arxiv: 2604.25038 · v1 · submitted 2026-04-27 · 🧬 q-bio.PE

Recognition: unknown

Equation Learning for multiscale models of infectious diseases

James W. G. Doran , Cameron A. Smith , Christian A. Yates , Ruth Bowness

Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:10 UTC · model grok-4.3

classification 🧬 q-bio.PE

keywords tuberculosismultiscale modelingequation learningagent-based modelssex differencesgenderinfectious disease dynamicsordinary differential equations

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The pith

A multiscale tuberculosis model learns ODEs from agent-based simulations to link within-host immune dynamics with population-level spread and sex differences.

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

The paper develops a proof-of-concept multiscale framework for tuberculosis that separates within-host and between-host scales to investigate why males experience higher disease burden. Within-host processes are represented by ordinary differential equations obtained through equation learning to reproduce the average behavior of a detailed agent-based model. Between-host population demographics evolve according to their own ODEs, and the scales connect through stochastic coupling functions. Counterfactual scenarios then test the separate and combined effects of sex-specific immune responses and gender-linked treatment completion rates on overall TB dynamics. A reader would care because the construction shows how to run integrated simulations at feasible cost while retaining key biological and demographic detail.

Core claim

We have developed a gender/sex-stratified multiscale framework for tuberculosis. We have learnt ordinary differential equations to capture the average output of an agent-based within-host model and used the resulting equations to describe the within-host scales of the multiscale framework. We evolve the population demographics at the between-host scale using ODEs and link the scales with stochastic coupling functions. We have considered counterfactual scenarios to elucidate the impact of sex and gender on the infectious disease dynamics of TB. This paper is intended to provide a proof-of-concept for the development and implementation of the presented multiscale framework.

What carries the argument

Ordinary differential equations learned from the average output of an agent-based within-host model, which are then embedded as the within-host component of the larger multiscale structure.

If this is right

The framework can separate the contribution of within-host immune differences from population-level treatment completion rates to the observed male excess in TB cases.
Stochastic coupling functions transmit variability between scales while keeping the overall simulation tractable.
Counterfactual runs can identify whether altering male treatment adherence or immune parameters produces larger shifts in epidemic size.
Replacing the agent-based within-host component with its learned ODE equivalent reduces computational cost enough to explore many demographic scenarios.

Where Pith is reading between the lines

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

The same learning step could be repeated for other pathogens once an agent-based within-host model exists, yielding reusable within-host modules for new multiscale studies.
If the learned equations remain accurate under parameter changes not seen during training, the framework could test interventions such as sex-targeted vaccines before they are trialed.

Load-bearing premise

The learned ODEs accurately represent the average dynamics of the agent-based within-host model with enough fidelity that they can be substituted into the multiscale framework without distorting the coupled population-level predictions.

What would settle it

A side-by-side run of the full agent-based within-host model inside the coupled framework versus the learned-ODE version, followed by a large mismatch in predicted sex-stratified TB incidence at the population level, would show the substitution fails.

Figures

Figures reproduced from arXiv: 2604.25038 by Cameron A. Smith, Christian A. Yates, James W. G. Doran, Ruth Bowness.

**Figure 1.** Figure 1: A schematic showing the different organisational levels of infectious disease systems, and their view at source ↗

**Figure 2.** Figure 2: Summary of the ground truth (Scenario 0) and three counterfactual scenarios (Scenarios 1 to 3) view at source ↗

**Figure 3.** Figure 3: Schematic outlining the model construction. Steps 1 to 4 represent the equation learning pipeline view at source ↗

**Figure 4.** Figure 4: Schematic showing the transitions between compartments at the between-host scale. The numbers view at source ↗

**Figure 5.** Figure 5: Average cell numbers observed in simulations ran using WHIDM that led to dissemination and view at source ↗

**Figure 6.** Figure 6: Plots showing a summary of the average densities of the Males With Active TB and Females With view at source ↗

**Figure 7.** Figure 7: Plots showing a summary of the average densities of the Males With Active TB and Females With view at source ↗

**Figure 8.** Figure 8: Plots showing a summary of the average densities of the Males With Active TB and Females With view at source ↗

