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Table 1 Notation used in the paper

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