**4. Discussion**

Given that climate change and the risk of plague outbreak are closely coupled [28], actions need to focus on the pathways and patterns of climate-plague nexus. In particular, the mechanism of those climatic effects—whether they are direct and/or indirect, remain largely unclear and understudied so far. In this study, we found that the effect of climatic forcing on the temporal distribution of plague outbreak was solely indirect in nature. Furthermore, the long-term trend of climate-plague nexus was only significant in the cold and wet periods.

#### *4.1. Direct and Indirect Paths Embedded in the Climate-Plague Nexus*

The statistical results from SEM led us to similar conclusions: (1) that climate has an indirect influence on plague dynamics; (2) that economic factors have a direct influence on plague dynamics; (3) that climate has a direct influence on economic factors, also meaning that the influence of climate on plague dynamics is mediated by economic systems. More specifically, the effect of temperature on plague dynamics is indirect but as a whole significant, whilst the effect of precipitation on plague dynamics is indirect but considerably insignificant as a whole.

Although many disease outbreaks are characteristically associated with climate directly [29,30], the indirect pathway is not uncommon [31]. However, the recognition of such an indirect climatic effect has not received significant attention in academia. Most often, previous studies considered climatic influence as a direct indicator to plague activities without testing the potential existence of an indirect pathway. Our results challenged the previous perspective and demonstrated that the economic system is an important element of the indirect effect of climate on plague outbreak. In fact, our SEM approach could not detect any direct climatic effect on plague activity; instead, only temperature displayed total effect on plague dynamics, and the pathways of temperature influence and precipitation influence were all indirect. Indeed, previous studies suggested that high summer temperature could inactivate human plague occurrence in the case of the United States [32,33] and may cause the reduction of flea survival, early-stage development, reproduction rate, and the ability to transmit the disease [34,35]. The influence of precipitation was previously well documented but defined in a complicated manner. The trend of precipitation was depicted as a positive and linear indicator of plague outbreak in the U.S. [36]. Nonetheless, the correlation is negative in Vietnam and Uganda, where dry seasons favored the risk of plague outbreak to a greater extent than wet seasons [37,38]. However, regardless of the disparity in the study area, the variation in climate (both temperature and precipitation) did not post any direct effect on plague dynamics in our study when we held the economic parameters constant.

Academically, much more is known about how climate a ffects economic systems, or how economic attributes led to epidemics–partly because climate-epidemics study is a comparatively new subject for researchers. A series of work by Pei et al. [16,39–41] is most prominent in justifying the casual pathway from cooling to the shrinkage of crop productivity, and thus, shock in the agricultural market and the stability of agrarian society. In fact, before the time of the Industrial Revolution, when most people were farmers, it is understandable that an agrarian society relies heavily on "good climate". The study by Zhang et al. [12] extended further the idea of climate-induced food shortage to malnutrition and hypothesized a declined cohort immunity through examining the time series of human height in Europe. Moreover, because of malnutrition, the undernourished population would easily be more susceptible to infectious diseases through dysfunctional immunological responses [42]. Thus, it is possible, with the support of past literatures, to demonstrate that climatic variables could be hypothetically correlated to increasing plague activities through their commands on the agro-economy. However, from our SEM result, only temperature and precipitation variations were deemed significant in such a pathway, with PDSI coming up short in showing a statistically significant relationship with plague dynamics both directly and indirectly. As a result, since not all the climatic variables we tested in this analysis were found to be correlated, additional climatic variables, or the term "climatic influence" should be considered carefully when we describe their impact on plague outbreak.

Our study also delineated the indirect e ffect of precipitation on plague outbreak in time series. In fact, previous results once questioned the role of precipitation in producing any significant change in plague dynamics [2]. Yet, those studies might have only considered the total e ffect of precipitation but not the indirect e ffect of it. Our study also highlighted the indirect positive e ffect of wetness on plague dynamics. However, our SEM results indicate that this association could be weak, ye<sup>t</sup> significant, in magnitude. The reason behind this might lie in the contextual variations in the agricultural markets or major crop types. In this study, we used wheat price as a representation of crop market and Europe as the study area, and it could be that wheat is more sensitive to wetness than dryness and historical Europe was capable of absorbing shocks in mild climatic variations, and thus, generating the result we saw from our analysis. In an alternative study adopting the same methodology of ours but working on a region with a completely di fferent market and key crop types, the role of precipitation in influencing plague dynamics might also appear di fferent.

