arxiv: 2604.11818 · v1 · submitted 2026-04-10 · 🧬 q-bio.PE · math.PR

Recognition: unknown

Scale-dependent Temporal Signatures of Arboviral Transmission in Urban Environments

Marc\'ilio Ferreira dos Santos , Cleiton de Lima Ricardo

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:10 UTC · model grok-4.3

classification 🧬 q-bio.PE math.PR

keywords arboviral transmissionspatiotemporal modelingepidemic differentiationtemporal scaleurban environmentsdenguezikachikungunya

0 comments

The pith

Differences between dengue, Zika and chikungunya transmission emerge only at specific temporal scales rather than from spatial proximity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds a probabilistic spatiotemporal model based on pairwise interaction kernels to examine arboviral spread using georeferenced case data from Recife, Brazil. Parameters are estimated by maximum likelihood, with separate terms for spatial distance and time-delayed influence, and with biological constraints applied. The fitted spatial component collapses to a non-discriminatory value, showing that closeness alone does not separate the three diseases at city scale. Temporal components, however, produce differentiation only after a critical window length; shorter windows yield apparent distinctions that vanish under constraints. The central conclusion is that epidemic differences are not fixed properties of the pathogens but arise as an emergent effect of the chosen observation scale.

Core claim

Interactions are expressed as a function of spatial distance and temporally delayed influence whose parameters are obtained by maximum likelihood. When fitted to the Recife data the spatial parameter collapses, indicating that proximity supplies no reliable separation among dengue, Zika and chikungunya. Temporal dynamics display scale dependence: statistical differentiation appears only beyond a minimum temporal window. Models without biological constraints mainly recover short-term co-occurrence and produce non-robust distinctions, whereas constrained models recover a shared underlying transmission structure. The resulting networks display localized, structured interaction patterns.

What carries the argument

Pairwise interaction kernel that encodes spatial distance and temporally delayed influence, with parameters estimated by maximum likelihood under biological constraints.

If this is right

Unconstrained models primarily capture short-term co-occurrence and therefore generate apparent but non-robust differences between diseases.
Biologically constrained models recover a common underlying transmission structure across the three arboviruses.
Reconstructed transmission networks exhibit localized and structured interaction patterns consistent with plausible epidemic propagation.
Epidemic differentiation is an emergent phenomenon that depends on the temporal scale at which the data are examined.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Public-health responses in dense cities may gain more from timing interventions to longer transmission windows than from purely spatial targeting.
The same kernel framework could be applied to other urban datasets to test whether the critical temporal window length is conserved across cities.
The collapse of spatial information raises the question of whether finer-scale mobility or vector-density layers would restore spatial discriminatory power.

Load-bearing premise

The pairwise interaction kernel with maximum-likelihood parameter estimation, once biologically constrained, correctly isolates the underlying transmission structure without missing unmodeled factors such as vector density variation or reporting biases.

What would settle it

Re-fitting the same model to the Recife data while removing the biological constraints and observing that temporal differentiation remains stable at all window lengths would falsify the claim that differentiation is scale-dependent.

Figures

Figures reproduced from arXiv: 2604.11818 by Cleiton de Lima Ricardo, Marc\'ilio Ferreira dos Santos.

**Figure 1.** Figure 1: Kernel density estimation of arboviral cases in Recife. The spatial distributions exhibit similar clustering patterns across diseases, with [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

**Figure 2.** Figure 2: Comparison between unconstrained (left) and biologically constrained (right) transmission networks. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: Most probable transmission network inferred under biolog [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Distribution of temporal parameters across diseases. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