**Figure 9.** Figure 9: Plots showing a summary of the average densities of the Males With Active TB and Females With view at source ↗

**Figure 10.** Figure 10: Plots showing a summary of the average density of the Females With Active TB compartment over view at source ↗

**Figure 11.** Figure 11: Plots showing a summary of the average density of the Males With Active TB compartment over view at source ↗

**Figure 12.** Figure 12: Plots showing a summary of the average density of the Males With Active TB compartment view at source ↗

**Figure 13.** Figure 13: Summary plots of the evolution of cell population numbers over time in WHIDM simulations view at source ↗

**Figure 14.** Figure 14: Plots showing a summary of the average density of the Females With Active TB compartment view at source ↗

**Figure 15.** Figure 15: Plots showing a summary of the average density of the Males With Active TB compartment over a view at source ↗

**Figure 16.** Figure 16: Plots showing a summary of the average density of the Males With Active TB compartment view at source ↗

**Figure 17.** Figure 17: Plots showing a summary of the average density of the Females With Active TB compartment view at source ↗

**Figure 18.** Figure 18: Plots showing a summary of the average density of the Males With Active TB compartment over a view at source ↗

**Figure 19.** Figure 19: Plots showing a summary of the average density of the Males With Active TB compartment view at source ↗

read the original abstract

Tuberculosis (TB) is an airborne disease caused by the pathogen Mycobacterium tuberculosis. In 2023, according to the World Health Organization, it ''probably'' replaced COVID-19 as the leading cause of death from an infectious agent globally; in the nineteenth century, one in seven of all humans deaths were as a result of tuberculosis. More than 10 million people are diagnosed with TB every year. The majority of cases in adults occur in males (62.5% of all global adult cases in 2023, compared to 37.5% in females). The main reasons for males suffering from a higher burden of global TB cases, compared to females, is likely to be a combination of within-host factors, such as differences in immune response, and population-scale factors, such as likelihood of completing treatment. To investigate the impact different scales have in determining this higher TB burden in males, we have developed a gender/sex-stratified multiscale framework. We have learnt ordinary differential equations (ODEs) to capture the average output of an agent-based within-host model, and used the resulting equations to describe the within-host scales of the multiscale framework. We evolve the population demographics at the between-host scale using ODEs, and link the scales with stochastic coupling functions. We have considered counterfactual scenarios to elucidate the impact of sex and gender on the infectious disease dynamics of TB. This paper is intended to provide a proof-of-concept for the development and implementation of the presented multiscale framework.

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

This is a proof-of-concept multiscale TB model that learns ODEs from an agent-based within-host simulation and couples them stochastically to a sex-stratified between-host model.

read the letter

The paper's core move is to take an existing agent-based within-host TB model, learn ODEs that match its average outputs, and plug those into a larger framework with between-host ODEs and stochastic scale links, all split by sex and gender to probe why males carry more of the global burden. That combination is new enough on its own terms. The authors are clear that this is meant as a framework demonstration rather than a finished set of predictions, and they lay out the counterfactuals they want to run to separate within-host immune effects from population-level factors like treatment adherence. That structure makes sense for the question they are asking. The writing is straightforward about the motivation from WHO data on male-female incidence gaps. The main limitation is that the abstract and the stress-test note both point to missing quantitative checks on how closely the learned ODEs track the original agent-based trajectories. Without reported error metrics, ensemble comparisons, or sensitivity tests on bacterial load or immune dynamics, it is hard to judge whether the approximation is tight enough for the counterfactual results to hold. The stochastic coupling functions also need explicit validation to show they do not add uncontrolled distortion when moving information between scales. Minor points include the usual proof-of-concept scope: limited parameter exploration and no external data hold-out. This is for people who build or use multiscale models of infectious diseases and want to see equation learning applied to make agent-based components more usable at population scale. A reader already working on TB dynamics or hybrid modeling could extract the framework idea even if the specific numbers require more work. I would send it to peer review so referees can check the validation steps and suggest concrete improvements to the fitting and coupling.

