The sample consisted of all children born over the 1868–1892 period within 14 parishes surrounding the town of Sundsvall (see Figure S1, supplementary material available online at https://doi.org/10.1553/p-33g4-pgab). We selected information on each child’s birthdate, place of birth, date of death, cause of death and last observation date. The town of Sundsvall experienced rapid population growth during the study period, which was primarily driven by an increase in the working-class population employed at the sawmills. As of 1890, the total population around the town of Sundsvall was approximately 63,353. While infant mortality was high in the town of Sundsvall, the area underwent the demographic transition during the study period, which led to a decline in infant mortality rates (Edvinsson, 1992).

Daily temperature data were collected from the Swedish Meteorological and Hydrological Institute (SMHI). We used observational data from 1868 to 1892 on temperature readings at three points within the day (morning, noon and afternoon) taken at the weather station in Härnösand, which is located about 40 kilometres north of the town of Sundsvall (Figure S1).

Temperatures spanned from −33.9 °C in the winter to +27.5 °C in the summer (Figure S3, supplementary material). Median monthly temperatures below zero were observed between November and March. The coldest days were observed in February, with a median daily temperature of −5.1 °C; while the hottest days were observed in July, with a median daily temperature of +15.9 °C.

From these observations, we calculated average daily temperature exposures over the past 14 days for each day between 15 January 1868 and 31 December 1892. It is important to note that there were five (non-adjacent) missing temperature readings in our data, which we approximated using non-linear interpolation to ensure the continuity and accuracy of our data.

Seasonality was measured using the day of the year from day 1 to day 366. This approach allowed us to capture the cyclical nature of seasonal variations in temperature and their potential impact on infectious disease mortality.

In this study, infant mortality is defined as the death of a child under one year old. Infectious disease mortality among infants was identified using data on causes of death from historical records. The POPUM population database contains information on causes of death originating from the death and burial registers. After 1860, causes of death were determined either by the parish ministers or, in cities and towns, by physicians. The primary and secondary causes were recorded in death certificates, which were transferred by the ministers to death and burial records (Rogers, 1999). Even though causes of death were recorded by members of different professions in rural and in urban areas, ministers and physicians followed the same nosological system defined in the national regulations (SFS, 1874:60, 1860:13, 1874:61). However, in cities and towns, the precision of the diagnoses was much higher, and the proportions of unknown causes of death were lower, than in rural areas.

In the present study, the ICD10h code system has been used to code and to classify the digitised historical cause-of-death (COD) data. The ICD10h system was designed for encoding historical COD data using the modern ICD10 (10th revision of the International Statistical Classification of Diseases and Related Health Problems) as a baseline. Given that medical knowledge and recording practices have changed over time, ICD10 is not fully applicable to historical data without the loss of important information. For example, the disease term “teething” was frequently used to refer to diarrheal conditions in infants. Thus, a historical contextual system of classification is necessary. The ICD10h further subdivides the ICD10 codes to retain historical information, while its use of ICD10 as a baseline allows us to link historical disease patterns to contemporary ones (Janssens, 2021). Therefore, the system enables us to compare deaths attributable to larger disease groups, such as AID, WFID and other causes of death, among infants.

We focused on deaths in which the primary cause of death (COD) was identified as any infectious disease. In cases of multiple causes of death, each COD was coded separately and then assigned to one of the three COD groups described above. If two or more infectious diseases were listed, we considered the disease that started the chain leading to death as the primary COD.

We noted that throughout the study period, a significant share of the infant deaths in our study population was not attributed to a specific cause. However, as time progressed, there was a noticeable increase in the share of infant deaths for which the specific cause of death was identified, reaching approximately 50% of all infant deaths by the 1890s (Figure S2, supplementary material).

In our analysis, we took into account the geographical contexts in which the deaths occurred, and specifically whether they took place in urban or rural areas. We found notable urban-rural differences in the proportions of unknown causes of death. In rural regions, the proportion of deaths without a known cause was high, at 75.5%. Conversely, in urban areas, this proportion was markedly lower, at just 8.3%. This discrepancy could be attributed to the higher precision of diagnoses in urban areas, which led to smaller proportions of deaths without a specified cause in cities and towns.

