A malaria risk model for the Mediterranean in antiquity based on the historical Carta della Malaria dell’Italia

ABSTRACT Growing interest in the health burden of malaria in ancient times is complimented by recent DNA confirmation of its presence at several archaeological sites in the Mediterranean. This study presents a model of ancient malaria risk for the region with utility for synthesis and application. The GIS-based model combines malaria risk factors that can be reasonably known for pre-modern times. Calibration, verification, and validation of the model is possible through use of a detailed map of pre-eradication malaria endemicity in Italy, the 1882 Carta della Malaria dell’Italia. The model provides a cross-disciplinary tool by bringing technical GIS capabilities to the evaluation of textual sources having potential malarial connections. The study’s main product is an open access relative malaria risk layer for GIS use and application to historical reconstruction. Example maps using model output and potential use are presented.


Introduction
The COVID-19 Pandemic highlighted and spurred implementation of already-advanced techniques in spatiotemporal disease mapping.This impetus has not extended to mapping past epidemics despite an increase in recent studies on the role of disease in ancient history (e.g.Harper, 2017).Specifically, while the impact of vector-borne disease in the ancient world is well-established (Sallares, 2002), no efforts to spatially model malaria risk in ancient times appeared prior to 2020.This may be due to a combination of model design difficulties and failure to appreciate the value of such a model.Both problems are addressed in this study.
An initial version of this project established the feasibility of a malaria risk model for antiquity and application to the issue of peril for travelers (Browning, 2020(Browning, , 2021)).The present study refines that work by incorporating a superior version of the baselinea historical map of pre-modern malaria endemicity datawith corresponding increased confidence in the malaria risk model product with expanded scope.That product, and the goal of the project, is a reliable spatial model of potential malaria risk for the pre-modern Mediterranean world.Presented in open-access GIS-capable form, model data and output maps provide tools for historical study, debate, reconstruction, and illustration.
The need for these tools arises because ancient and medieval writers, without understanding of malarial ecology or epidemiology, described significant disease symptoms that may or may not represent malaria, but often with significant geographical specificity.Debate over the potential role of malaria in these cases can benefit from model output which provides a quantification of potential malaria risk in specific locations.Its application utility is thus intentionally cross-disciplinary in bringing the technical capabilities of GIS to the task of evaluating nuanced textual sources as some brief examples will show.

Malaria and its impact in antiquity
Malaria is a staggeringly complicated disease caused by parasitic infection of the victim's blood by genus Plasmodium protozoans.It is vector-borne in that Plasmodium is introduced by female mosquitos of the genus Anopheles during blood meals (Carter & Mendis, 2002, p. 565).Particulars of malarial epidemiology and ecologies that impact modeling and mapping of the disease are reviewed in the original study (Browning, 2021, pp. 65-68).
Here it suffices to emphasize that the combinations of the four Plasmodium species and various regional malaria-capable Anopheles vectors, each having their own environmental limitations and preferences, coupled with natural and anthropogenic variation make malaria a manifestly local phenomenon.Outbreaks are thus highly localized and modeling malaria risk for antiquity can only establish spatial zones in which conditions are likely to align for favorable transmission.
Several ancient sources also reveal a spatial awareness of malarial risk, generally associated with miasma, 'noxious fumes' emitted from certain places with stagnant water (for details see Browning, 2021, pp. 68-69).This association eventually led to the common name assigned to the fevers: mal'aria (Italian, 'bad air').

Malaria risk model design
A model of spatial risk for malaria in antiquity has excellent antecedents in modern efforts to track and combat the disease.Malaria remains a significant health burden in many regions, and modeling with risk map production is crucial in ongoing work (Weiss et al., 2015, p. 2).
Contemporary malaria models employ a modified GIS version of multi-criteria evaluation (Eastman et al., 1999) and identify various risk factors, or covariates, as inputs (Weiss et al., 2015).Spatial datasets identified for each covariate are reclassified into a standard scale and weighted in combination to arrive at a cumulative risk assessment, with a target baseline for evaluation of the combination ratios.The choice of covariates is critical and will be treated below.A greater conceptual issue is establishing a reliable means of model evaluation.
The complexities of malaria are such that validation of contemporary risk models remains problematic (MacLeod & Morse, 2014;Tomkins & Thomson, 2018).It usually entails running the model using past data and comparing predicted results with observed spatiotemporal disease burden indicators (MacLeod et al., 2015).
The lack of data for antiquity makes usual evaluation methods unfeasible.An acceptable alternative would incorporate a spatial record of malaria endemicity from a pre-modern period, against which model risk predictions could be compared.A candidate map must necessarily depict controlled observations in an area of interest from a preeradication date.As it happens, quite fortunately, such a map exists.

