Feature importance of socio-economic parameters in Tuberculosis modeling

Andrei Neverov; Olga Krivorotko

REVIEW 4 major objections 4 minor 21 references

Feature importance of socio-economic parameters in Tuberculosis modeling

T0 review · 4 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that five socio-economic indicators—mean income per capita, workforce, number of HIV tested, unemployment, and total population—are the most influential features for reconstructing regional tuberculosis infection rates…

desk verdict An honest proof-of-concept that applies Shapley-based feature ranking to a simplified TB-HIV ODE inverse problem across Russian regions, but the numerical ranking rests on unvalidated β_c targets and needs robustness work before it can be trusted. read the letter →

arxiv 2412.01844 v1 pith:JRBBBR5R submitted 2024-11-23 physics.soc-ph q-bio.PE

Andrei Neverov , Olga Krivorotko This is my paper · ORCID

classification physics.soc-phq-bio.PE MSC 92D3065J20

keywords featureimportanceShapleyvaluestuberculosisHIVco-infectionmathematicalmodelinverseproblemGaussianprocesssocio-economicparameters

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether a single epidemic model can be adapted to different regions by feeding it socio-economic data instead of re-fitting epidemiological parameters for each region separately. It solves an inverse problem for a simplified TB–HIV co-infection ODE model on 87 Russian regions to obtain per-region infection rates $\beta_c$, then uses a Gaussian process regressor to predict $\beta_c$ from socio-economic indicators. Applying Shapley values ranks these indicators, identifying mean income per capita, workforce, number of HIV tested, unemployment, and total population as the most influential. The authors stress that the regression was accurate to under 10% in only 10 regions, so the ranking is a promising step rather than a finished tool.

What carries the argument

The central mechanism is the combination of (a) a simplified SIR-like ODE model (Eq. 2) that collapses latent-TB transfer into the active-TB transition and removes the treated compartment, making the inverse problem for $q = \{\beta_c, \lambda\sigma, r_1, r^{*}, k\}$ identifiable from measured compartments; and (b) Shapley values (Eq. 1), the unique payoff distribution satisfying linearity, symmetry, efficiency, and the null-player axiom, used to score each socio-economic feature's contribution to the Gaussian process regression of $\beta_c$.

What would settle it

Compute Shapley values for the same regression task using the full latent-TB model from [Kabanikhin et al., 2024] on the same 87 regions; if the top-five feature set changes or the 10-region under-10% accuracy disappears, the paper's ranking depends on the model simplification rather than on a stable socio-economic signal.

Watch

Extended reading notes

Core claim

The central claim is that the TB infection rate $\beta_c$, recovered separately for each region from a five-compartment ODE model of TB–HIV co-infection, can serve as a regression target for regional socio-economic data, and that Shapley values computed on a Gaussian process regressor single out five features—mean income per capita, workforce, number of HIV tested, unemployment, and total population—as the most influential. This ranking, however, reproduces $\beta_c$ within 10% relative error for only 10 of the 87 regions considered; for those regions the five parameters carry the reconstruction. The paper notes a negative correlation between infection rate and mean income or population below subsistence level, which the authors flag as unexpected and as a property of the chosen regression model rather than evidence of causation.

Load-bearing premise

The recovered infection rates $\beta_c$ that the regression targets are reliable, even though the simplified model omits the latent-TB compartment and the data had seasonal peaks and missing values that were skipped manually.