**Figure 5.** Figure 5: Dependence of statistical differentiation on temporal window. At short temporal scales, the system behaves homogeneously, with no significant differences detected between diseases. As the temporal window increases, differences begin to emerge. This behavior indicates the existence of a critical temporal scale beyond which disease-specific patterns become observable. 4.8. Co-occurrence versus Transmis… view at source ↗

read the original abstract

Understanding epidemic dynamics in urban environments requires models that capture interactions across space and time while incorporating biological constraints. In this work, we propose a probabilistic spatiotemporal framework based on pairwise interaction kernels to analyze arboviral transmission using large-scale georeferenced data from Recife, Brazil. The model describes interactions as a function of spatial distance and temporally delayed influence, with parameters estimated via maximum likelihood. Our results reveal a marked asymmetry between spatial and temporal components. The spatial parameter systematically collapses, indicating that spatial proximity does not provide discriminatory information between diseases at the urban scale. In contrast, temporal dynamics exhibit scale-dependent behavior: statistical differentiation between dengue, Zika, and chikungunya emerges only beyond a critical temporal window. We show that unconstrained models primarily capture short-term co-occurrence, leading to apparent but non-robust differences, while biologically constrained models reveal a common underlying transmission structure. Additionally, reconstructed transmission networks exhibit localized and structured interaction patterns consistent with plausible epidemic propagation. These findings demonstrate that epidemic differentiation is not intrinsic, but an emergent phenomenon dependent on temporal scale, highlighting the importance of biologically grounded and scale-aware modeling in spatiotemporal epidemic analysis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims spatial proximity adds little to distinguishing dengue, Zika, and chikungunya in Recife while temporal scale does under biological constraints, but the supporting evidence stays thin on validation and possible data artifacts.

read the letter

The central finding is that unconstrained pairwise kernels mostly recover short-term co-occurrence among the three arboviruses, while adding biological constraints makes spatial parameters collapse and lets temporal windows reveal a shared structure beyond some critical delay. That asymmetry is the concrete new observation from the Recife georeferenced cases. The work applies an established kernel approach to multi-disease urban data and produces reconstructed networks that look locally structured, which is a reasonable use of the data they have. Those are the parts that hold up on a first read. The weaknesses are more substantial than minor. The abstract supplies no explicit equations, no parameter uncertainties, no data exclusion rules, and no test on held-out time periods, so the post-hoc critical window cannot be checked for robustness. Maximum-likelihood fitting on the same observations used to declare the scale dependence creates the usual risk that the result partly reflects the fitting procedure rather than independent structure. The stress-test concern about unmodeled vector density or reporting biases is not obviously refuted by what is shown; those factors could still drive apparent lags. The paper therefore demonstrates an interesting modeling choice but does not yet close the loop on whether the scale dependence is intrinsic to transmission or an artifact of the Recife surveillance system. This is mainly for researchers already working on spatiotemporal kernels or arbovirus surveillance in dense cities. A reader looking for a worked example of constrained kernels on real multi-disease data could extract the data-handling steps and the reported asymmetry, but anyone needing reproducible methods or falsifiable predictions will find the current version under-specified. I would send it to peer review rather than desk-reject, with clear requests for the full model equations, error estimates, cross-validation, and checks against plausible confounders. The idea is worth the referee time if the authors can supply those pieces.

Referee Report

3 major / 2 minor

Summary. The paper claims to develop a probabilistic spatiotemporal framework using pairwise interaction kernels to model arboviral transmission in urban environments, applied to georeferenced case data from Recife, Brazil for dengue, Zika, and chikungunya. Key findings include the collapse of spatial parameters indicating lack of discriminatory information at urban scales, and scale-dependent temporal signatures where statistical differentiation between the diseases emerges only beyond a critical temporal window when biological constraints are applied. Unconstrained models are said to capture short-term co-occurrence leading to apparent differences, while constrained models reveal a common underlying structure, with reconstructed transmission networks showing localized patterns consistent with epidemic propagation. The overall conclusion is that epidemic differentiation is an emergent phenomenon dependent on temporal scale.

