ESTRATEGIA DE TRABAJO CON TECNOLOGÍAS DIGITALES

The main difficulties and limitations of the research in this thesis stemmed from a lack of data. The complex, mechanistic models in Chapters 3 to 6 required information on many individual-level, hospital-level or community-level variables and outcomes, includ- ing asymptomatic colonisation, symptomatic infections, recurrences, hospital length of stay, antibiotic prescription rates, and immunity to toxins. I did not have access to a dataset with all these variables for a single population let alone for individuals within a single population – such a dataset may not exist for any community. Instead my approach, common in mathematical modelling, has been to draw on the best available research to identify the value of parameters that are likely to be similar across all populations (such as mean time to C. difficile overgrowth or to development of immunity), infer the typical value of other parameters from population-level data (such as hospital length of stay and antibiotic prescription rates), and fit remaining parameters (e.g. transmission parameters) indirectly to other observations such as incidence and prevalence estimates. When pa- rameter values or assumptions were particularly uncertain, influential or variable between settings, extensive sensitivity analysis was used to explore the effect of these parameters and assumptions. Therefore, while the models in Chapters 3 to 6 are unlikely to be accu- rate representations of any single population, they are expected to reflect general trends and the breadth of epidemiology. The much simpler modelling framework in Chapter 7 avoided these problems by omitting much of the complexity of CDI, limiting its usefulness the estimation of the reproduction number and animal-driven thresholds.

It was difficult to obtain accurate estimates of the incidence or prevalence of hospi- tal and community-acquired infections and colonisations, which were essential to estimate the contributions of hospital-based and community-based transmission. The available esti- mates of hospital-acquired and community-acquired infection incidence use indirect means to classify infections as hospital or community-acquired (e.g. [6, 8]). Moreover, it is likely that community-onsetC. difficile infections – like other gastrointestinal diseases – go un- reported and so the incidence of community-onset infections is underestimated [129–132].

Accounting for the bias introduced by indirect classification of the location of acquisition is a major theme of this thesis (Theme 3). However, the ability of the models to account for this bias is dependent on the accuracy with which the model captures movement be- tween healthcare facilities and community and the timing of infections relative to these events. While extensive sensitivity analysis was used to assess the robustness of these findings (Chapter 4), inaccuracies in these parts of the models may have introduced their own biases. In particular, the model of hospital admissions and discharges was highly sim- plified. Though the hospital admission rates differed by patient type (dependent on CDI status, age and immune state), the model did not account for transfers between hospitals, the higher rate of hospital admission amongst recently discharged patients and other het- erogeneities [133–135] which would tend to recirculate some patients through the hospital system much more frequently than others. This may have affected the assessment of the classification system and underestimated the ability ofC. difficile to persist in hospitals.

A lack of data that could be used to infer the role of infants in the transmission of

C. difficile was another limitation of the thesis. In the absence of firm estimates of infant infectiousness, Chapters 5 and 6 used broad sensitivity analysis for the relative infectious- ness of infants and adults. Though these chapters demonstrated that infants are likely to be an important source of transmission in the community, the lack of data around infant infectiousness introduced a great deal of uncertainty into a number of model out- comes including the proportion of transmission in the community that is from infants or asymptomatic adults (Chapter 5), the effect of reducing transmission from infants (Chap- ter 6), and the value of the food-driven threshold (Chapter 5). Infants and transmission from infants were only modelled in the community. This is a reasonable simplification, as hospitalised infants often receive treatment in dedicated wards and so probably do not constitute a substantial transmission risk for hospitalised adults. Moreover, C. difficile

rarely causes disease in infants, with recommended surveillance definitions specifically ex- cluding infants [23, 49]. Therefore the omission of infants from the hospital sub-model is unlikely to have interfered with the comparison of the simulated and reported incidence of hospital and community-acquired infections.