Editorial extensions

If this is right

If the ranking is correct, public health agencies can prioritize collecting these five socio-economic indicators when building regional forecasts of TB incidence, reducing data collection burdens.
In the 10 regions where reconstruction stays under 10% error, the method supplies region-specific $\beta_c$ without re-solving an inverse problem for each region, making multi-region modeling cheaper.
The simplification of omitting a latent-TB compartment makes the inverse problem identifiable; accepting this simplification justifies calibrating co-infection models with routinely measured surveillance data alone.
The approach reinterprets socio-economic covariates as drivers of the transmission rate, creating a concrete numerical link between economics and epidemic parameters.
The negative correlation with mean income, if it survives broader testing, would complicate the common assumption that TB concentrates in poorer areas, though the authors present it as model-specific.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The 10-region success suggests the Shapley ranking may be an artifact of the Gaussian process kernel and the short 2009–2019 training window; a cross-validation with held-out years would test whether the five-feature ranking generalizes beyond the fitted regions.
Switching the regressor (e.g., to a tree ensemble or a linear model) would likely change Shapley rankings; the paper's choice of the dot-product-plus-white-noise Gaussian process is pragmatic but not theoretically defended, so the ranking is conditional on that choice.
The same pipeline could be applied to other endemic diseases whose regional transmission heterogeneity is suspected, provided the simplified compartment structure remains identifiable; the method is not TB-specific beyond the ODE structure.
If the manual exclusions of seasonal peaks and missing data were automated or replaced by an explicit missing-data model, the recovered $\beta_c$ values could shift, potentially changing the feature ranking; this makes the manual preprocessing a hidden load-bearing step.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Here's my take on the Neverov and Krivorotko preprint. The notable thing is the integration: nobody else seems to have paired Shapley values with a TB-HIV co-infection ODE inverse problem to rank socio-economic drivers of regional transmission rates. That is a genuinely useful idea for cutting data collection costs. The paper is also refreshingly honest: it tells you up front that regression only worked for 10 of 87 regions, and it explicitly avoids causal claims about the Shapley rankings.

The modeling choices are reasonable in context. The authors drop the latent-TB compartment because it creates identifiability problems, and they cite their own previous work showing the latent fraction had to be tuned to 1–5% to get realistic transition times. That is a legitimate practical justification, not a hand-wave. The Bayesian optimization approach is described well enough to follow.

Now the soft spots, in proportion. The biggest issue is the one the stress-test flags: the β_c values that the Shapley ranking explains are themselves the output of a simplified inverse problem with manually skipped seasonal peaks and missing observations. The paper says anomaly detection wasn't feasible, so they skipped points by hand. That is fragile. No sensitivity analysis shows how the ranking changes if those skips are altered. No error bars or uncertainty intervals appear anywhere. The regression itself only works for 10 regions, yet the Shapley values are computed on all 87; the paper doesn't show whether the ranking is stable when you restrict to the regions where the GP actually predicts well. Without those checks, the feature list—mean income, workforce, HIV testing, unemployment, population—is not yet established as meaningful, even for the successful subset.

There are minor issues too: Eq. (4) sums over 2007–2020 while the text says data cover 2009–2019; Fig. 2 shows monthly data through 2022 for one region; and the list of 10 successful regions actually contains 11 names, with a typo ("Rosvov"). These are cosmetic but suggest the manuscript needs a careful pass.

Who is this for? People working on regional epidemic modeling with limited data, inverse problem practitioners, and anyone interested in interpretable ML applied to public health. It deserves a serious referee because the idea is useful and the failures are reported rather than hidden. But it needs major revision: provide the code and data, add uncertainty quantification on the inverse problem, test sensitivity to the data-exclusion choices, and analyze the Shapley ranking on the successful subset. I'd send it to review, but I'd expect heavy revision before acceptance.

Recommendation: engage with it, but require the robustness work. The core concept is worth the effort.

Best, [Your name]

Referee Report

4 major / 4 minor

Summary. The manuscript presents a workflow for modeling regional heterogeneity in tuberculosis-HIV co-infection in 87 regions of the Russian Federation. The authors simplify an SIR-type model to five compartments, solve per-region inverse problems to estimate transfer rates including the infection rate beta_c, train a Gaussian process regressor to predict beta_c from five socio-economic features, and compute Shapley values to rank feature importance. They report that the final regression achieves relative errors below 10% for only 10 of 87 regions and select mean income per capita, workforce, number of HIV tested, unemployment, and total population as the most influential features.