Significance. If the central claims hold after addressing methodological concerns, this work would be significant for the field of spatiotemporal epidemiology. It provides evidence that apparent differences in arboviral transmission are not intrinsic to the pathogens but arise from scale-dependent temporal dynamics, emphasizing the value of incorporating biological constraints and scale awareness in modeling. This could lead to improved understanding of urban epidemic dynamics and more effective intervention strategies. The use of large-scale georeferenced data and network reconstruction adds practical value, though robustness needs confirmation.

major comments (3)

[Abstract] The abstract reports clear asymmetry between collapsed spatial and scale-dependent temporal parameters, yet provides no error bars, no explicit model equations, no data exclusion criteria, and no validation against held-out periods; post-hoc choice of the critical temporal window cannot be assessed.
[Methods] Parameters are estimated by maximum likelihood on the same data used to declare scale dependence; the claim that unconstrained models capture only short-term co-occurrence while constrained ones reveal common structure is therefore partly tautological with the fitting procedure itself.
[Results/Discussion] The central claim that differentiation is emergent at certain scales rests on the assumption that the pairwise interaction kernel with MLE and biological constraints correctly isolates the underlying transmission structure. Unmodeled factors such as vector density variation or reporting biases in the Recife data may confound the reported scale dependence, making it potentially an artifact of data collection rather than a true emergent property.

minor comments (2)

[Abstract] Consider adding a brief mention of the specific biological constraints used in the model to enhance clarity for readers.
[Figures] Ensure that any figures showing parameter estimates include error bars or confidence intervals for better interpretation of the collapse and scale dependence.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and insightful comments, which have helped us identify areas for clarification and strengthening of the manuscript. We address each major comment point by point below, outlining our responses and planned revisions where appropriate.

read point-by-point responses

Referee: [Abstract] The abstract reports clear asymmetry between collapsed spatial and scale-dependent temporal parameters, yet provides no error bars, no explicit model equations, no data exclusion criteria, and no validation against held-out periods; post-hoc choice of the critical temporal window cannot be assessed.

Authors: We agree that the abstract, constrained by length, omits several technical details that would aid assessment. In the revised manuscript, we will expand the abstract to briefly reference the model equations (detailed in Methods), report error bars or confidence intervals on the key collapsed spatial and scale-dependent temporal parameters, and specify data exclusion criteria such as removal of cases lacking precise geolocation or with incomplete temporal records. For validation, we will note that the framework includes checks against held-out temporal periods (with results in supplementary materials). Regarding the critical temporal window, we will clarify its determination via systematic variation of window sizes and identification of the threshold where likelihood-ratio tests indicate statistically significant differentiation between diseases, rather than arbitrary post-hoc selection. These changes will be incorporated to improve transparency. revision: yes
Referee: [Methods] Parameters are estimated by maximum likelihood on the same data used to declare scale dependence; the claim that unconstrained models capture only short-term co-occurrence while constrained ones reveal common structure is therefore partly tautological with the fitting procedure itself.

Authors: We appreciate this point and will revise the Methods to eliminate any ambiguity. The biological constraints (e.g., minimum incubation and infectious periods drawn from independent virological literature) are imposed a priori and are not fitted from the Recife case data. The unconstrained model permits free estimation of all kernel parameters via MLE, while the constrained version enforces these external priors. Scale dependence is assessed by varying the temporal window size independently of the fitting step and observing the emergence of differentiation. We will add explicit text separating the sources of constraints from the data, include a sensitivity analysis demonstrating that the common underlying structure holds across reasonable constraint variations, and clarify that the short-term co-occurrence capture in unconstrained models is a direct consequence of allowing parameters to fit noise at small scales. This revision will strengthen the non-tautological nature of the comparison. revision: yes
Referee: [Results/Discussion] The central claim that differentiation is emergent at certain scales rests on the assumption that the pairwise interaction kernel with MLE and biological constraints correctly isolates the underlying transmission structure. Unmodeled factors such as vector density variation or reporting biases in the Recife data may confound the reported scale dependence, making it potentially an artifact of data collection rather than a true emergent property.

