**Performing Department**

Biomedical & Diagnostic Sciences

**Non Technical Summary**

Non-O157 Shiga toxin-producing Escherichia coli (non-O157 STEC)is widespread in the cattle environment. Howeve,r the transmission dynamics of the non-O157 serotypes in cattle has not been investigated comprehensively so far. Most of our understanding of STEC ecology is limited to one serotype, O157, and it is unclear whether the other STEC serotypes have similar dynamics in the cattle reservoir. Although STEC serotypes may share common transmission pathways and habitats, differences in the ability to thrive and survive in different cattle and environment habitats may result in differences in transmissibility and persistence of the serotypes in beef production systems. The overall objective of the proposed modeling studies is to quantify the transmission of STEC serotypes in the beef production system.The proposed mathematical modeling studies will generate some basic knowledge regarding STEC serotypes dynamics that can inform mitigation efforts. We will be able to compare the transmission dynamics of the different STEC serotypes in the cattle populations, and provide some baseline estimates for key transmission parameters and the basic reproduction number.01/01/2014-12/31/2015, University of Nebraska-Lincoln, $55,032

**Animal Health Component**

100%

**Research Effort Categories**
Basic

100%

Applied

(N/A)

Developmental

(N/A)

**Goals / Objectives**

The overall objective of the proposed modeling studies is to quantify the transmission of shigatoxin E. Coli (STEC) serotypes in the beef production system.To accomplish our objective, we will carry out the following sub-objectives: 1. Develop a general stochastic model to describe the transmission of STEC serotypes in cattle. 2. Fit the developed model to the cross-sectional data generated in the STEC CAP. 3. Evaluate and compare transmission dynamics of STEC serotypes in cattle.

**Project Methods**

Develop a mathematical model for the transmission of STEC in cattle. Develop a Bayesian mathematical framework to fit the data. Test the frameworkwith synthetic and preliminary data. Develop fitted transmission parameters for STEC serotypes. Analyze the fitted models by comparing STEC dynamics.For a given STEC serotype, animals within a pen will be assumed to be in two states, either susceptible or infectious. Susceptible individuals can become infectious through transmission by contact with an infectious individual at a rate β, and with external sources outside the pen at a rate ε. Infectious individuals can return to susceptible at a rate γ once they stop shedding. If the pen size is assumed constant, then transmission dynamics can be described by a continuous-time discrete-state Markov chain, whose states are the number of j infectious individuals in a population of size N. The model can be described using the Kolmogorov forward equation, which describes the rate of change of the transition probabilities (Keeling and Ross, 2008)and can be used to obtain the stationary probability distribution. The stationary probability distribution represents the equilibrium of the Markov Chain, the probability distribution that remains fixed in time. As previously proposed in Matthews et al (2006), by assuming that the cross-sectional prevalence data reflects the stationary probability distribution of the system, we can fit the data to the model and obtain estimates for the transmission parameters. Based on existing research, we have a relatively accurate estimation of the transmission parameters for the O157 serotype, but hardly any a priori information for non-O157 STEC. Thus we will use a two-stage iterative Bayesian inference technique to estimate the transmission rate (β) and recovery rate (γ) for the non-O157 STEC serotypes (assuming the external transmission rate ε as a known constant) (Gelman et al., 2004). The likelihood function of both parameters (β and γ) can be derived from the Kolmogorov forward equation described above and the observation data. Assuming the parameters are independent, the joint likelihood function is expressed as L (β, γ D), where D represents the observations. During the first stage, the priors of the non-O157 STEC are set to be the same as observed O157 serotype parameter distributions. Then the prior is multiplied by the likelihood function of each non-O157 STEC to find the posterior distribution. At the second stage, these newly derived posterior distributions are set to be the prior distributions and the second-stage posterior distribution can be derived using the same procedure, since the likelihood functions remain the same for each non-O157 STEC. Technically, we will use Markov Chain Monte Carlo (MCMC), a widely applied numerical methods to implement Bayesian inference, to simulate the posterior distributions.Alternatively, a Bayesian approach with an uninformative prior (e.g. the prior comes from a very wide uniform distribution thus carries little a priori knowledge) will be applied as well. This approach is mathematically equivalent to optimizing the likelihood function (maximum likelihood methods), but it maintains a Bayesian perspective. We will derive posterior distribution of desired parameters (β and γ) for each of the non-O157 STEC and compare them with the previous approach (with prior information from O157 serotype). Once the transmission parameters have been derived, we can further investigate some important quantities, such as the basic reproduction number (R0) in for the STEC in cattle, and further simulate the stochastic models to compare the dynamics of the different STEC in the cattle population. For that purpose we will investigate the differences in the predicted probability of pathogen invasion and extinction and time to extinction for the different STEC serotypes.