Significance. If the beta_c estimates are reliable, the paper offers a useful template for combining mechanistic epidemic models, inverse problems, and model-agnostic feature attribution to reduce data collection for regional calibration. The paper is honest about the low success rate and explicitly avoids causal claims. However, because the feature ranking is derived from a regression that fails for most regions and from an unvalidated inverse problem, the central claim is conditional. The paper also provides no code, data, or uncertainty quantification, limiting reproducibility and the confidence that can be placed in the numerical results.

major comments (4)

[Section 2.1 and Eq. (4)] The data are described as annual time series from 2009 to 2019 in Section 2.1, while Section 3.2 says the machine-learning tests use data from 2011 to 2019, and the abstract mentions 2009 to 2023. The misfit functional in Eq. (4) sums over 2007 to 2020. This inconsistency makes the inverse-problem setup irreproducible, and depending on which time window is actually used, the recovered beta_c values and the subsequent Shapley ranking could change. Please state the exact time window for each step and correct the equations and text accordingly.
[Section 4 and Figure 7] The Shapley values are computed for a Gaussian process trained on all 87 recovered beta_c values, yet the text and Figure 7 state that relative regression errors are below 10% for only 10 of 87 regions. The paper does not report whether the feature ranking is stable when the regression is restricted to the 10 well-fitted regions, how per-region accuracy is weighted, or any uncertainty intervals or bootstrap replicates for the Shapley values. Additionally, Table 1 reports an averaged relative error of 0.030 for the Gaussian process, which is hard to reconcile with the 10/87 statement unless the average is dominated by regions with very small beta_c; this should be clarified. As it stands, the selected five features are not supported as the most influential for the full dataset.
[Section 3.1 and Section 3.2] The reduced five-compartment model is introduced primarily to avoid identifiability problems associated with latent and treated compartments, but no synthetic-data validation or comparison with the fuller model in Kabanikhin et al. (2024) demonstrates that the simplification preserves the value of beta_c. The authors cite the prior work's unrealistic latent-stage transition times as motivation, but that does not establish that the simplified model recovers the same beta_c as a fuller model. Without such a check, the beta_c targets used in the regression remain potentially biased, which would invalidate the Shapley-based feature selection.
[Section 2.1] Outliers and missing observations are skipped manually, and the authors state that anomaly detection algorithms are not applicable in this scenario. No sensitivity analysis is reported for these skips, so it is unknown whether the fitted beta_c values—and the resulting Shapley ranking—are robust to the data-handling choices. A perturbation analysis or a comparison with alternative inclusion/exclusion rules is needed to show that the chosen five features are not artifacts of manual data cleaning.

minor comments (4)

[Section 3.2] The word 'Gussian' should be 'Gaussian', and the caption of Figure 3 says 'Flu diagram' rather than 'flow diagram'.
[Section 4] The text says 'just 10 out of 87 parameters beta' but lists 11 regions: Kamchactka krai, Krasnoyarsk krai, Leningrad oblast, Republic of Dagestan, Republic of Mordovia, Republic of Northern Osetia, Rosvov oblast, Samara oblast, Smolensk oblast, Tver oblast, and Tomsk oblast. The count and the list need to be reconciled.
[References] The reference to 'Feng Z, 2000' and the associated author list are incomplete; the citation should follow the standard format used throughout the reference list.
[Section 2.1] The source of the epidemiological and socio-economic data, as well as the definitions of the variables, is not provided. A data availability statement or a link to the data sources would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the feature ranking is a descriptive output of the fitted regression, not a fit-free prediction, and the regression targets are not constructed from the feature inputs.