Authors: This concern is well-taken and highlights a genuine limitation in observational data. While the model infers pairwise interactions from georeferenced cases, factors like spatially varying vector density or differential reporting could influence patterns. However, the consistent collapse of spatial parameters across all three diseases argues against spatial confounders driving the results, as such biases would be expected to affect diseases similarly yet do not produce differentiation at small scales. Temporal scale dependence emerges robustly under constraints. In revision, we will add a dedicated limitations paragraph in the Discussion explicitly addressing these confounders, including how the large dataset size and focus on relative inter-disease differences provide some mitigation. We will also include supplementary robustness analyses, such as data subsampling to simulate reporting rate variations. We maintain that the emergent property interpretation is supported by the asymmetry and network reconstructions, but acknowledge that complete isolation of transmission dynamics would benefit from additional environmental covariates not present in the current dataset. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation follows from MLE on external data

full rationale

The abstract describes a pairwise interaction kernel model whose parameters are estimated via maximum likelihood on the Recife georeferenced case data. Claims of scale-dependent temporal signatures, spatial parameter collapse, and differentiation between constrained versus unconstrained models are presented as outcomes of applying the fitted model to that data and inspecting the resulting networks. No equations, self-citations, or definitional steps are quoted that would reduce any central result to an input by construction. The distinction between short-term co-occurrence and common structure is an interpretive finding from the fits rather than a tautological renaming or self-referential constraint. The chain therefore remains self-contained against the external benchmark of the observed transmission events.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The framework rests on the assumption that transmission can be represented by separable spatial-distance and temporal-delay kernels whose parameters are identifiable from case-location data alone; no new entities are postulated.

free parameters (1)

spatial and temporal kernel parameters
Estimated via maximum likelihood; their values determine the reported collapse of spatial component and the critical temporal window.

axioms (2)

domain assumption Pairwise interactions between cases are sufficient to capture urban transmission dynamics
Core modeling choice stated in the abstract.
domain assumption Biological constraints can be imposed by restricting the temporal kernel support
Used to contrast unconstrained versus constrained models.

pith-pipeline@v0.9.0 · 5498 in / 1362 out tokens · 33742 ms · 2026-05-10T16:10:24.514229+00:00 · methodology

discussion (0)

Forward citations

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Reference graph

Works this paper leans on

51 extracted references · 5 canonical work pages · cited by 1 Pith paper

[1]

R.Markov Chains

Norris, J. R.Markov Chains. Cambridge Univer- sity Press, 1998

1998
[2]

A.; Peres, Y .; Wilmer, E

Levin, D. A.; Peres, Y .; Wilmer, E. L.Markov Chains and Mixing Times. American Mathemati- cal Society, 2017

2017
[3]

Physical Review E, 77(3), 036111, 2008

Estrada, E.; Hatano, N.Communicability in com- plex networks. Physical Review E, 77(3), 036111, 2008

2008
[4]

Ball, M. O. Computational complexity of network reliability analysis.IEEE Transactions on Relia- bility, 35(3), 230–239, 1986

1986
[5]

J.The Combinatorics of Network Re- liability

Colbourn, C. J.The Combinatorics of Network Re- liability. Oxford University Press, 1987

1987
[6]

Ricci curvature of Markov chains on metric spaces.Journal of Functional Analysis, 256(3), 810–864, 2009

Ollivier, Y . Ricci curvature of Markov chains on metric spaces.Journal of Functional Analysis, 256(3), 810–864, 2009

2009
[7]

Graph curvature for differentiating cancer net- works.Scientific Reports, 5, 12323, 2016

Sandhu, R.; Georgiou, T.; Reznik, E.; Zhu, L.; Kolesov, I.; Senbabaoglu, Y .; Tannenbaum, A. Graph curvature for differentiating cancer net- works.Scientific Reports, 5, 12323, 2016

2016
[8]

Ricci cur- vature of the Internet topology.IEEE INFOCOM, 2019

Ni, C.-C.; Lin, Y .-Y .; Luo, F.; Gao, J. Ricci cur- vature of the Internet topology.IEEE INFOCOM, 2019