Furthermore, our results, sugges<sup>t</sup> that the sustainability and resilience of societies to climate change matters for their survival against the plague. Some researchers identify climate as the direct driver of plague activities in European history, with such climate-plague tropes supported by robust palaeoclimatic and reconstructed disease data. Yet, those hypotheses might have simplified social responses and failed to account for the complexity of disease dynamics in human society. To a certain extent, the lack of synchronous climate-driven plague outbreak mechanisms in China in the work of Xu et al. [4] should have already implied profound regional variations in plague resilience and bu ffers to climatic variability. Such recognition of regional variation in plague resilience had been stifled by treating the disease dynamics of plague to climatic variation as a homogenous and universal entity. Statistical analyses that assumed a single, homogenous and direct response of plague dynamics to climate forcing were therefore at odds with empirical data relevant only to a certain spatial level so that the results might appear dichotomous, inconsistent, mild, or insignificant. Consequently, there is a dissonance between method and hypothesis.

Five important caveats should be noted in interpreting our study results. First, our study results did not refute the role of climatic variation in any previous studies, although our study showed that climatic variation was not directly related to plague dynamics. Our intent was to demonstrate that the e ffects of climate on the economic system exert a stronger influence on temporal plague outbreak patterns, and to call for addressing the role of social responses to plague outbreak. Second, the disease dynamics of plague remained extremely complex. Our study is pilot in nature to outline the plausible indirect e ffect of climate on the plague outbreak dynamics at our study scale. Yet, the interpretation of such results should not be overgeneralized to plague dynamics in other contexts such as virus-host relationship, rodent plague outbreak dynamics, host-to-human transmission, and so on. Third, the indirect effect of climate change on plague dynamics might not only bypass social response. For example, Yue, et al. [43] explored the influence of trade routes on plague spreading patterns. Despite the fact that they assumed the transportation route as static over their study period, one can easily forecast the evolution of transportation could also contribute to plague dynamics in time. Forth, in a similar sense, the effect of other climatic variables on the plague dynamics should await further analysis. Plague dynamics might not only be influenced by temperature and precipitation. Instead, recent progress in climate-plague nexus had frequently suggested the role of large-scale climatic phenomenon [44,45]. Finally, this paper focused mainly on the climate-plague nexus at the macro-scale. However, we should not overlook the importance of studying micro-regions in Europe during this outbreak. A series of recent work [46–50] has called for attention between the balanced view of macro-scale study of plague dynamics and micro-perspective of it in medieval Europe.

#### *4.2. Long-Term Trends of the Climate-Plague Nexus*

Long-term trends between different variables suggested that human plague dynamics is sensitive to particular climatic situations, and economic attributes are potentially more consistent in influencing plague dynamics. To be more specific, the long-term trend of human plague activities with different predictors suggested that only temperature remained significant in correlating with plague outbreak patterns in cold and wet climate, whilst the effect of precipitation showed no significant relationship with plague directly in any sensitivity tests. Furthermore, the effect of temperature displayed no total or indirect relationship with plague outbreak when the climate is warm and dry. Similarly, the increasing temperature only promoted the drop of wheat price during cold and wet periods but made no significant impact on the wheat market when the climate was already warm and dry. In comparison, decreasing precipitation also contributed to the lowering of wheat price in cold and wet periods. On the one hand, the above long-term dynamics are consistent with and supportive of our SEM results. On the other hand, the pattern might also indicate that the direct/indirect/total effects of climate variation were spatio-temporally selective and variable-dependent. Thus, such reshaping of the idea of direct/indirect climate-plague nexus at the temporal domain might also be applicable in similar fashion at the spatial domain, or in a multi-scalar study [51]. Second, the results suggested that cooling during cold times and growing wetness in wet times could stimulate plague outbreak. In a similar vein, extreme coldness and flooding were the contributors to plague outbreak in Europe [2]. Third, to expand on the previous point, our result might have explained the insignificant climate-plague association in some other studies. To a large extent, the meticulous picture of the climate-plague association we obtained from this study was attributable to the centennial-scale historical panel data applied. Other studies that utilize shorter time frames or contemporary plague outbreak might unavoidably fall onto the "warm period", which provided a null result, rejecting the legitimacy of climate-plague relationship.

In addition, both wheat price and CPI exhibited a positive relationship with human plague outbreak regardless of any climatic situations. The consistent relationship between economic parameters and plague might seem persuasive in confirming their dominant role in governing plague dynamics. Yet, one should also consider that plague dynamics, or any other pandemics, would certainly shock agricultural markets and living standards [52]. Therefore, a cyclic correlation between epidemics and economic systems might reinforce each other, making their correlation become consistent and stable. Besides, factors such as wars, social turmoils, urbanizations, and famine could have a fundamental impact on both agricultural markets and infectious disease outbreak [10]. Based simply on the analysis performed in this study, it remained unknown whether socio-economic variables were more important than climatic variables in driving plague dynamics, and that whether factors like wars and urbanization might play a part in climate-plague nexus. Yet, given that our analytic results could address the consistent significant correlation between economic changes and plague dynamics, further research for the aforementioned questions should be warranted. As our analysis focused on the long-term relationship of climate-plague nexus over a continental spatial unit, future study could be arranged at case studies in the modern context with a smaller spatial study unit to capture the potential variation of climate-plague nexus with a moving scalar window.