full rationale

The paper's derivation chain is: (i) solve the inverse problem for epidemiological parameters such as beta_c using Eq. (4) against observed incidence series I, J1, J3; (ii) train a Gaussian-process regressor mapping socio-economic features to beta_c; (iii) compute Shapley values of that fitted regressor; (iv) select features with the largest Shapley dispersion. Step (iii)-(iv) is a transparent, descriptive summary of the fitted regressor: the ranking is the output of a well-defined calculation, not a hidden prediction claimed to be independent of the calculation. The paper explicitly disclaims causation ('these results do not show the causation, but causation from the point of view of chosen base regression model'), so the conclusion does not overstate the Shapley output. The beta_c targets are produced by an inverse problem whose data (disease incidence) are not the socio-economic features used in the regression, so the ranking is not forced by construction. Citations to the authors' own Kabanikhin et al. [2024] are methodological (parameter tables, Bayesian-type optimization) and illustrative (latent-TB identifiability), and they do not function as an unverified uniqueness theorem or as the sole support for model simplification; the paper argues the simplification separately from identifiability of unmeasured latent compartments. The acknowledged failure on 77 of 87 regions and the manual skipping of data points are limitations affecting validity and robustness, but they are not instances of circular reasoning. No equation or fitted parameter is renamed as a prediction in a way that reduces the result to its inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central results rest on the fitted inverse problem output and on several domain assumptions about how TB-HIV dynamics and socio-economic statistics relate. No new entities are postulated. The main free quantities are the per-region transfer rates, especially βc, which enter both the regression and the Shapley analysis.

free parameters (2)

Per-region infection rate βc = Estimated for 87 regions, values shown only as scatter in Fig. 5
Obtained by minimizing Eq. (4) with Optuna Tree Parzen Estimator; it is the dependent variable for the Gaussian process regression and the object of the Shapley importance analysis, so all downstream conclusions inherit its uncertainty.
Per-region transfer rates λσ, r1, r*, k = Not tabulated in the preprint
Reconstructed simultaneously with βc in the inverse problem, they define the model trajectory but are not used in the socio-economic regression.

assumptions (5)

domain assumption The simplified five-compartment ODE system (2) adequately represents TB-HIV co-infection in all studied regions after removing latent and treated compartments.
This simplification is justified in Section 3 by identifiability concerns, not by epidemiological validation; it determines the reconstructed βc values.
domain assumption Statistical data, after manual removal of outliers and missing points, accurately reflect regional TB-HIV incidence.
Section 2.1 says seasonal peaks are treated as artifacts and skips are detected manually; no sensitivity or robustness analysis is reported.
domain assumption Infection rate βc is a function of socio-economic parameters, since tuberculosis is a social disease.
Section 3 states this assumption; it justifies regressing βc on socio-economic features.
standard math Shapley value axioms and the use of Gaussian process predictions as the payout function are valid for feature ranking.
Section 2 defines Shapley values via Eq. (1); the axioms (linearity, symmetry, efficiency, null player) are standard and unproblematic.
ad hoc to paper The Gaussian process with dot product and white noise kernels is the appropriate surrogate model for computing Shapley values.
Chosen because it had the lowest average test error in Table 1, but hyperparameters are not given and no alternative explainer is compared.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Feature importance of socio-economic parameters in Tuberculosis modeling." pith.science (2026). https://pith.science/paper/JRBBBR5R

@misc{pith2026241201844,
  author       = {Pith},
  title        = {Pith review of: Feature importance of socio-economic parameters in Tuberculosis modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JRBBBR5R}},
  note         = {Machine review of arXiv:2412.01844}
}

read the original abstract

This paper considers the problem of modeling epidemic outbreaks in different regions with a common model, that uses additional information about these regions to adjust its parameters and relieve us of mundanity of data collecting, and inverse problem solving for each region separately. To that end, we study tuberculosis and HIV dynamics in regions of Russian Federation from 2009 to 2023 in connection with number of socio-economic parameters. SIR-like model was taken and modified as a dynamic model for tuberculosis-HIV co-infection and inverse problem of transfer rates between compartments was solved, based on statistical data of diseases incidence. To shorten the list of socio-economic parameters we make use of Shapley vector that allows us to estimate importance of these parameters in reconstruction of differential model parameters using regression algorithms.

Figures

Figures reproduced from arXiv: 2412.01844 by the authors.

