Norovirus is a disease of alimentary transmission. It normally causes single-source epidemics, i.e. outbreaks that can be linked to a source of contaminated food. This means that alimentation is a risk factor for norovirus. Alimentation may itself be linked to deprivation. We speculate that in deprived areas, there may be less access to safe food; less education on food handling and food safety or less opportunity to adhere to such recommendations as a result of fewer resources; as well as less access to nutritional options as a result of food deserts (impoverished areas with limited access to nutritional and nourishing food options). Due to these conditions, a greater risk of norovirus exposure is found in areas with greater deprivation. Norovirus outbreaks are initiated by contaminated food (single source epidemic), and the virus causes gastroenteritis (inflammation of the mucous membrane of the digestive system linked to vomiting and diarrhoea). The ongoing transmission occurs via the oral-faecal route, meaning that other transmission routes include contact with fomites or with infected people and their bodily fluids (Mathijs et al., 2012). Norovirus poses significant risks in public places such as schools, hospitals, and nursing homes, where close contact and shared spaces facilitate its rapid transmission. In such environments, outbreaks can spread swiftly due to the high density of susceptible individuals and the ease of fomite transmission. Studies have shown that public institutions like hospitals and nursing homes are particularly vulnerable, as the virus can cause severe illness in immunocompromised patients and elderly residents (de Graaf et al., 2016). Schools and childcare institutions are also high-risk settings due to frequent interactions among children, who are often less vigilant about hygiene practices (Gaythorpe et al., 2018b). The importance of understanding intrafamily norovirus transmission has been highlighted in household surveys, which demonstrate how easily the virus can spread in close quarters (Juniastuti et al., 2023). In Japan, for example, long-term surveillance has revealed that norovirus transmission dynamics in public settings remain persistent over time, demonstrating the need for ongoing vigilance in these high-risk environments (Misumi and Nishiura, 2021). Incorporating socio-economic and environmental factors into models of norovirus transmission is therefore crucial, as public institutions in deprived areas may experience even higher transmission rates due to overcrowding and limited resources for infection control.

Recent work in England by Buczkowska et al. (2023) found that an increase in deprivation is linked with an increase in norovirus cases. They suggest an almost 300-fold estimate of the true cases meaning that the norovirus cases reported in the surveillance system are expected to be severely under-ascertained and that the surveillance data “under-represents the true burden of norovirus”. At the time of writing, there is no pre-exposure prophylaxis (vaccine) for norovirus, and norovirus spread is not countered by hand sanitiser. Food-borne diseases pose an increasing risk to public health in Germany (Dietrich et al., 2023). The capital of Germany is Berlin. Berlin is the most culturally diverse city in Germany with a long history of migration and an increasing population. Berlin was divided following the Second World War into East Berlin (Soviet Union occupied; DDR) and West Berlin (American occupied, British occupied, and French occupied regions; BRD) with immigration from Turkey in the west and immigration from Viet Nam and North Korea in the east. We expect Berlin to have differences in levels of deprivation as a result of this historic division.

Deprivation indices measure the lack of advantages in a location. Worse health outcomes are found among residents of disadvantaged areas. Deprivation reflects the inequalities in “exposure to the social determinants of health: (…) working conditions, unemployment, access to essential good and services” (Bambra et al., 2021). The deprivation amplification theory states that the health effects of individual deprivation are amplified for people who live in areas that are more deprived (Bambra et al., 2023). Deprivation indices synthesise information gathered on these inequalities of exposure and quantify the poverty and disadvantages of an area numerically. The German Index of Socio-economic Deprivation (GISD) was developed in 2017 and updated in 2022 (Michalski et al., 2022). The GISD is constructed on the basis of three socio-economic domains through nine indicators: three educational, three employment-based, and three social indicators. The GISD takes values from 0 to 1, with a higher value indicating greater deprivation. The GISD is a relative measure, meaning that it is defined relative to the regions that have the best and the worst socio-economic situations. We have chosen to use the continuous deprivation score rather than the categorical deprivation index in our work (Altman and Royston, 2006). Germany is a country with low social mobility (defined as the ability of a person to attain an improved socio-economic status relative to their parents) (OECD, 2018).