2019
[9]

C.Socio-environmental determinants of dengue epidemics

Barcellos, C.; Sabroza, P. C.Socio-environmental determinants of dengue epidemics. Cadernos de Saúde Pública, 17, 77–86, 2001

2001
[10]

G.; Costa, M

Teixeira, M. G.; Costa, M. C. N.; Barreto, F.; Mota, E.Dengue: twenty-five years since its reemergence in Brazil. Cadernos de Saúde Pública, 25(Suppl 1), S7–S18, 2009

2009
[11]

A.; Nogueira, R

Honório, N. A.; Nogueira, R. M. R.; Codeço, C. T.; Carvalho, M. S.; Cruz, O. G.; Magalhães, M. A. F. M.; Lourenço-de-Oliveira, R.Spatial evalu- ation and modeling of dengue seroprevalence and vector density in Rio de Janeiro. PLoS Neglected Tropical Diseases, 3(11), e545, 2009

2009
[12]

J.; Rohani, P.Modeling Infectious Diseases in Humans and Animals

Keeling, M. J.; Rohani, P.Modeling Infectious Diseases in Humans and Animals. Princeton Uni- versity Press, 2008

2008
[13]

Topological persistence and simplification

Edelsbrunner, H.; Letscher, D.; Zomorodian, A. Topological persistence and simplification. In: Proceedings of the 41st Annual Symposium on Foundations of Computer Science (FOCS), 454– 463, 2000

2000
[14]

Computing persis- tent homology.Discrete and Computational Ge- ometry, 33(2), 249–274, 2005

Zomorodian, A.; Carlsson, G. Computing persis- tent homology.Discrete and Computational Ge- ometry, 33(2), 249–274, 2005

2005
[15]

An Introduction to

Chazal, F.; Michel, B.; Rinaldo, A. An in- troduction to topological data analysis: funda- mental and practical aspects for data scientists. arXiv:1710.04019, 2016

work page arXiv 2016
[16]

Understanding climate variability using topological data analysis

Lorenz, D.; Junge, M.; Kramm, A. Understanding climate variability using topological data analysis. Chaos, 31(3), 033122, 2021

2021
[17]

A topo- logical representation of branching neuronal mor- phologies.Biosystems, 199, 104286, 2021

Kanari, L.; Dlotko, P.; Williams, S.; et al. A topo- logical representation of branching neuronal mor- phologies.Biosystems, 199, 104286, 2021

2021
[18]

Topological meth- ods in spatial epidemiology: detecting hotspots using persistent homology.Scientific Reports, 13, 2043, 2023

Bhatt, S.; Kumar, D.; Singh, A. Topological meth- ods in spatial epidemiology: detecting hotspots using persistent homology.Scientific Reports, 13, 2043, 2023

2043
[19]

S.; Souza-Santos, R.; Barcellos, C

Carvalho, M. S.; Souza-Santos, R.; Barcellos, C. Machine learning and spatial epidemiology: A new approach to understand urban arboviruses. Revista de Saúde Pública, 55, 44, 2021

2021
[20]

I.Satellite earth observa- tion data in epidemiological modeling of malaria, 9 dengue and West Nile virus: A scoping review

Parselia, E.; Kontoes, C.; Tsouni, A.; Had- jichristodoulou, C.; Kioutsioukis, I.; Magiorki- nis, G.; Stilianakis, N. I.Satellite earth observa- tion data in epidemiological modeling of malaria, 9 dengue and West Nile virus: A scoping review. Re- mote Sensing, 11(16), 1862, 2019

2019
[21]

The physics of communicability in complex net- works.Physics Reports, 514(3), 89–119, 2012

Estrada, E.; Hatano, N.; Benzi, M. The physics of communicability in complex net- works.Physics Reports, 514(3), 89–119, 2012. doi:10.1016/j.physrep.2012.01.006

work page doi:10.1016/j.physrep.2012.01.006 2012
[22]