**Figure 2.** Monthly new cases of tuberculosis infection in Tula region from 2009 to 2022. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Flu diagram of ODE model of TB and HIV co-infection. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Representative results for prediction of models through the example of Krasnoyarsk region data. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: Reconstructed β for every region. Shapley values for chosen Gaussian process model, based on socio-epidemiological parameters were obtained. For all the following figures, red color of dot represents above average value of feature, and in contrast blue represents the l…

**Figure 6.** Figure 6: Shapley values of socio-economic parameters in relation to [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: Results of reconstruction of β from socio-economical parameters. Resulting relative error for each region (left) and comparison plot of true β versus β reconstructed (right). Blue dots show regions with error less than 10%, orange dots are the rest. Red line represents…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

21 extracted references · 20 canonical work pages

[1]

Castillo-Chavez

Juan Pablo Aparicio and C. Castillo-Chavez. Mathematical modelling of tuberculosis epidemics. Mathematical biosciences and engineering : MBE, 6 2: 0 209--37, 2009. URL https://api.semanticscholar.org/CorpusID:35985072

work page 2009
[2]

Feng Z, Castillo-Chavez C

Capurro AF. Feng Z, Castillo-Chavez C. A model for tuberculosis with exogenous reinfection. Theor Popul Biol, 57(3): 0 235--47, 2000. doi:https://doi.org/10.1006/tpbi.2000.1451

work page arXiv
[3]

Castillo-Chavez

Juan Pablo Aparicio and C. Castillo-Chavez. Transmission and dynamics of tuberculosis on generalized households. Theoretical Biology, 206(3): 0 327--41, 2000. doi:https://doi.org/10.1006/jtbi.2000.2129

work page arXiv
[4]

Spatial analysis of the spread of tuberculosis cases based on socio-economic factors using distance-based algorithm

Ayu Azizah, Amil Ahmad Ilham, and Syafaruddin. Spatial analysis of the spread of tuberculosis cases based on socio-economic factors using distance-based algorithm. In 2022 International Conference on Electrical Engineering and Informatics (ICELTICs), pages 19--24, 2022. doi:10.1109/ICELTICs56128.2022.9932043

work page arXiv 2022
[5]

Olga Krivorotko, Sergey Kabanikhin, and Nikolay Zyatkov et. al. Mathematical modeling and forecasting of covid-19 in moscow and novosibirsk region. SJNM, 4, 2020. ISSN 15607526. doi:10.15372/SJNM20200404. URL http://sibran.ru/journals/issue.php?ID=179923&ARTICLE_ID=179927

work page doi:10.15372/sjnm20200404 2020
[6]

Agent-based mathematical model of covid-19 spread in novosibirsk region: Identifiability, optimization and forecasting

Olga Krivorotko, Mariia Sosnovskaia, and Sergey Kabanikhin. Agent-based mathematical model of covid-19 spread in novosibirsk region: Identifiability, optimization and forecasting. Journal of Inverse and Ill-posed Problems, 31 0 (3): 0 409--425, 2023. doi:doi:10.1515/jiip-2021-0038. URL https://doi.org/10.1515/jiip-2021-0038

work page doi:10.1515/jiip-2021-0038 2023
[7]

Different disease, same challenges: Social determinants of tuberculosis and covid-19

Raquel Duarte, Ana Aguiar, Marta Pinto, Isabel Furtado, Simon Tiberi, Knut L \"o nnroth, and Giovanni Battista Migliori. Different disease, same challenges: Social determinants of tuberculosis and covid-19. Pulmonology, 27: 0 338 -- 344, 2021. URL https://api.semanticscholar.org/CorpusID:231965804

work page 2021
[8]

Effects of social protection on tuberculosis treatment outcomes in low or middle-income and in high-burden countries: systematic review and meta-analysis

Kaio Vinicius Freitas de Andrade, Joilda Silva Nery, Ramon Andrade de Souza, and Susan Martins Pereira. Effects of social protection on tuberculosis treatment outcomes in low or middle-income and in high-burden countries: systematic review and meta-analysis. Cadernos de saude publica, 34 1: 0 e00153116, 2018. URL https://api.semanticscholar.org/CorpusID:4943543

work page 2018

Show all 21 references

[9]