Carta della Malaria dell'Italia: The Torelli Map
The most detailed map of malaria endemicity from pre-eradication times comes from Italy in 1882.As railways were deemed essential to that country's recent unification, a parliamentary commission was formed to evaluate the system.Malaria, still endemic in much of Mediterranean Europe in the nineteenth century, especially in Italy (Majori, 2012;Snowden, 2006, pp. 12-26) quickly emerged as a major obstacle to railway construction and operation.Senator Luigi Torelli, with responsibility for health conditions, discovered a dismal situation far beyond already pessimistic estimations (Torelli, 1882, p. 3).
A report of the dire situation to the Senate in 1880 led to a decision to extend research beyond the railways to the entire country.To that end the Ministry of the Interior requested that all 259 provincial and district Health Councils identify malarial areas in their jurisdiction.Such areas were to be ranked in three gradations and marked on topographic maps.This initial attempt met with limited success, because many local regions had no access to suitable maps (Torelli, 1882, pp. 4-6)!Cooperation ensued with the Military Topographical Institute (MTI), then producing 1:100,000 maps of the entire country.Territory maps were sent to provincial councils with criteria and instructions for marking malarial areas in the three gradations: (1) leggiera, 'slight;' (2) grave, 'serious;' and (3) gravissimo, 'most serious.'The 590 returned sheets were collated into a 1:1,000,000 map, presented to Parliament in 1882 and published with a book detailing the problem and the process (Torelli, 1882).Carta della Malaria dell'Italia (hereafter, 'Torelli map') should be regarded as a landmark achievement in the history of medical mapping (Figure 1).

The Torelli map as a GIS model baseline
While the Torelli map is relatively modern, it was produced just prior to proof that malaria is caused by protozoan parasites in 1885 and sixteen years before establishment of the vector role of Anopheles mosquitos in 1898 (Bagnato, 2017;Celli, 1901;Snowden, 2006, pp. 35-38;).It thus provides an outstanding combination of modern mapping, controlled observation with ranking, and a record of pre-eradication conditions.
Torelli acknowledges that Carta della Malaria dell'Italia is not a perfect record and opines that such can never be achieved.He openly addresses the issue of data consistency essential for studies like the present one.Torelli emphasizes definition of criteria for the ranking of malarial areas so as to preclude arbitrary application, while also admitting the question of whether all 259 health offices 'placed equal zeal on them' (Torelli, 1882, p. 6).
For this version of the study, 1 a high-quality JPEG scan of the Torelli map was obtained from the Italian Military Geographic Institute (IGMI; renamed from the MTI in 1882).This was converted to TIFF format for georeferencing in GIS software.The projection of the Torelli map could not be determined, as geodetic systems used by the IGMI are subject to military confidentiality (Baiocchi et al., 2019, pp. 127-128).Georeferencing to the Monte Mario Roma reference system produced the minimal distortion and the registered image raster was subsequently projected to WGS 1984 for further editing and geoprocessing.
Georeferencing revealed that much of the Torelli map detail was hand drawn.Coastline details, for example, are sometimes impossible to align.More vexing are the generalizedand often simply inaccuratelines of rivers, railways, and administrative division boundaries in the georegistered product.The implication that indicated malarial areas are similarly inaccurate poses a threat to the project's viability.
Amelioration occurred during creation of a GIS layer representing Torelli's malarial areas in three values.Instead of reclassifying the Torelli map raster, as in the original study, a vector polygon layer was created by tracing each malarial area and assigning corresponding values.Individual polygons were edited, if necessary, under certain assumptions: (1) As the original focus of Torelli's project was railroads and regional Health Councils were responsible for reporting in their area, it is assumed that malarial areas were carefully designated relative to rail lines and regional boundaries.
(2) Malarial areas along river courses in the Torelli map are assumed to be placed relative to the rivers themselves.
(3) Therefore, where railways, boundaries, or rivers in the georegistered Torelli map do not align with their true locations, associated malarial areas can be edited to align with the actual features for accuracy without damage to data integrity.
River course data is easily obtained, but the assumptions also require accurate rail line and district boundary datasets of the period for editing.Happily, exactly those were created for other studies and kindly shared by their authors (Ciccarelli & Groote, 2017, 2018).Specifics of the editing procedure incorporating those datasets appear in the Supplementary material.
Despite its inherent limitations, the Torelli map is at once the only qualified pre-eradication source known and remarkably convenient for this study.Since the region was the focus of early eradication campaigns, copious data of various types report malarial conditions in Italy, ranging in date from the late nineteenth century back well into antiquity.Many sources have sufficient geographical specificity for comparison with a GIS model spatial risk prediction.Also, southern Italy shares latitude, climate, as well as identical and comparable mosquito vectors with application interest areas across the Mediterranean.The edited layer of Torelli malarial zones (Figure 2) provides a suitable baseline for calibration and validation of the model.

