Fig 1.
A basic illustration of key model features and chain of events.
Fig 2.
Queueing Network and Markov Chains.
The flow of people from one zone to another can be controlled by a first-order Markov Chain (see. Eq A.1 in S1 Appendix) Upon arriving at a location, individuals will queue to use one (of possibly many) identical TUIs (e.g. a bank of ATM machines). After interacting with the TUI, they join a ‘departure’ queue (effectively hanging around at that location) until finally rejoining the Markov Chain and moving on to a new zone/location. A pair of rate parameters associated with a particular TUI type (∼Pois(λTUI)) and zone (∼Pois(λZ)) determine how long they queue in the ‘arrival’ and ‘departure’ queues respectively.
Fig 3.
Dynamic equilibrium of surface bioburden.
A single individual (with clean hands) continuously touches a surface at the same location(s) e.g. the ‘buttons’ on a TUI. The geometric mean and standard deviation (GSD) of surface bioburden is depicted with three variations of the pickup/deposit rate model: fixed parameters (α = 0.05, β = 0.27) with (green) and without (red) loss due to pathogen decay/die-off, and (blue) random parameters α ∼ ftn(0.05, 0.3, 0, 1) (median average 0.22) and β ∼ ftn(0.27, 0.3, 0, 1) (median average 0.34) where ftn(μ, σ, a, b) is a truncated normal distribution on the domain [a, b]. The plots are consistent with Eq 4, which predicts an equilibrium point of 0.15 for the fixed parameter case and ≈0.40 for random parameters. Once pathogen loss is incorporated, all levels tend to 0 over time.
Fig 4.
Consider two shops (A & B) with customers (n = 32) arriving at each randomly, with equal probability. Some customers (2/3) at A will move on to B afterwards (and vice-versa). The remaining 1/3 will visit only one of the shops (it can be assumed that they then move on to other locations outside the simulation’s focus). The TUI at shop A has already been contaminated with an initial bioburden. There is a particular interest in Alice and Bob; Alice will visit shop A exclusively while Bob will visit shop B exclusively. Therefore, Bob can only be infected from secondary transfer of pathogens from shop A (even though he will never visit A). Alice will receive ‘first-hand’ exposure to the contaminated screen. How does the risk of infection differ for the these two individuals?.
Fig 5.
Geometric mean bioburden (log10 scale and normalised) and standard deviation (GSD) on TUIs A and B. A is initially contaminated. Over time microbes are transferred to B (0.1% avg. at 20 minutes) through sequential use. The eventual decay of both curves can be explained by pathogen die-off, personal-touching and the fact that 1/3 of people will visit only one location before leaving the simulation (mitigating further cross-contamination between A and B).
Fig 6.
Parameter sensitivity on infection risks.
Average infection risk (n = 40000 realisations) with 95% CI. (a) Initial bioburden seeded on TUI A (over a range of ID50) (95% CI omitted for clarity). Bioburdens range from baseline (∼101) to ‘heavy’ contamination (105). (b) Pathogen surface half-life (minutes). (c) Inoculation period (time-constant γ of the dynamic dose response model). (d) Average number of touch interactions, nt required for TUI use. (e) Number of TUIs available for use at B. (f) Deposit rate associated with personal-touching events αpt.
Fig 7.
Average Infection risk (n = 40000 realisations) with 95% CI. Solid lines depict infection risk when cleaning rates applied at location B only. Dashed lines are associated with cleaning at A only. Dotted lines correspond to cleaning rates applied both at A and B. Decontamination at B alone has little impact on the risk to Alice (though a slight decrease is observed at higher cleaning rates as pathogens are prevented coming full-circle back to A from B). Decontamination at A alone has slightly better outcomes for Bob than cleaning at B alone. This suggests the risk to customers at one location can be subject to hygiene standards and cleaning regimens at another independent location.