Cumulative attack rates against children’s population trigger, in the absence of inter-group transmission (β_AC = β_CA = 0).

<p>Values of R_0A are varied: R_0A = 1.25 (left); 1.5 (middle); 1.75 (right). For all panels, R_0C = 2; 50% adults; 50% children. Everything else as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-g005" target="_blank">Figure 5</a> caption.</p

Time series of a simulated epidemic in a population in which transmission between adults (black) and children (gray) is 1% of intra-group transmission (β_AC = 0.01 * β_AA; β_CA = 0.01 * β_CC; left), or 10% (β_AC = 0.1 * β_AA; β_CA = 0.1 * β_CC; middle), or 100% (β_AC = β_AA; β_CA = β_CC; right), in the absence of intervention.

<p>Broken line: susceptible; solid line: infected. In the right panel, the black and gray broken lines overlap each other exactly. R_0A = 1.25; R_0C = 2. 50% adults; 50% children. All other parameters and initial conditions are listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-t001" target="_blank">Tables 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-t002" target="_blank">2</a>. The reason why in the right panel, the curves of susceptible adults and children overlapped, while the curves of infected adults and children did not, was that adults and children had different rates of recovery and therefore their average durations in the model compartment of the infected/infectious were different.</p

Cumulative attack rates (CA) against the start day of intervention, in the absence of inter-group transmission (β_AC = β_CA = 0).

<p>In the upper row, the denominator in the adults’ and children’s CA is the whole population (S_W0 = 1); blue dotted line: CA_AW; cyan broken line: CA_CW; red solid line: CA_W = CA_AW + CA_CW. In the lower row, the denominator in the adults’ and children’s CA is their respective proportion in the whole population (SA₀ and SC₀ respectively); black dotted line: CA_AA; grey broken line: CA_CC; red solid line: CA_W = S_0A*CA_AA + S_0C*CA_CC. Proportion of adults in the population, from left to right: 10%, 30%, 50%, 70% and 90%. Intervention efficacy, <i>f_AA</i> = <i>f_AC</i> = <i>f_CA</i> = <i>f_CC</i> = 1. R_0A = 1.25, R_0C = 2; long intervention; interrupt all routes of transmission. All other parameters and initial conditions are listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-t001" target="_blank">Tables 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-t002" target="_blank">2</a>. For the definition of the different cumulative attack rates, please refer to the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#s2" target="_blank">Materials and Methods</a> section, “Cumulative attack rates”, in the main text.</p

Model parameters.

<p>Model parameters.</p

Model variables.

<p>Model variables.</p

Illustration of the concept of optimal control for multiple outbreaks.

<p>We assume that multiple outbreaks can occur, with the intervention only being feasible during the first outbreak. If the intervention is weak (or absent), the first outbreak will be large enough to deplete the number of susceptible people below a critical threshold level (the herd immunity level below which effective reproduction number <1), such that if the infection is re-introduced, its effective reproductive number would be too low to cause a second outbreak (black and cyan lines). If the intervention is very strong, it is possible that after the first outbreak, the number of susceptible people remaining is large enough to support a second (uncontrolled) outbreak upon re-introduction of the pathogen, leading to an overall number of people infected that might be the same as that reached during just one outbreak (red line). In both the “too much” and “too little” intervention scenarios, the number of susceptible people drops below the critical threshold level, which defines the level of herd immunity. The excess drop is termed ‘overshoot’. The optimal intervention is one that minimizes the overshoot by allowing the susceptible population to drop to the critical threshold level during the first outbreak, such that a second outbreak cannot occur (green line). The solid lines represent the susceptible people and the broken lines represent the infected people.</p

Cumulative attack rate of the whole population (CA_W) under school closure with short intervention (28 days) with different levels of efficacy against time trigger (different start day of intervention, left) and population trigger (cumulative proportion of children infected, right).

<p>The legend colour panel displays CAW levels. All other parameters follow <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-g011" target="_blank">Figure 11</a>.</p

Flowchart illustrating the model.

<p>White boxes represent adults, while black boxes represent children. Light grey arrows indicate movements from one stage to another (susceptible to infected to recovered). White arrows represent infection of adults and children by contact with infected adults; likewise, black arrows represent a similar process with infected children.</p

Time series of a simulated epidemic in a population in which there is no transmission between adults (black) and children (grey), in the absence (left) or presence (right) of an intervention.

<p>Broken line: susceptible; solid line: infected. CA_AW: Cumulative attack rate (adults, with whole population as the denominator); CA_CW: Cumulative attack rate (children, with whole population as the denominator). Infection was re-introduced into the population on day 300. The intervention (<i>f_AA</i> = <i>f_AC</i> = <i>f_CA</i> = <i>f_CC</i> = 1) started on day 100 (when the children’s epidemic is at its peak) and lasted until the first outbreak was over. β_AC = β_CA = 0; R_0A = 1.25; R_0C = 2. 50% adults; 50% children. All other parameters and initial conditions are listed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-t001" target="_blank">Tables 1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-t002" target="_blank">2</a>.</p

Cumulative attack rates against children’s population trigger in the presence of inter-group transmission.

<p>Everything else as described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0036573#pone-0036573-g008" target="_blank">Figure 8</a> caption. Note that again the x-axis does not go beyond a threshold level of 0.8 since even an unmitigated outbreak (even in the absence of coupling) did not reach a higher attack rate among the children and therefore intervention would not be triggered.</p