Building a malaria risk model for antiquity
Contemporary malaria risk studies vary widely in identifying risk factors and relative weighting of corresponding datasets.Weight assignments frequently appear in a table without comment.Certain datasets are assumed as relevant, while others are selected subjectively or as a matter of convenience and availability.A 'meta-analysis' of such studies identified nine covariate categories of datasets, published with discussion as an aid to researchers by 'limiting subjective decisions within the variable selection process' (Weiss et al., 2015, pp. 2-7, 17).The Malaria Atlas Project (MAP; Hay & Snow, 2006) incorporated study results to improve its very complex contemporary risk model (Weiss et al., 2019, p. 324).Those categories provide a starting point for this model.
Data for anthropogenic categories cannot be known with spatial accuracy for antiquity and thus cannot be factored into the model.The same applies to datasets dependent on remote sensing platforms.These limitations cannot be avoided and thus necessarily reduce expectations for a model of ancient malaria risk vis-à-vis the standards for contemporary work.This study assumes the remaining categories are sufficient to produce a viable model.Those categories and rationale for inclusion of individual risk layers for this study's malaria risk model follow: Elevation.The meta-analysis expressed doubt about elevation's expected direct contribution because of its association with temperature and precipitation (Weiss et al., 2015, pp. 6-7).A far greater contribution for elevation is assumed here for several reasons: (1) elevation acts as a partial proxy for risk factors that cannot be known, such as land use and ground cover; (2) areas of known pre-eradication endemicity appear to have a high spatial correlation with lower elevations; (3) Anopheles mosquitos are poor fliers and cannot easily ascend, making local high spots theoretically safer as anecdotal data seems to confirm (Sallares, 2002, p. 57); and (4) ancient textual sources reveal an awareness of this factor (Vitruvius, On Architecture 1.4.1;Varro, On Agriculture 1.12; Antyllus, quoted by Stovaios, Florilegium 1010.18;trans.Sallares, 2002, p. 57).A Digital Elevation Model (DEM) derived from the 2000 Shuttle Radar Topography Mission (SRTM) dataset (Farr et al., 2007) serves as a primary layer in the model.
Temperature.Temperature is the most-used risk factor in previous studies.While MAP moved to dynamic data (Weiss et al., 2015, pp. 4-7), they earlier developed 'temperature support' layers with the metric of days per year temperatures can support infectious vectors (Gething et al., 2011b), for both P. falciparum and vivax.These datasets mitigate the necessary use of modern climatological data and potential effects of recent climate change by incorporating temporal data over a large span  with a 0-365 range of values (Gething et al., 2011a).
Precipitation.This study follows MAP in using WorldClim project precipitation data (Weiss et al., 2015, p. 5).Version 1.4interpolated from observed data 1960-1990(Hijmans et al., 2005) ) is used so the temporal range better aligns with the temperature layer.DEM Derivatives.Slope is the most frequently incorporated DEM derivative in surveyed studies and considered here.Surface moisture merits its own category in contemporary models that use dynamic datasets.For this study a Topical Wetness Index, also derived from the DEM layer, is used as a proxy for surface moisture. 2 Chosen covariates, with dataset sources, relevant metadata, and layer geoprocessing specifics appear in Supplementary material, Table 1.

