I refer to J.H. Jones' Notes on R0.

More details in this question at Mathematics SE: How does the reproduction number depend on characteristics of the physical contact graph of a population?

The basic SIR model - as described in Jones' Notes - considers three factors that make up the reproduction number:

  • $\tau$ = the transmissibility (i.e., probability of infection given contact between a susceptible and infected individual)

  • $\overline{c}$ = the average rate of contact between susceptible and infected individuals

  • $d$ = the duration of infectiousness

The (basic) reproduction number then is

$$R_0 = \tau \cdot \overline{c} \cdot d$$

I wonder how to model social structure in a SIR model, which might influence both transmissibilty $\tau$ and average rate of contact $\overline{c}$ and thus the reproduction number $R_0$, resp. the infection rate $\beta = \tau \cdot \overline{c} = R_0 / d$.

Specifically I wonder which "control parameters" appropriately describe the social structure of a population and may influence transmissibilty $\tau$ and average rate of contact $\overline{c}$ in a specific and comprehensible way.

Among these parameters may be:

  • typical (mean) numbers of household members and acquainted persons

  • typical ratio of shared acquaintances

  • typical numbers of strangers one meets (e.g. per month)

  • typical times of contact to household members, acquainted persons, and strangers

  • the amount of persons with outstanding many social contacts, better: the standard deviation of the contact rate

  • the accepted physical distance to family members, acquainted persons and strangers
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I am looking for approaches that let go such parameters into the infection rate $\beta = \tau \cdot \overline{c}$ in a quantitative way.


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