A dose response model for Staphylococcus aureus

Abstract

Dose-response models (DRMs) are used to predict the probability of microbial infection when a person is exposed to a given number of pathogens. In this study, we propose a new DRM for Staphylococcus aureus (SA), which causes skin and soft-tissue infections. The current approach to SA dose-response is only partially mechanistic and assumes that individual bacteria do not interact with each other. Our proposed two-compartment (2C) model assumes that bacteria that have not adjusted to the host environment decay. After adjusting to the host, they exhibit logistic/cooperative growth, eventually causing disease. The transition between the adjusted and un-adjusted states is a stochastic process, which the 2C DRM explicitly models to predict response probabilities. By fitting the 2C model to SA pathogenesis data, we show that cooperation between individual SA bacteria is sufficient (and, within the scope of the 2C model, necessary) to characterize the dose-response. This is a departure from the classical single-hit theory of dose-response, where complete independence is assumed between individual pathogens. From a quantitative microbial risk assessment standpoint, the mechanistic basis of the 2C DRM enables transparent modeling of dose-response of antibiotic-resistant SA that has not been possible before. It also enables the modeling of scenarios having multiple/non-instantaneous exposures, with minimal assumptions.

Figure 1

Model overview. (a) 2C model schematic. (b) Phase plot of 2C model. (c) Variations in 2C stochastic simulation (each region bounds mean $\pm$ SD of 50 simulations). (d) Human health outcome classification according to SA dynamics.

Figure 2

2C deterministic model fit and parameters. (a) 2C model fit to growth data. (b, c, e, f) Posterior distribution of parameters with top 100 solutions ranked by objective value Eq. (5). (d) Joint distribution of the posteriors of $r_1$ and $r_2$ parameters.

Figure 3

2C stochastic model fit and parameters. (a) Comparison of fits to the growth data ($f_{\text{SSE}}$) and dose-response data ($f_{\text{dev}}$). (b) Dose-response probabilities for the 2C model cases, along with RH and aBP models. Two colored 2C models with $d_1=0$ are the solutions at the extremes of the Pareto front in A. (c) Outcome probabilities as a function of dose for the 2C model with $d_1=0$ and $f_{\text{dev}}=6.34$.

Figure 4

2C model in the absence of alcohol pre-treatment. Two different hypotheses ($r_1^{\ast }$ and $r_{\text{mf}}$, described in text) were investigated. (a) Fit of the two hypotheses to data from Rose and Haas. (b) Outcome probabilities for $r_1^{\ast }$ hypothesis. (c) $r_{\text{mf}}$ hypothesis respectively.