# Dose response relationship epidemiology and infection

### A generalized dose-response relationship for adenovirus infection and illness by exposure pathway.

However, by itself, exposure data are insufficient to assess the public health development of models that describe dose-response relations for enteric factors that influence the frequency and severity of foodborne infections in a population. The fitted dose response relationship in conjunction with population estimates Keywords: Escherichia coli OH7; Risk assessment; Dose-response; Epidemiology for laboratory confirmed infection to be 8 per. Dose. Number of. Positive. A generalized dose-response relationship for adenovirus infection Health, Rollins School of Public Health,Emory University,Atlanta, GA,USA.

We find that i middle- and high-dose data do not constrain the low-dose response, and different dose—response forms that are equally plausible given the data can lead to significant differences in simulated outbreak dynamics; ii the choice of how to aggregate continuous exposure into discrete doses can impact the modeled force of infection; iii low-dose linear, concave functions allow the basic reproduction number to control global dynamics; and iv identifiability analysis offers a way to manage multiple sources of uncertainty and leverage environmental monitoring to make inference about infectivity.

By applying an environmentally mediated infectious disease model to the Milwaukee Cryptosporidium outbreak, we demonstrate that environmental monitoring allows for inference regarding the infectivity of the pathogen and thus improves our ability to identify outbreak characteristics such as pathogen strain.

Author summary Many infectious disease interventions, including water treatment, hand hygiene, and surface decontamination, target pathogens in the environment. Explicitly modeling the concentration of pathogens in the environment within transmission models can be a useful way to consider not only the impact of such mitigation efforts but also the spatial spread of pathogens and sampling strategies for environmental monitoring. However, we need to understand the dose—response relationship, that is, how exposure to pathogens translates into a probability of infection.

The field of quantitative microbial risk assessment has developed dose—response models from experimental data, but little work has been done to assess the impact the choice of dose—response model has on transmission model dynamics. We show that dynamics of simulated transmission models incorporating a dose—response model that has been fit to experimental data can vary widely despite little statistical difference in the fit to the experimental dose—response data. This and other results allow us to give specific guidance for the use of dose—response functions in a transmission modeling context.

We also underscore the usefulness of environmentally mediated transmission models by demonstrating how environmental monitoring data can be used to provide new information about pathogen strain. Introduction Modeling infectious disease transmission by person-to-person contact has a long history in the scientific community. Explicit modeling of pathogens in the environment can generate additional insight into how environmental processes affect infectious disease dynamics and allow modelers to incorporate knowledge from experimental studies into their models.

In particular, it allows for consideration of pathogen fate and transport [ 20 ] and the functional relationship, called the dose—response relationship, between the amount of pathogen a person is exposed to dose and the probability of infection, illness, or death response. Ultimately, because many interventions work through environmental media e.

Microbial dose—response modeling has largely grown out of the field of quantitative microbial risk assessment QMRA and was established, for gastrointestinal pathogens in particular, by seminal work by Haas [ 2122 ] and Teunis [ 23 ]. Work in this area has emphasized the biological plausibility of the exponential and beta—Poisson single-hit models, which semi-mechanistically model pathogen distribution in doses and survival in the host.

Empirical models, which come from the field of chemical toxicology and are based on the theory of tolerance distributions [ 24 ], have also been used, particularly for foodborne diseases [ 2526 ].

### A primer on risk assessment modelling: focus on seafood products

In practice, those seeking to develop a dose—response relationship for QMRA must find data for an appropriate host organism that aligns with the exposure route and desired endpoint e. Once appropriate data are found, the choice of functional form from among a plausible set is usually a statistical one goodness-of-fit or best-fit.

In applied work, transmission modelers have thus far considered only the most mathematically tractable of dose—response relationships in transmission models that explicitly consider pathogen dynamics: However, the relationship between exposure and infection risk could be more complex, and the consequences of the misspecification of this relationship on model dynamics and predictions have not been explored in detail.

The dose-response data is often collected using higher doses than would be observed in the real world, while the dose-response function is often used to extrapolate results in dose ranges beyond the observed data.

As a result, using a purely empirical function fit to the observed data does not give us a lot of confidence in our estimates when outside the observed range. The second approach is to develop a dose-response function that is more mechanistic in nature, or based upon our understanding of how the infection process works, and to translate that into a mathematical function. There is some finite probability that the pathogen will succeed in passing each of the barriers, and taking this into consideration, the concept can be translated into probability statements and subsequently mathematical functions.

In order to get a complete treatment of the derivation of dose-response functions, the reader is referred to Haas et al.

## Field Epidemiology Manual

This reference also provides an excellent overview of dose-response modelling in general. This can be represented by P1, which essentially captures the variation in the actual number of organisms ingested, and in probability terms can be written as: This can be represented by P2, which captures the host and microbe interaction and can be written as: If both processes, P1 and P2, are independent, then the overall probability can be written as: Response occurs if some critical kmin organisms survive.

There are two hypotheses that can be used to describe the way in which infection and illness occur upon ingestion of the pathogens. In this assumption, kmin is greater than 1.

## A generalized dose-response relationship for adenovirus infection and illness by exposure pathway.

In this assumption kmin is equal to 1. The independent action theory is the theory currently accepted for microbial infection. This is reasonable in terms of biological plausibility and on the grounds of conservatism in the face of no additional information the threshold approach would predict a lower risk than non-threshold.

This theory assumes that one cell is capable of initiating a response because the survival of one cell has the ability to initiate an infectious process since pathogens have the ability to multiply, unlike chemicals which may have a threshold.

**Agonist Dose Response Curves**

In the non-threshold assumption, it is recognized that although the probability that a single ingested cell is able to successfully survive all the barriers in the body is small, it is non-zero. If we take the non-threshold assumption, which is the recommended assumption for pathogen infection as stated earlier, then depending upon the assumptions related to P1 and P2, specifically the types of probability distributions used to characterize them, and following some mathematical manipulations, we can arrive at various mathematical functional forms.

Two commonly used dose-response functions are described below. Exponential dose-response function The exponential dose-response function has the following assumptions: One cell can initiate infection no threshold ; Organisms are randomly distributed in the serving, P1 The probability of ingesting an organism in a serving is described by a Poisson process.

The probability associated with this parameter is a constant value; there is no variation in the probability. Using these assumptions, the exponential dose-response function shown below is derived Haas, For instance, at 3. The beta-Poisson function has two parameters, and a change in each translates to a different effect on the dose-response curve.

Keeping alpha fixed, changes in the beta parameter produce a shift in the curve similar to that observed in the exponential dose-response function. The effect of changing the value of the alpha parameter is shown in Figure 4. Altering the alpha parameter of the beta-Poisson dose-response function produces a change in the slope of the curve.

So, the curve can be both shifted altering the beta parameter and its slope increased or decreased changing the alpha parameter.