Model design and implementation
The model's design allows variable mathematical weighting of risk layers to determine the best combination for prediction of malaria risk.The Torelli map serves as 'field observation data,' with endemicity levels assumed as risk levels.It presents ordinal data that is reclassified on a discrete scale.This results in four values: non-malarial area polygons were assigned the value 0 (sometimes labeled nessuna = no risk); leggiera areas 1 ( = slight risk); grave areas 2 ( = serious risk); and gravissimo areas 3 ( = most serious risk).
All risk layer datasets feature continuous data with varying scales.Each was rescaled to a continuous value range of 0-3 for comparison with the discrete Torelli layer values in the calibration process (see below).
Rescaling functions and values for each dataset appear in Supplementary material, Table 2.
The study area was limited to Southern Italy with the boundaries 12-19° E and 36-42° N (see Figure 4).In a change from the original study, Sardinia was excluded after realization that Torelli map data for that region was reported on significantly lower resolution maps (Torelli, 1882, p. 6).
Calibration, verification, and validation (Thacker et al., 2004) used a 'withheld area' approach.Within the study area one region was selected for calibration and verification, using the Torelli layer as a baseline.Ideal parameters determined by calibration for the 'selected area' were then applied to the 'withheld area' for validation.This procedure was repeated for different 'selected' and 'withheld' areas within the study boundaries for comparison.
Calibration occurred in rescaling each risk layer raster to the 0-3 range.Optimal rescale functions and values were determined by iterative nested loop processes executed via tailored Python scripts.Each iteration produced zonal statistics and calculated root mean square error (RMSE) values for the resulting raster against each Torelli map zone.Average RMSE for the four zones (mean of the means) served as the evaluation datum for the input values of each iteration.Overall minimum values were used for rescaling layers for combination in the selected area.(Supplementary material, Table 2).An example of Torelli map zones and rescaled risk layers within the study area appear in Figure 3.

Evaluation methods
For validation and verification in the full model, Python-scripted iterative nested loop process combined the calibrated risk layers in all possible percentage combinations within selected ranges. 3For each iteration, two main assessment criteria were calculated: (1) As in the original study, zonal statistics were calculated against Torelli zones for the selected area, with the average of RMSEs (mean of the means) for each zone providing the target assessment value.This ultimately remained the overall assessment criterion.Standard deviation of the zonal RMSE values was calculated as a supplementary statistic considering the class imbalance problem.
(2) Because of significant imbalance among the Torelli map risk classes (see Supplementary material, Table 3), each of the final series of iterations incorporated the ArcGIS Pro 'Compute Confusion Matrix' tool that outputs a table with the kappa index as an assumed evaluation metric.
The confusion matrix table includes user's and producer's accuracies for each class and an overall accuracy value.Overall accuracy was selected over kappa (see discussion in Stehman & Foody, 2019, p. 15, 19) as the second potential overall assessment criterion.However, a limitation of the confusion matrix approach in this case is the necessary use of ground truth data on a discrete scale (the Torelli layer) to assess the model's 0.00-3.00continuous risk layer calculations.Modeled layers must be reclassified to the discrete 0-3 classes to produce confusion matrices (see Supplementary material, Table 4).In the final analysis, confusion matrices and associated overall accuracy values are documented as supplemental statistics.
As trends emerged, the process was repeated with increasingly focused percentage ranges for each risk surface to obtain the minimum average RMSE and maximum overall accuracy.At the most focused percentages, average values for both metrics became random within narrow ranges (with overall accuracy having relatively wider ranges) for the lowest values.This phenomenon is likely due to the variance in spatial resolution of the risk layer sources.Therefore, 0.5% increments for each risk layer were the smallest used.For validation, the full model was applied with the same iterative process and metrics to the withheld area and criteria values compared.