We applied time-series analysis to model the relationship between daily cause-specific infant mortality, seasonality and ambient temperature exposure. Data were aggregated to count data on deaths per day by age group (0–13, 14–30, 31–365 days old). We estimated the effect of ambient temperature on the number of infant deaths using Poisson regressions.

The expected number of deaths in a day Y was modelled as a function of person-days log(α) and a model matrix, X, and β the corresponding matrix of coefficients. X included not only ambient temperature exposure, but several other factors as well. We adjusted for the type of parish (urban or rural) and for the age group of the individuals. In addition, we accounted for the non-linear effect of the day of the year, specified as a cubic spline with six degrees of freedom and the year as a cubic spline with three degrees of freedom (Boor, 1978; Hastie, 1991/1997).

It has been shown that ambient temperature has a lagged non-linear relationship to infant mortality (Junkka et al., 2021; Schumann et al., 2019). Thus, the association was modelled as a nonlinear function, specified as a cubic spline with four degrees of freedom, using the distributed lag linear and non-linear models framework. The lagged response was specified as a cubic spline with four degrees of freedom, with lag knots set at logged intervals (Gasparrini et al., 2010). Furthermore, in the cause-specific analysis, the models were simplified by specifying the temperature association as a linear threshold function. The threshold was set at the proximate minimum mortality temperature (MMT), as shown by the nonlinear specifications (see Figure 1). The results were presented as incidence rate ratios (IRR) with 95% confidence intervals (CI), which represented the relative risk of mortality compared to the MMT, or, for the seasonality analysis, 1 February. The models were specified and evaluated within the programming language R (R Core Team, 2021).

In our study, we performed additional sensitivity analyses to account for potential biases and limitations in our data. We recognised that the causes of death were not similarly distributed by age (Figure S5), and that very few deaths from infectious diseases were recorded during the neonatal period (i.e., the first 28 days of life). To address these issues, we limited our sample to cases of post-neonatal mortality, defined as deaths occurring in infants aged between 28 days and one year old. The results from this sensitivity analysis showed patterns similar to those of our main findings (Figures S6 and S7, supplementary material).

Given the large proportions of deaths with unknown causes, we performed analyses in which we grouped these deaths into categories beyond the “other causes” classification. These analyses showed that deaths due to unknown causes have seasonal and temperature patterns that are similar to those of deaths due to known causes (Figures S8 and S9, supplementary material). Thus, the results indicated that unknown causes of death did not have a bias towards either AID or WFID mortality.

We conducted a placebo test to further validate our findings. This test involved examining the association between temperature at a future time point (two months after death, t + X) and mortality risks. If the observed associations between temperature and mortality in our main analysis were due to some unobserved confounding factor, rather than a direct causal effect of temperature, we might expect to see a similar association in this placebo test. However, our placebo test (see Figure S10) showed no association between the temperature two months after death and the risk of dying from other causes, airborne infectious diseases (AID) or water and foodborne infectious diseases (WFID). These results support the validity of our main findings, which suggests that the observed associations between temperature and mortality are likely to be causal, rather than due to chance or confounding.

Breaking down mortality rates by temperature exposures revealed distinct cause-specific patterns (Figure 2). For all-cause infant mortality, there was a u-shaped pattern with a MMT of around +3.5 to +12 °C, with mortality increasing above and below this range. For infant mortality due to AID, there was a linear negative relationship: as temperatures increased, infant mortality declined. Mortality due to waterborne diseases showed the opposite pattern: as temperatures increased, infant mortality increased.

The regression model (Figure 1) that adjusted for seasonality and the long-term trend showed that being exposed to temperatures over +5 °C in the past 14 days was associated with higher mortality. At the 99th percentile temperature exposure of +19 °C, the IRR was 1.48 (95% CI 1.24, 1.76) compared to the reference at the minimum mortality temperature of +5 °C. Temperature exposures below +5 °C did not show any significant association with the IRR of infant mortality, while the IRR was 1.17 at −17 °C (95% CI 0.95, 1.45).