Referee Report

2 major / 2 minor

Summary. The paper develops a gender/sex-stratified multiscale framework for tuberculosis (TB) to investigate factors behind higher male burden. It learns ODEs via equation learning to approximate average trajectories from a sex-stratified agent-based within-host model, substitutes these into the within-host component of the multiscale model, evolves between-host population demographics with ODEs, and links scales via stochastic coupling functions. Counterfactual scenarios are then used to separate within-host (e.g., immune response) and population-scale (e.g., treatment completion) contributions; the work is framed as a proof-of-concept.

Significance. If the learned ODEs are shown to reproduce ABM averages with quantified fidelity and the stochastic couplings preserve key dynamics, the framework would offer a practical template for embedding detailed within-host biology into population-level infectious-disease models without prohibitive computational cost. The explicit sex/gender stratification and counterfactual design address a documented epidemiological disparity and could inform targeted interventions once validated.

major comments (2)

[Methods (equation-learning and multiscale coupling subsections)] The central substitution step—that learned ODEs can replace the agent-based within-host model—requires demonstration that approximation error is small enough not to distort multiscale predictions. No error metrics (RMSE, R², or ensemble trajectory overlays on bacterial load or immune-cell counts), parameter regimes tested, or sensitivity checks on how residual mismatch propagates through the stochastic coupling functions are reported. This directly undermines in the counterfactual results on sex/gender effects.
[Results (counterfactual scenarios)] The counterfactual scenarios are presented as the primary application, yet the manuscript supplies neither the specific parameter shifts used to isolate within-host versus between-host contributions nor any quantitative outcomes (incidence ratios, burden differences) or robustness tests against the within-host approximation. Without these, it is impossible to assess whether the framework successfully disentangles scales.

minor comments (2)

[Multiscale framework description] The stochastic coupling functions are described at a high level; an explicit mathematical definition (including how noise is sampled and how state variables are mapped between scales) would improve reproducibility.
[Figures] Figure captions and axis labels for any within-host trajectory comparisons or population-level outputs should explicitly state the number of ABM realizations averaged and the time window used for equation learning.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which highlight important aspects for strengthening our proof-of-concept multiscale framework. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Methods (equation-learning and multiscale coupling subsections)] The central substitution step—that learned ODEs can replace the agent-based within-host model—requires demonstration that approximation error is small enough not to distort multiscale predictions. No error metrics (RMSE, R², or ensemble trajectory overlays on bacterial load or immune-cell counts), parameter regimes tested, or sensitivity checks on how residual mismatch propagates through the stochastic coupling functions are reported. This directly undermines in the counterfactual results on sex/gender effects.

Authors: We agree that explicit quantification of the learned ODE approximation error is necessary to support the substitution into the multiscale model and to lend credibility to the counterfactual findings. The current manuscript presents the overall framework conceptually as a proof-of-concept and therefore omits these metrics. In the revision we will add RMSE, R², and ensemble trajectory comparisons for bacterial load and immune-cell counts across the tested parameter regimes. We will also include sensitivity analyses showing propagation of residual mismatch through the stochastic coupling functions. These will appear in the Methods section with supporting figures. revision: yes
Referee: [Results (counterfactual scenarios)] The counterfactual scenarios are presented as the primary application, yet the manuscript supplies neither the specific parameter shifts used to isolate within-host versus between-host contributions nor any quantitative outcomes (incidence ratios, burden differences) or robustness tests against the within-host approximation. Without these, it is impossible to assess whether the framework successfully disentangles scales.

Authors: We accept that the counterfactual scenarios, as the main demonstration of the framework, need explicit parameter values and quantitative results to allow readers to evaluate scale disentanglement. The present version describes the scenarios at a conceptual level. In the revised manuscript we will state the precise parameter shifts used for within-host (immune-response) and between-host (treatment-completion) factors, report quantitative outcomes such as incidence ratios and sex-specific burden differences, and add robustness checks against the within-host ODE approximation. These details will be placed in the Results section together with tables and figures. revision: yes

