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Copy file name to clipboardExpand all lines: contact-matrices.md
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1 & 3
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\end{bmatrix}
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$$
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In this example, we would use this to represent that children meet, on average, 2 other children and 2 adult per day (first row), and adults meet, on average, 1 child and 3 other adults per day (second row). We can use this kind of information to account for the role heterogeneity in contact plays in infectious disease transmission.
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\frac{dR}{dt} &=\gamma I \\
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\end{aligned}
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$$
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To add age structure to our model, we need to add additional equations for the infection states $S$, $I$ and $R$ for each age group $i$. If we want to assume that there is heterogeneity in contacts between age groups then we must adapt the transmission term $\beta SI$ to include the contact matrix $C$ as follows :
Share with learners the code for the baseline model.
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It has **different** disease parameters than previous episode.
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Then start with the livecoding directly with interventions.
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::::::::::::::::::::::
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## Baseline model
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We will investigate the effect of interventions on a COVID-19 outbreak using an SEIR model (`model_default()` in the R package `{epidemics}`). To be able to see the effect of our intervention, we will run a baseline variant of the model, i.e, without intervention.
[Non-pharmaceutical interventions](../learners/reference.md#NPIs) (NPIs) are measures put in place to reduce transmission that do not include the administration of drugs or vaccinations. NPIs aim at reducing contacts between infectious and susceptible individuals by closure of schools and workplaces, and other measures to prevent the spread of the disease, for example, washing hands and wearing masks.
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[1] "[0,15)" "[15,65)" "65+"
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```
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Therefore, we specify `reduction = matrix(c(0.5, 0.01, 0.01))`. We assume that the school closures start on day 50 and continue to be in place for a further 100 days. Therefore our intervention object is:
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Therefore, we specify `reduction = matrix(c(0.5, 0.01, 0.01))`. We assume that the school closures start on day 50 and continue to be in place for a further 100 days. Therefore our intervention object is:
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```r
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We expect that mask wearing will reduce an individual's infectiousness, based on multiple studies showing the effectiveness of masks in reducing transmission. As we are using a population-based model, we cannot make changes to individual behavior and so assume that the transmission rate $\beta$ is reduced by a proportion due to mask wearing in the population. We specify this proportion, $\theta$ as product of the proportion wearing masks multiplied by the proportion reduction in transmission rate (adapted from [Li et al. 2020](https://doi.org/10.1371/journal.pone.0237691)).
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We create an intervention object with `type = rate` and `reduction = 0.161`. Using parameters adapted from [Li et al. 2020](https://doi.org/10.1371/journal.pone.0237691) we have proportion wearing masks = coverage $\times$ availability = $0.54 \times 0.525 = 0.2835$ and proportion reduction in transmission rate = $0.575$. Therefore, $\theta = 0.2835 \times 0.575 = 0.163$. We assume that the mask wearing mandate starts at day 40 and continue to be in place for 200 days.
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We create an intervention object with `type = "rate"` and `reduction = 0.161`. Using parameters adapted from [Li et al. 2020](https://doi.org/10.1371/journal.pone.0237691) we have proportion wearing masks = coverage $\times$ availability = $0.54 \times 0.525 = 0.2835$ and proportion reduction in transmission rate = $0.575$. Therefore, $\theta = 0.2835 \times 0.575 = 0.163$. We assume that the mask wearing mandate starts at day 40 and continue to be in place for 200 days.
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```r
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:::::::::::::::::::::: instructor
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Make a pause.
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Use slides to introduce the topics of:
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- Pharmaceutical interventions.
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Then continue with the livecoding.
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::::::::::::::::::::::
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## Pharmaceutical interventions
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\frac{dV_i}{dt} & =\nu_{i,t} S_i\\
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\end{aligned}
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$$
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Individuals in age group ($i$) at specific time dependent ($t$) are vaccinated at rate ($\nu_{i,t}$). The other SEIR components of these equations are described in the tutorial [simulating transmission](../episodes/simulating-transmission.md#simulating-disease-spread).
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To explore the effect of vaccination we need to create a vaccination object to pass as an input into `model_default()` that includes age groups specific vaccination rate `nu` and age groups specific start and end times of the vaccination program (`time_begin` and `time_end`).
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