This paper makes several key contributions to the current work on infectious disease modelling. First, it introduces the use of the GISD as a covariate in endemic-epidemic models, offering one of the first studies to explicitly account for socio-economic deprivation in this context. Second, it responds to calls for more region-specific analysis by demonstrating how deprivation influences disease transmission at the district level in Berlin. Third, it advances the application of deprivation amplification theory to infectious disease epidemiology, providing empirical support for the theory. Finally, it innovates by integrating socio-economic factors with time-varying contact matrices, thereby enhancing model accuracy and robustness. Our work addresses various calls for further investigation. •

Michalski et al. (2022) noted that “official notification data for various infectious diseases (…) represent further data sources, for which socioeconomic inequalities could be analysed by linking them to regional deprivation measures”, which our work addresses;

While the initial results suggested that the default model including every detail had the best fit in terms of AIC, we thought that given the unique historic situation of Berlin (having been split by a physical barrier) the Berlin Wall (Figure 6) might be a stronger determinant of deprivation amplification than the GISD. We considered the inclusion of the historical east and west parts of Berlin in place of the deprivation index to see if this provided a better explanation of the specific differences in Berlin. To investigate this question, we determined which districts were on each side of the wall and categorised this division as a variable. In cases in which the wall was located within the district, we assigned the district to a third category of “both” (meaning both sides), and expected that any conclusions drawn about the effect of the wall would be a bit more complicated for those districts. Rather than the east-west divide we had expected to find, we instead observed a “halo” effect, whereby the innermost districts were less deprived than those surrounding them (the “landlocked” regions in Figure 6 with ranks 1–3). We elected to examine a model with solely an effect of the GISD log ( ν a b w ) = α ( ν ) + ξ b ( ν ) z b w (8) log ( φ a b w ) = α ( φ ) + ξ b ( φ ) z b w (9) as well as a model with only the historic east and west parts of Berlin (Figure 6), and a model with both for completion.

After this investigation showed that the model with the historical division of the Berlin Wall did not seem to perform better than our initial model, and given that our work is focused on deprivation in general, we considered the model suite in which the GISD appears only in the epidemic component in line with previous work considering such an effect by Di Biagio et al. (2022).

This means that we exclude ξ ( ν ) and replace c a ′ a w with the original c a ′ a in our full model. All other effects remain as originally intended. The inclusion of time-varying transmission weights (the demographically updated contact matrices c a ′ a w ) does not seem necessary according to our results. We then calculated the relative log likelihood L / L default where L denotes the likelihood. We considered calculating the relative likelihood from the AIC as exp ( A I C − A I C default 2 ) = exp ( κ ) L L default (10) but we are not interested in the exponentiated difference in the number of parameters between the two models exp ( κ ) = exp ( k − k default ) which is extremely large.

This is also a pragmatic choice for the situation under investigation given that there seems to be collinearity in the GISD coefficient in the endemic component (Table 5), as the coefficient estimates and associated standard errors are very large and might be inflated. Inclusion of the wall in place of the GISD did not solve the problem of diverging effects for deprivation in the endemic component (in Table 5 the estimates have even greater absolute values when the wall is included in addition to the GISD).

To address the diverging coefficients of GISD, we consider instead the final model with log-linear predictors log ( ν a b w ) = α ( ν ) + α a ( ν ) + α b ( ν ) + β x w + γ a ( ν ) sin ( 2 π w 52 ) + δ a ( ν ) cos ( 2 π w 52 ) (11) and log ( φ a b w ) = α ( φ ) + α a ( φ ) + θ log ( n b ) + γ a ( φ ) sin ( 2 π w 52 ) + δ a ( φ ) cos ( 2 π w 52 ) + ξ z b w (12)

This model has an AIC of 28,631.64 (other values are given in Table 6 for comparison). The fit of the model is shown in Figure 7 and the model coefficients are given in Table 7. We see that the model shows greater relative influence of the endemic component than usual endemic-epidemic models. This may be indicative of the nature of the disease, which leads to single source outbreaks within a stratum, rather than of person-to-person spread across strata. We recall for the interpretation that the 65+ age group has the most cases followed by the 0–4 age group while the 5–14 and 15–24 age groups have the fewest cases. By district, the most cases seem to be observed in Steglitz-Zehlendorf and Pankow, and the fewest cases are observed in Charlottenburg-Wilmersdorf and Friedrichshain-Kreuzberg (Figure 5). Because the model has log-transformed predictors we can consider the exponentiated values as the multiplicative term of an expected increase when observed cases increase by 1, whereby values close to 1 indicate low-or-no association. See the supplementary material for visualisations of the coefficients on this scale.

Deprivation ξ ^ has the greatest effect. We see a negative effect corresponding to a small multiplicative increase for the holiday season β ^ which is likely responsible for the dips in overall cases observed around the start of a new calendar year (Figure 7). Reductions in norovirus cases in this period are likely due to people eating out less and eating more home-cooked meals, and to people mixing with a smaller group. The estimate for popularity θ ^ suggests more cases would be expected to reach areas with larger populations. The greatest effect of age in the epidemic compartment is α ^ 65 + ( φ ) . This is the only age effect greater than the intercept in either component (we have provided a plot of the effects relative to the reference level in the supplementary material, which shows that this effect is the only one that is higher than the reference). Besides this effect, the largest effect is found in the 0–4 age group. This suggests an association of infancy and old age with norovirus.