Results
Sicily served as the initial 'selected area' for calibration and verification with the remnant of Southern Italy as the 'withheld area.'As in the previous study (Browning, 2021, pp. 73-77), the remainder of Southern Italy optimized at slightly lower elevation and precipitation with slightly higher temperature and TWI percentages.This was unsurprising given the higher temperatures and lower precipitation in Sicily.
This procedure was repeated with different selected and withheld areas within the study area for comparison.Low contributions of P. vivax temperature support and slope led to their exclusion from the final model, with improved results.The former essentially duplicates the P. falciparum layer with higher peak values.Similarly, slope is a major component of the topical wetness formula, so its contribution is effectively contained in TWI.
In all pairs of selected and withheld areas, the lowest average RMSE values differed within 5%.Overall accuracy derived from confusion matrices differed by as much as 20.8%.Lowest average RMSEs and highest overall accuracies obtained by the best performing layer combinations consistently show elevation contributing 55-72%, precipitation 22-28%, temperature support for P. falciparum 6-12%, and wetness potential 1-3%.
Iterations producing the highest overall accuracy values (calculated via confusion matrices) showed a greater variance in percent contribution for most risk layers at the most focused ranges when compared to the variances in the lowest average RMSE ranges.This phenomenon is demonstrated visually by Supplementary materials, Figures S1 and S2.
Because of this and the inherent limitations of the confusion matrix approach (see 3.4 above), the average of zonal RMSEs remained the final evaluation criterion.Data from the lowest layer combinations for the final selected and withheld areas appear in the Supplementary material, Tables 5  and 6. Results demonstrate the model's validity against a record of pre-eradication malaria endemicity.For application and creation of a malaria risk layer for the Mediterranean region, final contribution values (percentages) must be applied to each risk layer.As choosing the lowest values from a selected area would be arbitrary, values for model output are determined from the lowest modeled combinations from the entire study area; 12-19° E and 36-42° N. Supplementary material, Table 7 presents data from the twenty best combinations for the entire study area with full RMSE values and overall accuracy scores determined from confusion matrices.The final values for model application are: Elevation 62.1%; Precipitation 29.4%; Temperature 7.1%; and Topical Wetness Index 1.4%.A confusion matrix is provided for the full study area using the final values in Supplementary material, Table 8.
The study area is indicated in Figure 4 along with model output for Italy and surrounding areas with an extent allowing visual comparison to Torelli's map (Figure 1) and the derived Torelli layer (Figure 2).The main model goal and output, however, is an open-access GIS-capable layer of pre-modern potential malaria risk for the entire Mediterranean region.The profoundly local nature of malaria risk makes a single full-extent map of that layer impractical.Even a regional extent, as in Figure 6 for the NE Mediterranean, can only highlight major problematic areas.The Main Map accompanying this article is therefore limited to the areas covered in the following discussion of skeletal and anecdotal support for model validity.Even so, the much larger scale Figure 5 best illustrates the model's application utility.

Comparative skeletal evidence for malaria in antiquity
Conclusive evidence for malaria in antiquity is increasingly available through analysis of excavated skeletal remains.Significant examples come from Italy within the study area.
Burial remains from a Roman rural estate of the 1st-2nd century CE at Vagnari contain P. falciparum mitochondrial DNA.The cemetery itself lies on a hill with a moderate risk of 0.97 according to the model.But surrounding valleys yield a higher risk, with values of 1.19 within three km.This risk was likely heightened in the Roman period by the estate's deforestation and agricultural works (Marciniak et al., 2016(Marciniak et al., , 2018, pp. 218-220), pp. 218-220).
The Vagnari evidence demonstrates the issue of spatial certainty for the grave providing malarial evidence versus the unknown geographical range within which the individual contracted it.It is reasonable to assume, but not certain, that the person routinely visited the estate's larger extent.Mitochondrial DNA of P. falciparum from a grave at the port Velia yields a less uncertain relationship between the individual and risk (Marciniak et al., 2016).The modeled risk value at the tomb is a high 2.50, with main parts of the city and the majority of surrounding 'working' territory having mean value of 2.31 within 1500 m of the cemetery.
A remarkable cemetery of infant, child, and premature birth burials of the mid-5th century CE was uncovered near the River Tiber at Poggio Gramignano, outside the study area north of Rome.The cemetery lies in an abandoned Roman villa; like Vagnari, on a hilltop with high medium model risk (1.30), surrounded by higher risk areas (1.81 within 1500 m and 2.05 at 3 km).Skeletal deformations and the short span of over fifty child burials suggested a P. falciparum malaria epidemic cause.Grave goods suggestive of witchcraft or magicperhaps desperate ritual measures to contain the outbreakare cited as support (Lane, 1999;Soren 2003;Soren & Soren, 1999).At least one skeleton has conclusively yielded P. falciparum ribosomal DNA (Sallares & Gomzi, 2002) with testing of others ongoing (Montagnetti et al., 2020).