Circularity Check

0 steps flagged

No circularity: equation learning derives ODEs from independent ABM simulations

full rationale

The derivation begins with an external agent-based within-host model whose trajectories are generated independently; ODEs are then learned to match the average output of those simulations. These learned ODEs are substituted into the multiscale framework alongside separate between-host ODEs and stochastic coupling functions. No step reduces a claimed prediction or result to a quantity defined by the same fitted parameters, nor does any load-bearing premise rest on a self-citation chain that itself lacks external verification. The construction is therefore self-contained against the ABM benchmark and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract provides insufficient detail to enumerate specific free parameters, axioms, or invented entities. The framework presumably relies on standard assumptions in ODE and agent-based modeling plus whatever parameters were used during equation learning, but none are identifiable here.

pith-pipeline@v0.9.0 · 5580 in / 1301 out tokens · 85020 ms · 2026-05-07T17:10:09.965948+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

57 extracted references · 2 canonical work pages

[1]

The replication-transmission relativity theory for multiscale modelling of infectious disease systems

Garira W. The replication-transmission relativity theory for multiscale modelling of infectious disease systems. Scientific Reports 2019; 9

2019
[2]

Crossing the scale from within-host infection dynamics to between-host transmission fitness: a discussion of current assumptions and knowledge

Handel A and Rohani P. Crossing the scale from within-host infection dynamics to between-host transmission fitness: a discussion of current assumptions and knowledge. Philosophical Transactions of the Royal Society B: Biological Sciences 2015; 370

2015
[3]

Linked within-host and between-host models and data for infectious diseases: a systematic review

Childs LM, El Moustaid F, Gajewski Z, Kadelka S, Nikin-Beers R, Smith Jr JW, Walker M, and Johnson LR. Linked within-host and between-host models and data for infectious diseases: a systematic review. PeerJ 2019; 7

2019
[4]

A primer on multiscale modelling of infectious disease systems

Garira W. A primer on multiscale modelling of infectious disease systems. Infectious Disease Modelling 2018; 3

2018
[5]

The research and development process for multiscale models of infectious disease systems

Garira W. The research and development process for multiscale models of infectious disease systems. PLoS computational biology 2020; 16

2020
[6]

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Doran JWG, Thompson RN, Yates CA, and Bowness R. Mathematical methods for scaling from within-host to population-scale in infectious disease systems. Epidemics 2023

2023
[7]

Global tuberculosis report 2024

World Health Organization. Global tuberculosis report 2024. 2024. Available from: https://iris.who.int/bitstream/handle/10665/379339/9789240101531-eng.pdf?sequence=1

2024
[8]

Modelling challenges in context: lessons from malaria, HIV, and tuberculosis

Childs LM, Abuelezam NN, Dye C, Gupta S, Murray MB, Williams BG, and Buckee CO. Modelling challenges in context: lessons from malaria, HIV, and tuberculosis. Epidemics 2015; 10

2015
[9]

Pathogenesis, immunology, and diagnosis of latent Mycobacterium tuberculosis infection

Ahmad S. Pathogenesis, immunology, and diagnosis of latent Mycobacterium tuberculosis infection. Clinical and Developmental Immunology 2011; 2011

2011
[10]

Global Epidemiology of Tuberculosis.Seminars in Respiratory and Critical Care Medicine

Glaziou P, Floyd K, and Raviglione MC. Global Epidemiology of Tuberculosis.Seminars in Respiratory and Critical Care Medicine. Vol. 39. 3. 2018

2018
[11]

Modelling the effects of bacterial cell state and spatial location on tuberculosis treatment: Insights from a hybrid multiscale cellular automaton model

Bowness R, Chaplain MA, Powathil GG, and Gillespie SH. Modelling the effects of bacterial cell state and spatial location on tuberculosis treatment: Insights from a hybrid multiscale cellular automaton model. Journal of Theoretical Biology 2018; 446. Available from: https://www.sciencedirect.com/science/article/pii/S0022519318301206

2018
[12]

The immune response in tuberculosis

O’Garra A, Redford PS, McNab FW, Bloom CI, Wilkinson RJ, and Berry MPR. The immune response in tuberculosis. Annual review of immunology 2013; 31

2013
[13]

The host immune response to tuberculosis

Schluger NW and Rom WN. The host immune response to tuberculosis. American journal of respiratory and critical care medicine 1998; 157

1998
[14]