The spatio-temporal analysis of the incidence of tuberculosis and the associated factors in mainland china, 2009-2015

Qihuan Li, Mengyang Liu, Yingjie Zhang, Shangwu Wu, Yang Yang, Yue Liu, Endawoke Amsalu, Lixin Tao, Xiangtong Liu, Feng Zhang, Yanxia Luo, Xinghua Yang, Weimin Li, Xia Li, Wei Wang, Xiaonan Wang, and Xiuhua Guo. The spatio-temporal analysis of the incidence of tuberculosis and...

2009
[10]

Podgayeva, D.N

V.A. Podgayeva, D.N. Golubev, I.D. Medvinsky, I.A. Chernyaev, and P.L. Shulev. Impact of social and economical factors on indicators describing epidemiological situation on tuberculosis in urals. Ural medicine journal, 85(7): 0 62 -- 66, 2011

2011
[11]

Aminev, A

E. Aminev, A. Bakirov, Kh. Aminev, T. Zulkarnaev, and M. Azamatova. Risk factors for tuberculosis in the present socio-economic conditions. Social aspects of population health, 2(30): 0 1 -- 10, 2013

2013
[12]

Interpretable Machine Learning

Christoph Molnar. Interpretable Machine Learning. https://christophm.github.io/interpretable-ml-book/, 2019. https://christophm.github.io/interpretable-ml-book/

2019
[13]

A value for n-person games

Lloyd S Shapley. A value for n-person games. In Harold W. Kuhn and Albert W. Tucker, editors, Contributions to the Theory of Games II, pages 307--317. Princeton University Press, Princeton, 1953

1953
[14]

A contribution to the mathematical theory of epidemics

William Ogilvy Kermack and Anderson G McKendrick. A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character, 115 0 (772): 0 700--721, 1927

1927
[15]

Behr, Eva Kaufmann, Jacalyn Duffin, Paul H

Marcel A. Behr, Eva Kaufmann, Jacalyn Duffin, Paul H. Edelstein, and Lalita Ramakrishnan. Latent tuberculosis: Two centuries of confusion. American Journal of Respiratory and Critical Care Medicine, 204: 0 142 -- 148, 2021. URL https://api.semanticscholar.org/CorpusID:232354429

2021
[16]

The global prevalence of latent tuberculosis: a systematic review and meta-analysis

Adam Cohen, Victor Dahl Mathiasen, Thomas Sch \"o n, and Christian Morberg Wejse. The global prevalence of latent tuberculosis: a systematic review and meta-analysis. European Respiratory Journal, 54, 2019. URL https://api.semanticscholar.org/CorpusID:195190002

2019
[17]

Alexeeva G.I

Kravchenko A.F. Alexeeva G.I. Bacteral carrier state or latent tuberculosis? Acta Biomedica Scientifica, 5(1): 0 22--24, 2012

2012
[18]

Screening for Latent Tuberculosis Infection in Adults: US Preventive Services Task Force Recommendation Statement

US Preventive Services Task Force. Screening for Latent Tuberculosis Infection in Adults: US Preventive Services Task Force Recommendation Statement . JAMA, 329 0 (17): 0 1487--1494, 05 2023. ISSN 0098-7484. doi:10.1001/jama.2023.4899. URL https://doi.org/10.1001/jama.2023.4899

2023
[19]

Rein Mgj Houben and Peter J. Dodd. The global burden of latent tuberculosis infection: A re-estimation using mathematical modelling. PLoS Medicine, 13, 2016. URL https://api.semanticscholar.org/CorpusID:18467277

2016
[20]

A. A. Romanyukha K. K. Avilov. Mathematical models of tuberculosis extension and control of it (review). Mat. Biolog. Bioinform., 2: 0 188--318, 2007. URL http://mi.mathnet.ru/mbb26

2007
[21]

Identification of the mathematical model of tuberculosis and hiv co-infection dynamics

Sergey Kabanikhin, Olga Krivorotko, Andrei Neverov, Grigoriy Kaminskiy, and Olga Semenova. Identification of the mathematical model of tuberculosis and hiv co-infection dynamics. Mathematics, 12 0 (23), 2024. ISSN 2227-7390. doi:10.3390/math12233636. URL https://www.mdpi.com/2...