Anecdotal support for model validity
The quantitative results demonstrate the model's validity against a systematic record of data-collection from pre-eradication Italy and scientific evidence confirms the presence of malaria in modeled risk areas in Roman times.Anecdotal evidence from textual sources can extend confidence in the model to other periods.
Numerous sources detail pre-eradication malarial conditions in Italy, ranging in date from the late nineteenth century back well into antiquity.Some have geographical specificity sufficient for comparison with the model's risk prediction.Those based on textual sources also anticipate and preview application of the ancient malaria risk model to such cases in other regions (see Browning, 2021, pp. 68-69).Limited examples suffice here.
The Pontine Marshes, lying between the coast and mountains south of Rome and now drained, were chronically endemic from antiquity until the twentieth century (Sallares, 2002, p. 4, 168-191).The model calculates the region as especially problematic (Figure 5).
Nineteenth century malariologists investigating the hill town Sezze (ancient Setia), noted that residents whose homes on the slope facing the marsh contracted malaria far more frequently than those on the opposite slope.Women, who tended to stay at home, were also less infected than men who worked the fields below the town.It was not unusual for a woman to have lost three husbands to malaria before the age of thirty (Celli, 1901, p. 84;Sallares, 2002, pp. 55-57)!Norma (ancient Norba) sits atop a steep defile overlooking the Marshes and was malaria free in the nineteenth century.A kilometer distant at the base of the cliff, Ninfa was so pestilent that it was eventually abandoned in the late seventeenth century (Celli, 1901, p. 85;Hackett, 1937, pp. xi-xii;Sallares, 2002, pp. 57-60).The model's risk map alone (Figure 5) clearly distinguishes the contrasting risk levels of the neighboring towns.GIS consultation of the risk layer reveals a moderate mean risk for Norba's urban area of 1.21 and a high risk of 2.38 for the center of Ninfa.
References to the pestilential nature of the Pontine Marshes extend to the Roman period.The poet and satirist Horace describes the frustrations of travel along the Via Appia in 36 BCE.At the road station called Forum Appii (modeled high risk of 2.56) below Setia, he curses the 'damned mosquitos' of the region (Horace, Satires 5.14).Horace highlights the favorable vector capacity of the area, made all the greater by construction of the road itself (Sallares, 2002, p. 181).A canal Horace mentions is described in the late first century BCE by Strabo as serving for transport along the Via Appia, supplied by water from the marshes (Strabo 5.3.6.233).In the sixth century, locals called it 'Decennovium in the Latin tongue, because it flows past nineteen milestones' (Procopius, History of the Wars 5.11.2).The presence of a canal suggests the once fertile region had become permanently marshy by the first century BCE; transformed by deforestation and road construction (O'Sullivan et al., 2008, p. 758).The malaria model thus appears useful for predicting potential spatial risk, even when the actual peril is dependent on anthropogenic conditions.