Regarding seasonal effects, re-parameterising the sine-cosine waves in terms of amplitude (variability in size of peak) and phase (variability in timing), we see that the oldest age group (65+) has a different seasonality pattern than the other age groups in both components. This is likely due to how different the older age group’s pattern of observed cases is (Figure 5), with its maximum observed counts being more than twice as large as those of other groups. The waves show period patterns that are not flat, indicating that the temporal association with cases is seasonal, which is not surprising when looking at the oscillating peaks and troughs in the observed cases. There seems to be a greater association of seasonality for the 0–14 and 15–24 age groups, with the latter having the highest amplitude overall. The effects of districts are lowest for Friedrichshain-Kreuzberg, Berlin-Mitte, and Berlin-Neukölln, two of which are the most central districts, and could thus be responsible for the “halo” effect.

The main goal of this work was to include deprivation in an endemic-epidemic model. Our motivation is similar to that of Hank’s razor which states that any outcome that could be influenced by socio-economic status likely is influenced by socio-economic status. Here we have postulated that health (represented by norovirus incidence) is influenced by deprivation (a measure that includes socio-economic factors) which may additionally act as an amplifier (cf. the deprivation amplification theory). We determined the impact of including the GISD in a known model for norovirus incidence in Berlin that is used for model development in endemic-epidemic surveillance. Including deprivation in the model leads to a lower AIC value (Table 6), indicating its usefulness in capturing variance currently not incorporated in the existing model as an exogenous factor. We could have considered age-standardised norovirus rates, but this would have removed the comparison opportunities with the previous endemic-epidemic modelling work, and we wanted to evaluate the inclusion of deprivation in these model types.

As Meyer and Held (2017) called for the inclusion of time-varying contact matrices in endemic-epidemic models with contact matrices, we established these matrices using the Arregui et al. (2018) demographic updating method and included them in our modelling approach as a secondary goal. The updated contact matrices were shown visually and summarised using known measures for contact matrices. While norovirus is primarily transmitted through contaminated food, it can also spread via person-to-person contact and contaminated surfaces, which highlights the importance of using contact matrices in the modelling framework. These matrices capture the interactions between different demographic groups, which are crucial for understanding interpersonal transmission in community settings like schools and workplaces. In areas with higher levels of socio-economic deprivation, crowding and limited access to sanitation, person-to-person transmission can be accelerated, making the integration of socio-economic status measures, such as the GISD, essential. By combining contact matrices with socio-economic status data, the model provides a more comprehensive view of norovirus transmission, accounting for both food-related and social transmission pathways, thus enhancing the accuracy of the endemic-epidemic models. We do note, however, that contact matrices are used as a way to inform mixing patterns that rely on contact as a proxy for transmission opportunities and thus only capture direct contact.

Under-ascertainment is a known problem for norovirus data (specific analyses of the data used in this work are given by Bernard et al., 2014; Hofmann et al., 2020). Currently, however, under-ascertained data can only be accounted for in univariate endemic-epidemic models (Bracher and Held, 2021), while the under-ascertainment of norovirus is known to be age-dependent (Gaythorpe et al., 2018a), and is therefore more meaningfully analysed in a multivariate approach. Furthermore, such an approach requires external knowledge of the reporting rate, which adds additional complexity. This means that we have implicitly assumed no under-reporting of data. We have also implicitly assumed that the data quality does not deteriorate or change. However, we know that this is not the case as we noted changes in how population is counted and had to manually redistribute it (Figure 2). A final assumption we have made is that there is no change in the serial interval, but we do not believe that this is an issue for norovirus.

In this work we have examined the impact of deprivation within a city. We expected to see more deprived areas in the east (Heblich et al., 2021), not least because of historical division in the setting considered in our work. However, this did not seem to be the case. There are two competing effects in a city that could influence deprivation: cities selectively receive people seeking higher education and employment but they also attract people with lower levels of socio-economic status pursuing opportunity. In a larger analysis, such as a country level analysis, deprivation in rural areas may need to be considered.

In conclusion, while Galobardes et al. (2006b) highlighted that socio-economic indices may not always be essential in every context, our findings suggest that for infectious disease surveillance, particularly for diseases like norovirus, socio-economic variables can play a critical role. Norovirus transmission is influenced not only by biological factors, but also by social determinants, such as deprivation, overcrowding, and access to resources. This underscores the need to integrate socio-economic considerations from the outset of surveillance model development. We propose that a multidisciplinary approach, incorporating both social and biological sciences, is essential to comprehensively capture the dynamics of disease spread, particularly in populations with large socio-economic disparities. Including these elements early in the surveillance process can lead to more accurate models and better-targeted interventions, ultimately improving public health outcomes in vulnerable communities but more work needs to be done to incorporate deprivation indices in surveillance models.