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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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(a) The proportion of recovered individuals, , (b) the fraction of treated (controlled) individuals,  and (c) the total cost of epidemic as a fraction of the system size, , for  and various control sizes .Red solid line: model 1; blue dotted line: model 2. Results of simulations with parameters , , ,  and  performed on regular networks. Inserts show the relevant magnifications of the graph.
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pone-0063813-g003: (a) The proportion of recovered individuals, , (b) the fraction of treated (controlled) individuals, and (c) the total cost of epidemic as a fraction of the system size, , for and various control sizes .Red solid line: model 1; blue dotted line: model 2. Results of simulations with parameters , , , and performed on regular networks. Inserts show the relevant magnifications of the graph.

Mentions: In the absence of control, the disease will either progress through the population until it exhausts a large part of initially susceptible population (for large values of the infection probability ) or it will quickly stop spreading (for small values of ). As control is applied in extended neighbourhood of radius centred at a symptomatic individual, the number of recovered (R) individuals declines rapidly, see fig. 3a. Models 1 and 2 examined in this work differ in the way they treat or not treat the recovered class, R, cf fig. 1 We observe the same behaviour for both considered models (with and without treating R class). However, when we allow the control of R individuals (model 2), the proportion of recovered declines faster than in model 2, see fig. 3a (insert). The proportion of preventively treated individuals, V, in both models is similar for the whole range of control size, . With increasing control neighbourhood, V(z) grows very quickly, then drops near and finally rises monotonically till (fig. 3b). Combination of these two relationships, and , according to eq(1), gives total cost of epidemic, , as a function of , see fig. 3c. For a very low treatment cost, e.g. , total cost of control of epidemic, , is almost equal for both models, with difference less than , see fig. 3c (insert). The choice of optimal strategies is different for model 1 (GS) than for model 2 (LS), although the corresponding X values are similar. In model 1 the minimal value of X corresponds to the highest value of control size, (GS), whereas in model 2, the minimum is identified with , (LS) fig. 3c.


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

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

(a) The proportion of recovered individuals, , (b) the fraction of treated (controlled) individuals,  and (c) the total cost of epidemic as a fraction of the system size, , for  and various control sizes .Red solid line: model 1; blue dotted line: model 2. Results of simulations with parameters , , ,  and  performed on regular networks. Inserts show the relevant magnifications of the graph.
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Related In: Results  -  Collection

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

pone-0063813-g003: (a) The proportion of recovered individuals, , (b) the fraction of treated (controlled) individuals, and (c) the total cost of epidemic as a fraction of the system size, , for and various control sizes .Red solid line: model 1; blue dotted line: model 2. Results of simulations with parameters , , , and performed on regular networks. Inserts show the relevant magnifications of the graph.
Mentions: In the absence of control, the disease will either progress through the population until it exhausts a large part of initially susceptible population (for large values of the infection probability ) or it will quickly stop spreading (for small values of ). As control is applied in extended neighbourhood of radius centred at a symptomatic individual, the number of recovered (R) individuals declines rapidly, see fig. 3a. Models 1 and 2 examined in this work differ in the way they treat or not treat the recovered class, R, cf fig. 1 We observe the same behaviour for both considered models (with and without treating R class). However, when we allow the control of R individuals (model 2), the proportion of recovered declines faster than in model 2, see fig. 3a (insert). The proportion of preventively treated individuals, V, in both models is similar for the whole range of control size, . With increasing control neighbourhood, V(z) grows very quickly, then drops near and finally rises monotonically till (fig. 3b). Combination of these two relationships, and , according to eq(1), gives total cost of epidemic, , as a function of , see fig. 3c. For a very low treatment cost, e.g. , total cost of control of epidemic, , is almost equal for both models, with difference less than , see fig. 3c (insert). The choice of optimal strategies is different for model 1 (GS) than for model 2 (LS), although the corresponding X values are similar. In model 1 the minimal value of X corresponds to the highest value of control size, (GS), whereas in model 2, the minimum is identified with , (LS) fig. 3c.

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