Potential utility
The model's potential as a tool goes beyond corroborating risk in cases where malaria is otherwise confirmed and outside the study area.My earlier article demonstrated its utility for assessing ancient text sources that imply malarial conditions along Roman roads (Browning, 2021, pp. 81-83).
In one such case, Sidonius Apollinaris wrote of a 467 CE trip from Ravenna to Rome along the Via Flaminia, where he describes continual malarial conditions and apparently contracted the disease (Sidonius Apollonaris, Letters 1.5.6-9).The model shows high malaria threat along most of the route.Current investigators at Poggio Gramignano note the spatial and temporal proximity of Sidonius' account with their infant cemetery burials (Montagnetti et al., 2020, p. 284, n. 6).Could both be evidence of the same malarial outbreak?In 452, fifteen years before Sidonius' journey, Attila the Hun attacked Italy and sacked Milan.His subsequent and otherwise inexplicable retreat was attributed by one ancient source to 'famine and some kind of disease' (Hydatius,Chronicle 29).Malaria is a reasonable suspect, especially given evidence from the Poggio Gramignano cemetery (Harper, 2017, pp. 196-197, 338, n. 74;Sallares, 2002).The malaria risk model presented here can contribute substantively to such discussions.

Study limitations
To summarize limitations referenced above, a model for malaria risk in antiquity can only include risk factors that can be reasonably known with spatial specificity for pre-modern times.Anthropogenic layers, potentially major risk factors, are thus eliminated.Validation of a pre-modern model is rendered possible only by existence of the Torelli map.The Torelli map, however, complicates evaluation of the model's continuous scale output with its nominal classification.As a result of these things, model expectations are accordingly reduced compared to contemporary malaria risk projections.Consequently, evaluation statistics should be understood as relative.For example, the typical 85% overall accuracy target is unrealistic for this study (Stehman & Foody, 2019, p. 19).
The model is also limited in that it does not attempt temporal risk assessment (for different months, for example).In keeping with the Torelli map data, it does not differentiate between P. falciparum and P. vivax or other malaria species.
It is important to note that the model and maps of its results do not predict where malaria did or will occur; nor do they provide a measure of absolute risk.They rather show potential spatial risk in terms of favorable conditions for malaria endemicity or outbreaks, based on relative risk layers that can be reasonably known for pre-modern times.

Conclusions
Quite like the conclusion Luigi Torelli drew regarding his own map (Torelli, 1882, p. 6), the model developed here is not perfect but has great potential.It performs satisfactorily against pre-eradication data and enjoys scientific and anecdotal corroboration well into antiquity.It thus appears to be a viable tool for its intended purpose: application to appropriate cases involving nuanced text sources for historical debate and reconstruction.
The main product of the study is an open-access malaria risk layer suitable for GIS analysis.The model-produced maps presented here are for illustration and presented accordingly with unclassed stretched symbology.For analysis, exact modeled risk values for points or areas should be obtained from the full malaria risk layer using GIS tools.In addition to the other maps, Figure 6 provides a smaller-scale illustration of the layer for the northeast Mediterranean.

Software
Map images requiring georeferencing were prepared using editing and conversion features of ACDSee Photo Studio 2020.All geoprocessing and map production utilized ArcGIS Pro 3.

Notes
1.For the original study (Browning, 2020(Browning, , 2021)), neither an original copy, nor a high-resolution scan of the map could be located.A large JPEG image of an unfolded original was obtained from an online article (Bagnato, 2017).Preparation of the image for GIS use entailed: (1) conversion to TIFF format; (2) manual removal of labeling and roads; (3) reduction of color/bit depth; (4) georegistration; and (5) an iterative process of comparing with other layers and manual clarification as needed.The resulting raster was reclassified, producing a suitable but far from ideal layer for model verification.
2. Distance to stream was also incorporated in the original study but was eliminated as a contributor to risk in the verification process (Browning, 2021).3.This represents a functional improvement in model development over the original version, in which 'powers' of layer combinations were converted to percentages after the fact, limiting comparison slightly.

Figure 1 .
Figure 1.The unfolded map from Carta della Malaria dell'Italia (Torelli, 1882) as provided by the Italian Military Geographic Institute.

Figure 2 .
Figure 2. The Torelli Map layer, against which risk layer combinations were compared in model verification and validation.

Figure 3 .
Figure 3.The Torelli Map zones with discrete 0-3 values and the four final risk layers with continuous 0-3 data, for Sicily and lower Calabria.

Figure 4 .
Figure 4. Model output for Italy and surrounding area with study area indicated.

Figure 5 .
Figure 5. Model output for the environs of Rome and the Pontine Marshes.

Figure 6 .
Figure 6.Model output for the northeast Mediterranean, including Greece and Anatolia.