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Theory and Modern Applications

Table 1 Physical meaning, value, dimension and references for model states and parameters. (Dim. = Dimension, Ref. = References, Est. = Estimated, Arbit. = Arbitrary)

From: Impact of reduction in contact time activity of infected individuals on the dynamics and control of directly transmitted respiratory infections in SIR models

Symbol

Description

Value

Dim.

Ref.

S(t)

Total number of susceptible individuals at time t.

I(t)

Total number of infected individuals at time t.

R(t)

Total number of recovered individuals at time t.

μ

Per-capita birth/death rate.

1/70

Year−1

[8, 20]

β

Per-capita effective contact rate at which susceptible individuals acquire the infection.

553.77

Year−1

Est.

γ

Per-capita recovery rate for infected individuals.

365/3.38

Year−1

[20, 27]

α

Per-capita treatment rate for infected individuals.

365/2

Year−1

Arbit.

\(R_{\Diamond}\)

The basic reproduction number for model (11).

1.525

[20, 27]

\(p_{0}\)

The proportion of time during which a non-infected individual stays at rest.

0.2

Arbit.

\(p_{1}\)

The proportion of time during which an infected individual stays at rest.

0.3

Arbit.

\(q_{0}\)

The proportion of time during which a non-infected individual mingles with other individuals in the total population.

0.8

Arbit.

\(q_{1}\)

The proportion of time during which an infected individual mingles with other individuals in the total population.

0.7

Arbit.

\(\widehat{P}_{r}\)

The percent reduction in the mingling proportion of time due to acquiring the infection.

12.5

Arbit.