Table 1 Notation used in the paper
Notation | Meaning |
|---|---|
\({\mathcal {V}}=\{1,\ldots ,n\}\) | Population |
\({\mathcal {C}}=\{1,\ldots ,{\tilde{n}}\}\) | Children |
\({\mathcal {A}}=\{{\tilde{n}}+1,\ldots ,n\}\) | Adults |
\({\mathcal {F}}=\{{\mathcal {F}}_1,\ldots ,{\mathcal {F}}_k\}\) | Families |
\({\mathcal {S}}=\{{\mathcal {S}}_1,\ldots ,{\mathcal {S}}_m\}\) | School classes |
\({\mathcal {B}}=\{{\mathcal {B}}_1,\ldots ,{\mathcal {B}}_p\}\) | School buildings |
\(\phi :{\mathcal {V}}\rightarrow {\mathcal {F}}\) | Function that associates individuals with their families |
\(\psi :{\mathcal {C}}\rightarrow {\mathcal {S}}\) | Function that associates children with their classes |
\(\beta :{\mathcal {C}}\rightarrow {\mathcal {S}}\) | Function that associates children with their buildings |
\({\mathcal {E}}_F\subseteq {\mathcal {V}}\times {\mathcal {V}}\) | Family layer |
\({{\mathcal {E}}_S}(t)\subseteq {\mathcal {C}}\times {\mathcal {C}}\) | Class layer at time t |
\({{\mathcal {E}}}_B(t)\subseteq {\mathcal {C}}\times {\mathcal {C}}\) | School building layer at time t |
\({\mathcal {E}}_C(t) \subseteq {\mathcal {A}}\times {\mathcal {A}}\) | Contact layer at time t |
\(a_i\in [0,1]\) | Activity of individual i |
\(m_c\in {{\mathbb {Z}}_{>0}}\) | Interactions initiated by an active child |
\(m_a\in {{\mathbb {Z}}_{>0}}\) | Interactions initiated by an active adult |
\(X_i(t)\in \{S,E,I_D,I_U,R,V\}\) | Health state of individual i at time t |
\(A_i(t)\in \{0,1\}\) | Home-isolation state of individual i at time t |
\(\lambda _a\in [0,1]\) | Adult per-contact infection probability |
\(\lambda _c\in [0,1]\) | Children per-contact infection probability |
\(\nu \in [0,1]\) | Probability of becoming infectious |
\(\mu \in [0,1]\) | Recovery probability |
\(q_a\in [0,1]\) | Adults detection rate |
\(q_c\in [0,1]\) | Children detection rate |