Some parameters are identifiable to a reasonable degree through model fitting, but there is a large degree of uncertainty in the viral transport efficiencies and the AD kinetic parameters. While this could be a consequence of fitting a limited number of data points with several parameters, the viral load at harvest and risk estimates were well constrained. This large variation in parameters and ‘usefully tight quantitative predictions’ is termed the sloppiness of parameter sensitivities, and has been observed in physics and systems biology. Well-designed experiments may simultaneously reduce uncertainty in the parameters as well as predictions and therefore increasing confidence in predictions. One possible experiment to reduce parameter uncertainty is recording the transpiration and growth rate to fit eq. independently to get at and bt . An interesting outcome of my analysis is the strong association of risk with plant growth conditions. The health risks from consuming lettuce irrigated with recycled wastewater are highest in hydroponic grown lettuce, followed by soil grown lettuce under Sc2 and the least in soil grown lettuce under Sc1 . This difference in risk estimates stems to a large degree from the difference in AD kinetic constants . Increasing katt,s will decrease risk as more viruses will get attached to the growth medium, while increasing kdet,s will have the opposite effect , as more detached viruses are available for uptake by the plant. The combined effect of the AD parameters depends on their magnitudes and is portrayed in Fig. A.4. This result indicates that a better understanding of the virus interaction with the growth environment can lead to an improved understanding of risk. More importantly,livestock fodder system this outcome indicates that soil plays a vital role in the removal of viruses from irrigation water through the adsorption of viral particles. An investigation focused on understanding the influence of soil composition on viral attachment will help refine the transport model.
The risk predicted by this dynamic transport model is higher than the EPA annual infection risk as well as the WHO annual disease burden benchmark. The reasons for this outcome are many-fold. First, there is a significant variability in the reported internalization of viruses in plants. In research of data for modeling NoV transport in plant, I filtered the existing data using the following criteria: 1) human NoV used as the seed agent, 2) presence of quantitative viral results in the growth medium and different locations of the plant. Based on these criteria, the data from represent the best available data on viral internalization and transport in lettuce. However, it is also important to note that a similar study by did not observe human NoV internalization in lettuce. This discrepancy could be due to the specific subspecies of the plant and growth conditions used in the studies. Besides, minor changes such as damages in roots or decrease in humidity of the growing environment can promote pathogen internalization. Alternatively, tracking viral transport through the growth medium and the plant is challenging, which may yield false results due to reaction inhibitions in genome amplification and inferior detection limit. The risk outcome of this study is conservative because it assumes an individual consumes the wastewater irrigated lettuce daily for an entire year. This assumption and the corresponding higher risk estimates are only applicable to a small portion of consumers, while most consumers in the U.S. are likely to have a more diverse diet. While the model outcomes presented here represent the best attempt given the available data, it is also possible that the internalization observed by is an extreme case and and typically internalization occurs to a lesser extent.As previously discussed by others , risk estimates by different NoV dose-response models differed by orders of magnitude. This study primarily aims to introduce a viral transport model without advocating any one dose-response model. The future refinement of pathogen dose-response models will reduce variability in risk estimates.
The risk of consuming lettuce grown in soil as predicted by is higher than my predictions, although I used the results of in both studies. This is a consequence of considering the greater adsorption capability of soil, which is not reflected when assuming a simple input:output ratio. Using different inoculating concentrations of NoV, body weight and consumption rate distributions also contributed to the difference in the outcomes but to a lesser extent. In addition to a transport model predicting the NoV load in lettuce, I explored strategies to reduce the risk of NoV gastroenteritis by increasing holding time of the produce after harvesting or using larger hydroponic culture volumes. Although neither strategy could significantly alleviate the risks, the process highlights two strengths of modeling: 1)It provides analytical support for arguments that would otherwise be less convincing; 2) It predicts outcomes of experiments without the physical resources required to perform them. For instance, the model can be used to explore alternate irrigation schedules to reduce the NoV internalization risk. Modeling also helps encapsulate our understanding of the system and generate hypotheses. For example, simple first-order decay did not produce the trend observed in the water, which suggests that additional mechanisms are at play. I postulated the attachment of virus particles on the walls of the hydroponic system as one possible mechanism and examined the fit of the model. Although viral attachment to glass or other materials has been observed before, here it stands as a hypothesis that can be tested. In addition to generating and testing hypotheses, some of my model assumptions raise broader questions for future research. For example, I assumed that viruses are transported at the transpiration rate from the growth medium to the roots. However, not much is known regarding the role of roots in the internalization of viruses. Investigating the defense mechanisms of plants’ roots to passive viral transport, i.e., through rhizosphere microbiome interactions, may shed light on the broad understanding of plant and microbe interactions. The question of extending this model to other pathogen and plant systems draws attention to the dearth of data in enabling such efforts. While modeling another virus may not require changes to the model, understanding transport in other plants can be challenging.