The adjusted Poisson regression models that broke down the associations by causes showed significantly different patterns (Figure 3). No association was found between AID mortality and ambient temperature exposures over the past 14 days. By contrast, a strong positive association was observed between WFID mortality and temperatures above +7 °C, with an IRR of 5.50 (95% CI 3.12, 9.71) at +20 °C (the 99th percentile temperature exposure), while no association was found between WFID mortality and cold temperatures. For mortality related to other causes, the IRR increased slightly at temperatures both +1 °C hotter and +1 °C colder than the MMT; at −17 °C (first percentile), the IRR was 1.26 (95% CI 1.01,1.59); and at +19 °C (99th percentile), the IRR was 1.40 (95% CI 1.10, 1.77).

The associations were not uniform across lag time. Figure 4 shows the IRR of cause-specific infant mortality at exposure to temperatures of −20 °C and +20 °C (the first and the 99th percentile daily temperature exposures) over the past 1–14 days. The lagged IRR confirms that AID was not associated with any temperature changes in the past 14 days. Exposure to high temperatures (+20 °C) was associated with an increase in the IRR of WFID mortality 10 days after exposure, to 1.19 (95% CI 1.06, 1.33). A small positive association was found between mortality due to other causes and exposure to heat two days after exposure, with an IRR of 1.13 (95% CI 1.01, 1.27).

In terms of seasonality, all-cause IM was highest in the winter months (December-February), followed by in the summer months (June-August); see Table 2. AID and WFID mortality displayed opposite patterns. AID mortality peaked in the winter and was lowest in the summer, while WFID mortality peaked in the summer and was lowest in the winter.

The Poisson regression models confirmed these seasonal patterns; see Figure 5. IRR and CI were calculated compared to the day of the year with the lowest observed cause-specific mortality. For all-cause mortality, the unadjusted IRR peaked in the winter months of January and February and in the summer months of July and August. However, after adjusting for temperature exposures, the IRR reached a low point in the summer season, and the IRR peak in the winter months increased (Figure 6).

The seasonal models uncovered a strong association between seasonality and cause-specific mortality (Figure 6). AID mortality followed a strong u-shaped seasonal pattern, with mortality reaching a low point in the summer (August) and a peak in the winter (December-March). The opposite, bell-shaped pattern was found for WFID mortality, with mortality reaching a peak in the summer and a low point in the winter (February). The association between the seasons and mortality from other causes followed the same patterns as those for all-cause mortality.

After adjusting for the day-of temperature and a seven-day average lagged temperature, the seasonal patterns increased for AID mortality and for mortality from other causes, while they decreased for WFID mortality. The model showed no significant relationship between the seasons and WFID mortality, which suggests that the seasonal patterns were primarily due to temperature exposure rather than to seasonal exposure.

Ours is among the first studies on infectious disease mortality and its relationship to seasonality and temperature in a 19th-century population. Without access to cause-specific data, previous studies have only been able to speculate about the mechanisms driving the relationship between the climate and infant mortality, which we have been able to address (Ekamper et al., 2009; Huck, 1994; Junkka et al., 2021; Schumann et al., 2019; Tymicki, 2009). Nonetheless, historical cause-specific data on infectious diseases have important limitations. The medical knowledge and nomenclature used by parish ministers and provincial doctors during the 19th century differ from modern medical diagnoses (Revuelta-Eugercios et al., 2021). Although the historical causes of death are focused on descriptions of symptoms, infectious and non-infectious diseases are, in general, easier to differentiate than individual conditions using the ICD10h coding system, which is tailored for historical cause-of-death data (Janssens, 2021). Furthermore, additional sensitivity analyses were performed that limited the sample to post-neonatal mortality and differentiated between unknown and other causes of death. The results of these analyses were similar to those of the main findings (Figures S5, S6, S7, S8, S9 in the supplementary material).

As we limited our measurements of climate conditions to seasonality and ambient temperatures, the importance of humidity was overlooked. Especially for WFID, humidity in combination with heat is an important factor in exposure and mortality (Martinez, 2018; Pappas et al., 2008). Our study also lacked data on indoor environmental conditions, such as on levels of air pollution. Thus, we were not able to disentangle different forms of seasonal variations in behaviour and the environment that might have driven the seasonal patterns.