and cost,  ((c) and (d)) for model 1 (left column) and model 2 (right column).In (a) and (b)  (red line),  (green dashed line),  (blue dotted line). All simulations done with parameters , , , . Disease spreading on regular networks.
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pone-0063813-g005: Total cost of epidemic at optimum, , as a function of the treatment cost ((a) and (b)) and as a function of both infectiousnes, , and cost, ((c) and (d)) for model 1 (left column) and model 2 (right column).In (a) and (b) (red line), (green dashed line), (blue dotted line). All simulations done with parameters , , , . Disease spreading on regular networks.

Mentions: Increasing cost of treatment, , decreases the optimal control neighbourhood, . For very cheap control the optimal scenario is identified with (GS) for model 1, regardless of the recovery rate, (fig. 4a). The more expensive the treatment, the higher the total costs spent on controlling outbreaks. This leads to change in optimal strategy, see fig. 4a, b. We cannot afford the preventive control of the whole population (GS) and have to shift into treating in neighbourhood of symptomatic individuals. We observe that rapidly decreases with increasing costs, especially for model 1. For intermediate values of , drops to depending on recovery rate, . Higher recovery rate, , results not only in a shorter plateaux for LS (see fig. 4a, b) but also moves the plateaux towards larger control size, . As treatment becomes more expensive, second threshold is observed that describes change from LS to NS. Although for model 2 the global strategy is selected rather than the local one as for model 1 (fig. 4b, d) for the high values of recovery rate, and low , the total cost of epidemic, , does not differ much between the two models, see fig. 5. The highest costs are associated with fast spreading diseases (large ) and expensive treatment (large ) for both models (upper right part of plots in fig. 5). Slow spreading disease does not significantly affect the budget for control regardless of treatment costs (lower part of plots in fig. 5) and model selected. For model 2 the global strategy is predominantly selected for high values of recovery rate and at low , in contrast to model 1 (fig. 4b, d) where the local strategy prevails. Despite these differences, the total cost of epidemic, , does not differ between the two models, see fig. 5.


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

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

Total cost of epidemic at optimum, , as a function of the treatment cost  ((a) and (b)) and as a function of both infectiousnes, , and cost,  ((c) and (d)) for model 1 (left column) and model 2 (right column).In (a) and (b)  (red line),  (green dashed line),  (blue dotted line). All simulations done with parameters , , , . Disease spreading on regular networks.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0063813-g005: Total cost of epidemic at optimum, , as a function of the treatment cost ((a) and (b)) and as a function of both infectiousnes, , and cost, ((c) and (d)) for model 1 (left column) and model 2 (right column).In (a) and (b) (red line), (green dashed line), (blue dotted line). All simulations done with parameters , , , . Disease spreading on regular networks.
Mentions: Increasing cost of treatment, , decreases the optimal control neighbourhood, . For very cheap control the optimal scenario is identified with (GS) for model 1, regardless of the recovery rate, (fig. 4a). The more expensive the treatment, the higher the total costs spent on controlling outbreaks. This leads to change in optimal strategy, see fig. 4a, b. We cannot afford the preventive control of the whole population (GS) and have to shift into treating in neighbourhood of symptomatic individuals. We observe that rapidly decreases with increasing costs, especially for model 1. For intermediate values of , drops to depending on recovery rate, . Higher recovery rate, , results not only in a shorter plateaux for LS (see fig. 4a, b) but also moves the plateaux towards larger control size, . As treatment becomes more expensive, second threshold is observed that describes change from LS to NS. Although for model 2 the global strategy is selected rather than the local one as for model 1 (fig. 4b, d) for the high values of recovery rate, and low , the total cost of epidemic, , does not differ much between the two models, see fig. 5. The highest costs are associated with fast spreading diseases (large ) and expensive treatment (large ) for both models (upper right part of plots in fig. 5). Slow spreading disease does not significantly affect the budget for control regardless of treatment costs (lower part of plots in fig. 5) and model selected. For model 2 the global strategy is predominantly selected for high values of recovery rate and at low , in contrast to model 1 (fig. 4b, d) where the local strategy prevails. Despite these differences, the total cost of epidemic, , does not differ between the two models, see fig. 5.

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