Data required includes models for growth rate and transpiration, plant growth characteristics including density, water content, as well as internalization studies to determine transport efficiencies. However, from the perspective of risk management, lettuce may be used as the worst-case scenario estimate of risk in water reuse owing to its high consumption with minimal pathogen inactivation by cooking. This worst-case scenario can be used to set water quality standards for irrigation water for the production of fresh produce eaten raw. The models can also be extended to include pathogen transport to the plant tissue from manure/biosolids that are used as organic fertilizer. By assuming that SA transitions from an un-adapted state to an adapted state, the model is grounded in first principles. The stochastic aspect of dose-response emerges naturally from a stochastic simulation of the growth kinetics. In addition, the model predicts carrier outcomes without additional data. Armitage et al. interpret results from several studies to posit that pathogens, including bacteria,hydroponic nft gully show an initial exponential increase in all individuals. We argue that this is not inconsistent with the initial decrease assumption for three reasons. Firstly, the exponential increase is observed in organs like the liver or spleen, and not the whole body or site of inoculation . This does not refute the possibility of an initial decrease at the inoculation site or the whole body. Secondly, the posited decrease is transient, and samples may not have been collected during this window. Thirdly, the magnitude of decrease is low at higher inocula and consequently less detectable. Further, compared to the initial decrease observed when all bacteria are in the S1 state, one would expect 1) no initial decrease if seeding with bacteria all in the S2 state, and 2) a smaller initial decrease if seeding with a mixture of bacteria in the S1 and S2 state. These trends have been observed when pathogens from in-vivo cultures were used for infecting the host . We note that the transition from S1 to S2 is perhaps not instantaneous, and the pathogen population may constitute a continuum of states between S1-S2. When loads were measured in the whole body, a transient decrease was observed in some cases . Clumping of bacteria was offered as a possible explanation, but this does not rule out an actual reduction in viable counts observed in other systems . Armitage et al. also note that non-responders show a subsequent decrease after the initial exponential increase. These were substantiated by measurements from survivors who were killed at later time points. This decrease is probably due to the activation of the adaptive immune response inside the host, which could be incorporated in a within-host variant of the 2C model. Using the concept of IED to evluate reponse, I am able to explain the data with a single IED. It has been observed that the toxic dose of a chemical can vary between individual subjects or with the season.
A similar stochasticity may be expected in IED between individuals which can be attributed to differences in covariates such as body weight, sex, immune history and biological noise. However, assuming this was not necessary to produce an acceptable fit. The model was fit to data by following a two step optimization procedure. Direct multi-objective optimization was not pursued since the objective functions were very different from each other. The deterministic ODE model was easy to evaluate and a global optimization algorithm was employed to guard against local minima while fitting the growth data. Fitting the dose-response data was computationally challenging for 3 reasons: a non-smooth objective function, stochastic simulations have to be repeated many times, and the number of stochastic entities being modeled is not small. Hence, a simple brute-force optimization was adopted. The RH model exhibits a sharp initial decline in SA density and predicts values lower than the observed minimum for each initial load . The 2C model only goes as low as the lowest load observed on the skin. Experiments similar to that of with greater time resolution are necessary to ascertain the time of true minimal SA density. The 2C model stochastic model does not perform as well as the RH model . However, the 2C model fit to dose-response data improves along the Pareto front . It is possible that exploring solutions with a higher growth objective may yield a solution that fits as well as, if not better than, the RH fit to the dose-response data. Moreover, the proposed approach offers advantages over the existing approach in that 1) it is fully mechanistic, and hence is more applicable in other scenarios , and 2) in addition to response outcomes, the proposed approach also accounts for carrier outcomes. Perhaps the most interesting outcome of this study is the incorporation of quorum sensing in dose-response modeling. The rejection of the absence of cooperativity in SA pathogenesis and the adequate fit of cooperativity make a strong case for the cooperativity in action hypothesis. Experimental support for this hypothesis include the well studied Agr system of quorum sensing . In the words of Le. et al, the Agr system “generally enhances pathogenesis by increasing expression of aggressive virulence determinants such as toxins and degradative enzymes”.This system is activated when bacteria reach a certain density, which results in a disease response such as a murine abscess. However, the 2C model posits that quorum sensing enhances bacterial growth rate, for which I propose two possible explanations. The direct explanation is the existence of an as yet undiscovered signaling mechanism responsible for density dependent growth enhancement. A second explanation relates to the events initiating response in a host, which is the interaction of the toxins/enzymes produced by SA with the host tissue. The 2C model captures these dynamics at a higher level of abstraction, with the mathematical variable i representing the amount QS signals and toxins. We can interpret b2 as the rate of enhanced production of these factors.