2024 doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [1]

Castillo-Chavez

Juan Pablo Aparicio and C. Castillo-Chavez. Mathematical modelling of tuberculosis epidemics. Mathematical biosciences and engineering : MBE, 6 2: 0 209--37, 2009. URL https://api.semanticscholar.org/CorpusID:35985072

work page 2009

[2] [2]

Feng Z, Castillo-Chavez C

Capurro AF. Feng Z, Castillo-Chavez C. A model for tuberculosis with exogenous reinfection. Theor Popul Biol, 57(3): 0 235--47, 2000. doi:https://doi.org/10.1006/tpbi.2000.1451

work page arXiv

[3] [3]

Castillo-Chavez

Juan Pablo Aparicio and C. Castillo-Chavez. Transmission and dynamics of tuberculosis on generalized households. Theoretical Biology, 206(3): 0 327--41, 2000. doi:https://doi.org/10.1006/jtbi.2000.2129

work page arXiv

[4] [4]

Spatial analysis of the spread of tuberculosis cases based on socio-economic factors using distance-based algorithm

Ayu Azizah, Amil Ahmad Ilham, and Syafaruddin. Spatial analysis of the spread of tuberculosis cases based on socio-economic factors using distance-based algorithm. In 2022 International Conference on Electrical Engineering and Informatics (ICELTICs), pages 19--24, 2022. doi:10.1109/ICELTICs56128.2022.9932043

work page arXiv 2022

[5] [5]

Olga Krivorotko, Sergey Kabanikhin, and Nikolay Zyatkov et. al. Mathematical modeling and forecasting of covid-19 in moscow and novosibirsk region. SJNM, 4, 2020. ISSN 15607526. doi:10.15372/SJNM20200404. URL http://sibran.ru/journals/issue.php?ID=179923&ARTICLE_ID=179927

work page doi:10.15372/sjnm20200404 2020

[6] [6]

Agent-based mathematical model of covid-19 spread in novosibirsk region: Identifiability, optimization and forecasting

Olga Krivorotko, Mariia Sosnovskaia, and Sergey Kabanikhin. Agent-based mathematical model of covid-19 spread in novosibirsk region: Identifiability, optimization and forecasting. Journal of Inverse and Ill-posed Problems, 31 0 (3): 0 409--425, 2023. doi:doi:10.1515/jiip-2021-0038. URL https://doi.org/10.1515/jiip-2021-0038

work page doi:10.1515/jiip-2021-0038 2023

[7] [7]

Different disease, same challenges: Social determinants of tuberculosis and covid-19

Raquel Duarte, Ana Aguiar, Marta Pinto, Isabel Furtado, Simon Tiberi, Knut L \"o nnroth, and Giovanni Battista Migliori. Different disease, same challenges: Social determinants of tuberculosis and covid-19. Pulmonology, 27: 0 338 -- 344, 2021. URL https://api.semanticscholar.org/CorpusID:231965804

work page 2021

[8] [8]

Effects of social protection on tuberculosis treatment outcomes in low or middle-income and in high-burden countries: systematic review and meta-analysis

Kaio Vinicius Freitas de Andrade, Joilda Silva Nery, Ramon Andrade de Souza, and Susan Martins Pereira. Effects of social protection on tuberculosis treatment outcomes in low or middle-income and in high-burden countries: systematic review and meta-analysis. Cadernos de saude publica, 34 1: 0 e00153116, 2018. URL https://api.semanticscholar.org/CorpusID:4943543

work page 2018