From: Activity-driven network modeling and control of the spread of two concurrent epidemic strains
Notation | Meaning |
---|---|
n | Number of individuals |
\({\mathcal {N}}=\{1,\ldots ,n\}\) | Population set |
t | Discrete time variable |
\(\Delta\) | Time step |
\({\mathcal {G}}(t)\) | Time varying graph denoting the network of contacts |
\({\mathcal {E}}(t)\) | Node set (interaction links) at time t |
\(x_i(t)\) | State of individual i at time t |
\({\mathcal {X}}\) | Discrete set of health states |
\(\text {S}\) | Susceptible to both strains |
\(\text {E}_1\) | Exposed to strain 1 |
\(\text {E}_2\) | Exposed to strain 2 |
\(\text {I}_1\) | Infectious with strain 1 |
\(\text {I}_2\) | Infectious with strain 2 |
\(\text {R}_1\) | Recovered from strain 1 |
\(\text {R}_2\) | Recovered from strain 2 |
\(\widetilde{\text {E}}_1\) | Exposed to strain 1 after being recovered from an infection |
\(\widetilde{\text {E}}_2\) | Exposed to strain 2 after being recovered from an infection |
\(\widetilde{\text {I}}_1\) | Infectious with strain 1 after being recovered from an infection |
\(\widetilde{\text {I}}_2\) | Infectious with strain 2 after being recovered from an infection |
\(\text {R}\) | Recovered from both strains |
\(\ell\) | Index to denote a particular strain |
\(\lambda _\ell\) | Per-contact infection probability of strain \(\ell\) |
\(\sigma _\ell\) | Latency to become infectious of strain \(\ell\) |
\(\mu \ell\) | Recovery rate for strain \(\ell\) |
\(\rho _{\ell \ell }\) | Strain-specific re-infection probability for strain \(\ell\) |
\(\rho _{\ell \bar{\ell }}\) | Cross-strain re-infection probability for strain \(\bar{\ell }\) |
m | Average number of contacts per individual |
\(a_i\) | Activity potential of individual i |
\(f(\cdot )\) | Probability distribution of the activity potentials |
\(\langle {a}\rangle\) | First order moment of the probability density function \(f(\cdot )\) |
\(\langle {a^2}\rangle\) | Second order moment of the probability density function \(f(\cdot )\) |
T | Time period of the control strategy |
D | Duration of the home-isolation period |
p | Fractions of home-isolated individuals in the control strategy |