C. difficile is common in livestock and pets and has been isolated in produce and wa- ter [19]. However, because the minimum infectious dose (or minimum colonising dose) is unknown [10], it is difficult to determine how often these sources lead to infection (or colonisation). This in turn has made it difficult to develop models that account for trans- mission from both humans and animals. For this reason, many of the results in this thesis – such as the impact of reducing person-to-person transmission rates (Chapter 6) or the estimates of reproduction number Chapter 5 – had to be calculated assumingnotransmis- sion from animals. Consequently, the estimates of the reproduction numbers in Chapter 5 are really estimates of upper bounds for person-to-person reproduction numbers. Argu- ments introduced in Chapter 5 and further developed in Chapter 7 were used to estimate the minimum frequency of transmission from animal sources that would imply that trans- mission from animal reservoirs drives human disease. Though it is not implausible that

transmission from animals exceeds this threshold, this thesis does not provide a way to determine whether it isprobable, nor does it estimate the effect of preventing transmission from animals.

The initial model of C. difficile in this thesis captured only events inside hospitals (Chapters 3 and 4). Subsequent models incorporated transmission in the community but did not explicitly model transmission in long-term care facilities or the potential for exposure through outpatient care (Chapters 5 and 6). The two settings in the latter models (hospital and community) were assumed to be homogenous and well-mixed. However, since the elderly are at higher risk of infection and infants have very high colonisation rates, age-dependent mixing is likely to have a significant impact in the community [136]. Other authors have modelled multiple wards within hospitals or the contact networks of patients and healthcare workers [95–97]. In general, accounting for population heterogeneity and non-random mixing increases estimates of the reproduction number. Consequently, the estimates of the reproduction number and the effort required to interrupt transmission may have been somewhat underestimated in this thesis.

C. difficile has numerous strains with different toxin profiles, antibiotic susceptibili- ties, and epidemiology [137]. However, most of the models in this thesis (and most models in the literature) are single-strain models. There is some evidence that strains differ in their relative frequency of isolation between adults and infants [18], hospitals and com- munities [138], and humans and animals [122]. Whole genome sequencing of European

C. difficile has identified two distinct transmission patterns, with genetically related iso- lates of some (predominantly fluoroquinolone-resistant) strains clustering locally or region- ally, but isolates from other (predominantly fluoroquinolone-susceptible) strains sharing close genetic relationships across long distances [139]. By pooling all toxigenic strains, the models in Chapters 3 to 6 have overlooked this variability. Thus some of the key findings in this thesis – such as estimates of hospital and community reproduction numbers, animal- driven thresholds and the efficacy of hospital and community-based interventions – may have quantitatively and qualitatively different true values for individual strains. This is demonstrated in Chapter 7 where the simple framework was extended to a strain-by-strain analysis. Using this extension I concluded that in the study hospital ([15]) ribotype 027 had a higher reproduction number than other types.

This thesis relies on the threshold property of the basic reproduction number to ar- gue that transmission in hospitals is insufficient to maintain endemicity in hospitals and calculate the animal-driven threshold. However, the threshold property of the basic repro- duction number can be blurred by a backward bifurcation if the depletion of susceptibles is balanced by a mechanism that increases population susceptibility or pathogen trans- missibility with increasing prevalence [86, 87]. When a mechanism of this kind exists, certain parameter combinations allow both the disease-free equilibrium and the endemic equilibrium to be locally stable if the reproduction number is less than but close to one. In such a scenario, the introduction of a small number invectives is unlikely to lead to endemic disease, but reducing the reproduction number to less than one is not a sufficient

criterion for eliminating endemicity in the absence of importation [86, 87]. C. difficile has a potential mechanism that may lead to a backward bifurcation; namely, the antibiotic treatment of symptomatic patients increases the number of people in the population who have disrupted gut flora and who are therefore at higher risk of subsequent infection and long-lasting colonisation. However, formal bifurcation analyses were not performed for any of the models in this thesis, so the basic reproduction numbers and animal-driven thresholds may not be true thresholds for disease endemicity. However, I believe this is unlikely for two reasons. First, even in populations with very high incidence of C. difficile

infections, the antibiotic treatment of these infections only accounts for a small minority of antibiotic prescriptions. Second, if a backward bifurcation was operating for the pa- rameter values used, one would expect to observe an abrupt (discontinuous) decrease in prevalence and incidence once the bifurcation parameter was reduced to below a critical threshold. This was not observed for either the transmission parameters or the antibiotic prescription rate parameters in the analyses in Chapter 6.