Scientific Reports, 9(1), 16911, 2019

Massaro, E.; Kondor, D.; Ratti, C.Assessing the interplay between human mobility and mosquito- borne diseases in urban environments. Scientific Reports, 9(1), 16911, 2019

2019
[23]

I.; Simoy, M

Simoy, M. I.; Simoy, M. V .; Canziani, G. A.The effect of temperature on the population dynamics of Aedes aegypti. Ecological Modelling, 314, 100– 110, 2015

2015
[24]

Infectious Diseases of Poverty, 8, 1–12, 2019

Zheng, L.; Ren, H.-Y .; Shi, R.-H.; Lu, L.Spa- tiotemporal characteristics and primary influenc- ing factors of typical dengue fever epidemics in China. Infectious Diseases of Poverty, 8, 1–12, 2019

2019
[25]

C.; Brown, H

Moore, T. C.; Brown, H. E. EstimatingAedes ae- gyptiflight distance: meta-data analysis.Journal of Medical Entomology, 59(4), 1164–1170, 2022

2022
[26]

A.; et al

Pruszynski, C. A.; et al. Estimation of population age structure, daily survival rates, and potential to support dengue virus transmission for Florida KeysAedes aegypti.PLoS Neglected Tropical Dis- eases, 18(8), e0012350, 2024

2024
[27]

Geographical Analysis, 27(2), 93– 115, 1995

Anselin, L.Local Indicators of Spatial Associ- ation—LISA. Geographical Analysis, 27(2), 93– 115, 1995

1995
[28]

B.; Da Cunha, J

De Souza, D. B.; Da Cunha, J. T. S.; Dos Santos, E. F.; Correia, J. B.; Da Silva, H. P.; De Lima Filho, J. L.; Albuquerque, J.; San- tos, F. A. N. Using discrete Ricci curvatures to infer COVID-19 epidemic network fragility and systemic risk.Journal of Statistical Mechanics, 2021(5), 053501, 2021

2021
[29]

American Chemical So- ciety, 2012

Estrada, E.The Structure of Complex Networks: Theory and Applications. American Chemical So- ciety, 2012

2012
[30]

Forman–Ricci communicability curva- ture of graphs and networks.European Journal of Applied Mathematics, 1–25, 2025

Estrada, E. Forman–Ricci communicability curva- ture of graphs and networks.European Journal of Applied Mathematics, 1–25, 2025

2025
[31]

H.; De La Nuez, R.; Estrada, E

Grass-Boada, D. H.; De La Nuez, R.; Estrada, E. Graph/Network Reduction Based on Commu- nicability Vertex Similarity. 2025. (Manuscrito em processo de publicação.)

2025
[32]

P.Spatial Econometrics: From Cross- Sectional Data to Spatial Panels

Elhorst, J. P.Spatial Econometrics: From Cross- Sectional Data to Spatial Panels. Springer, 2014

2014
[33]

Wiley, 2015

Blangiardo, M.; Cameletti, M.Spatial and Spatio- Temporal Bayesian Models with R-INLA. Wiley, 2015

2015
[34]

arXiv:2510.13672, 2025

Ferreira dos Santos, M.; Dos Santos Rodrigues de Melo, A.Hierarchical Bayesian Model- ing of Dengue in Recife, Brazil (2015–2024). arXiv:2510.13672, 2025

work page arXiv 2015
[35]

Zenodo.https://doi.org/10

Ferreira dos Santos, M.; Dos Santos Rodrigues de Melo, A.Spatial and Socioenvironmental Dengue Dataset of the Recife Metropolitan Area (2015–2024). Zenodo.https://doi.org/10. 5281/zenodo.17364863, 2025

2015
[36]

Zenodo.https://doi.org/10.5281/ zenodo.17849496, 2025

Ferreira dos Santos, M.; Dos Santos Rodrigues de Melo, A.Dengue Cases in Recife, Brazil (2015–2024): Clean and Geocoded Dataset (v1.0). Zenodo.https://doi.org/10.5281/ zenodo.17849496, 2025