Phenotypic resistance in mycobacteria: is it because I am old or fat that I resist you? Journal of Antimicrobial Chemotherapy 2015; 70

Hammond RJH, Baron VO, Oravcova K, Lipworth S, and Gillespie SH. Phenotypic resistance in mycobacteria: is it because I am old or fat that I resist you? Journal of Antimicrobial Chemotherapy 2015; 70

2015
[15]

Defining dormancy in mycobacterial disease

Lipworth S, Hammond R, Baron V, Hu Y, Coates A, and Gillespie S. Defining dormancy in mycobacterial disease. Tuberculosis 2016; 99. Available from: https://www.sciencedirect.com/science/article/pii/S1472979216300658

2016
[16]

A virtual host model of Mycobacterium tuberculosis infection identifies early immune events as predictive of infection outcomes

Joslyn LR, Linderman JJ, and Kirschner DE. A virtual host model of Mycobacterium tuberculosis infection identifies early immune events as predictive of infection outcomes. Journal of theoretical biology 2022; 539

2022
[17]

Biological differences between the sexes and susceptibility to tuberculosis

Nhamoyebonde S and Leslie A. Biological differences between the sexes and susceptibility to tuberculosis. The Journal of infectious diseases 2014

2014
[18]

Genetic and hormonal mechanisms underlying sex-specific immune responses in tuberculosis

Gupta M, Srikrishna G, Klein SL, and Bishai WR. Genetic and hormonal mechanisms underlying sex-specific immune responses in tuberculosis. Trends in immunology 2022; 43

2022
[19]

Testosterone in pathogenesis of tuberculosis

Shrivastava P and Bagchi T. Testosterone in pathogenesis of tuberculosis. Chemical Biology Letters 2021; 8

2021
[20]

Predictors of Pulmonary Cavitation among Tuberculosis Patients

Balogun OO, Fawole A, Osemwinyen E, and Balogun B. Predictors of Pulmonary Cavitation among Tuberculosis Patients. J Infect Dis Epidemiol 2021; 7 31

2021
[21]

Cavitary tuberculosis: the gateway of disease transmission

Urbanowski ME, Ordonez AA, Ruiz-Bedoya CA, Jain SK, and Bishai WR. Cavitary tuberculosis: the gateway of disease transmission. The Lancet Infectious Diseases 2020; 20

2020
[22]

Risk of tuberculosis in public transport sector workers, Lima, Peru

Horna-Campos OJ, Bedoya-Lama A, Romero-Sandoval NC, and Martin-Mateo M. Risk of tuberculosis in public transport sector workers, Lima, Peru. The international journal of tuberculosis and lung disease 2010; 14

2010
[23]

Barriers and delays in tuberculosis diagnosis and treatment services: does gender matter? Tuberculosis research and treatment 2014; 2014

Yang WT, Gounder CR, Akande T, De Neve JW, McIntire KN, Chandrasekhar A, Lima Pereira A de, Gummadi N, Samanta S, and Gupta A. Barriers and delays in tuberculosis diagnosis and treatment services: does gender matter? Tuberculosis research and treatment 2014; 2014

2014
[24]

Gender differences in delays in diagnosis and treatment of tuberculosis

Karim F, Islam MA, Chowdhury AMR, Johansson E, and Diwan VK. Gender differences in delays in diagnosis and treatment of tuberculosis. Health policy and planning 2007; 22

2007
[25]

An assessment of factors contributing to treatment adherence and knowledge of TB transmission among patients on TB treatment

Kaona FAD, Tuba M, Siziya S, and Sikaona L. An assessment of factors contributing to treatment adherence and knowledge of TB transmission among patients on TB treatment. BMC Public health 2004; 4

2004
[26]

A systematic review on the role of gender in tuberculosis control

Hof S van den, Najlis CA, Bloss E, and Straetemans M. A systematic review on the role of gender in tuberculosis control. Report prepared for Tuberculosis Control Programme (TB CAP) September 2010

2010
[27]

A nested model for tuberculosis: Combining within-host and between-host processes in a single framework

Pereira RS, Bauch CT, Penna TJP, and Esp´ ındola AL. A nested model for tuberculosis: Combining within-host and between-host processes in a single framework. International Journal of Modern Physics C 2021; 32