2015
[37]

Ferreira dos Santos, M.Dengue Risk Model- ing and Network Curvature Analysis – Code Repository. GitHub. Disponível em:https: //github.com/DocDengueResearcher/ dengue-risk-recife-anonymous/blob/ main/Graph_Prototype_2_0.ipynb
[38]

T.; Ajelli, M.; et al.The effect of travel restrictions on COVID-19 spread

Chinazzi, M.; Davis, J. T.; Ajelli, M.; et al.The effect of travel restrictions on COVID-19 spread. Science, 368(6489), 395–400, 2020

2020
[39]

M.; Botai, J

Adeola, A. M.; Botai, J. O.; Olwoch, J. M.; Raut- enbach, C. J. H.; Adisa, O. M.Landsat-derived environmental metrics for mapping mosquito habi- tats. South African Geographical Journal, 99(1), 14–28, 2017

2017
[40]

Borges, I. V . G.; Musah, A.; Dutra, L. M. M.; et al.Interrelationship between precipitation and dengue in Recife. Frontiers in Public Health, 12, 1456043, 2024

2024
[41]

M.; et al.Dengue Monitoring Dashboard

Oliveira, M. M.; et al.Dengue Monitoring Dashboard. Cadernos de Saúde Pública, 38, e00252021, 2022. 10

2022
[42]

F., Melo, A

Santos, M. F., Melo, A. R. S., & Ricardo, C. L.Simulation SIR in Graphs: Het- erogeneous Curvature-Weighted Models. Zenodo (2025). Available at:https: //doi.org/10.5281/zenodo.17884569. doi:10.5281/zenodo.17884569

work page doi:10.5281/zenodo.17884569 2025
[43]

F.; Ricardo, C

Santos, M. F.; Ricardo, C. L.; Melo, A. S. R.,Correlation-Weighted Communicability Cur- vature as a Structural Driver of Dengue Spread: A Bayesian Spatial Analysis of Recife (2015–2024), arXiv:2512.00315, 2025. Available at:https: //arxiv.org/abs/2512.00315

work page arXiv 2015
[44]

W.Systems of differential equations which are competitive or cooperative I: Limit sets

Hirsch, M. W.Systems of differential equations which are competitive or cooperative I: Limit sets. SIAM Journal on Mathematical Analysis, 16(2), 423–439, 1985

1985
[45]

L.Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems

Smith, H. L.Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems. Mathematical Surveys and Monographs, V ol. 41. American Mathematical So- ciety, 1995

1995
[46]

Kluwer Academic Publishers, 1988

Anselin, L.Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, 1988

1988
[47]

P.; Pace, R

LeSage, J. P.; Pace, R. K.Introduction to Spatial Econometrics. CRC Press, 2009

2009
[48]

J.; Folmer, H.; Rey, S

Florax, R. J.; Folmer, H.; Rey, S. J. Specification searches in spatial econometrics. Regional Science and Urban Economics, 33(5), 557–579, 2003

2003
[49]

Approximate Bayesian inference for latent Gaussian models us- ing INLA

Rue, H.; Martino, S.; Chopin, N. Approximate Bayesian inference for latent Gaussian models us- ing INLA. Journal of the Royal Statistical Society B, 71(2), 319–392, 2009

2009
[50]

H.; Simpson, D.; Rue, H

Riebler, A.; Sørbye, S. H.; Simpson, D.; Rue, H. An intuitive Bayesian spatial model for dis- ease mapping that accounts for scaling. Statistical Methods in Medical Research, 25(4), 1145–1165, 2016

2016
[51]

An ex- plicit link between Gaussian fields and Gaussian Markov random fields: the SPDE approach

Lindgren, F.; Rue, H.; Lindström, J. An ex- plicit link between Gaussian fields and Gaussian Markov random fields: the SPDE approach. Jour- nal of the Royal Statistical Society B, 73(4), 423– 498, 2011. 11

2011