2021
[28]

Modeling of gender differences in tuberculosis prevalence

Kisselevskaya-Babinina VY, Sannikova TE, Romanyukha AA, and Karkach AS. Modeling of gender differences in tuberculosis prevalence. Matematicheskaya Biologiya i Bioinformatika 2018; 13

2018
[29]

Drivers of sex differences in the South African adult tuberculosis incidence and mortality trends, 1990–2019

Kubjane M, Cornell M, Osman M, Boulle A, and Johnson LF. Drivers of sex differences in the South African adult tuberculosis incidence and mortality trends, 1990–2019. Scientific Reports 2023; 13

1990
[30]

The dynamics of tuberculosis transmission model with different genders

Wang S and Cao H. The dynamics of tuberculosis transmission model with different genders. Journal of Biological Dynamics 2024; 18

2024
[31]

Learning differential equation models from stochastic agent-based model simulations

Nardini JT, Baker RE, Simpson MJ, and Flores KB. Learning differential equation models from stochastic agent-based model simulations. Journal of the Royal Society Interface 2021; 18

2021
[32]

Efficient coupling of within-and between-host infectious disease dynamics

Smith CA and Ashby B. Efficient coupling of within-and between-host infectious disease dynamics. Journal of Theoretical Biology 2025

2025
[33]

A model of tuberculosis progression using CompuCell3D

Doran JWG, Rowlatt CF, Powathil GG, Bowness R, and Yates CA. A model of tuberculosis progression using CompuCell3D. arXiv preprint arXiv:2602.24258 2026

work page arXiv 2026
[34]

Initiation and regulation of T-cell responses in tuberculosis

Urdahl KB, Shafiani S, and Ernst JD. Initiation and regulation of T-cell responses in tuberculosis. Mucosal immunology 2011; 4

2011
[35]

Uncertainty and sensitivity analyses methods for agent-based mathematical models: An introductory review

Hamis S, Stratiev S, and Powathil GG. Uncertainty and sensitivity analyses methods for agent-based mathematical models: An introductory review. THE PHYSICS OF CANCER: Research Advances 2021

2021
[36]

When is an outbreak not an outbreak? Fit, divergent strains of Mycobacterium tuberculosis display independent evolution of drug resistance in a large London outbreak

Shorten RJ, McGregor AC, Platt S, Jenkins C, Lipman MCI, Gillespie SH, Charalambous BM, and McHugh TD. When is an outbreak not an outbreak? Fit, divergent strains of Mycobacterium tuberculosis display independent evolution of drug resistance in a large London outbreak. Journal of Antimicrobial Chemotherapy 2013; 68

2013
[37]

A flow cytometry method for rapidly assessing Mycobacterium tuberculosis responses to antibiotics with different modes of action

Hendon-Dunn CL, Doris KS, Thomas SR, Allnutt JC, Marriott AAN, Hatch KA, Watson RJ, Bottley G, Marsh PD, and Taylor SC. A flow cytometry method for rapidly assessing Mycobacterium tuberculosis responses to antibiotics with different modes of action. Antimicrobial agents and chemotherapy 2016; 60

2016
[38]

Quantitative study on the production and kinetics of mononuclear phagocytes during an acute inflammatory reaction

Van Furth R, Diesselhoff-den Dulk MMC, and Mattie H. Quantitative study on the production and kinetics of mononuclear phagocytes during an acute inflammatory reaction. The Journal of Experimental Medicine 1973; 138

1973
[39]

Identifying control mechanisms of granuloma formation during M

Segovia-Juarez JL, Ganguli S, and Kirschner D. Identifying control mechanisms of granuloma formation during M. tuberculosis infection using an agent-based model. Journal of Theoretical Biology 2004; 231

2004
[40]

Lifespans of naive, memory and effector lymphocytes

Sprent J. Lifespans of naive, memory and effector lymphocytes. Current Opinion in Immunology 1993; 5 32

1993
[41]

The global burden of latent tuberculosis infection: a re-estimation using mathematical modelling

Houben RMGJ and Dodd PJ. The global burden of latent tuberculosis infection: a re-estimation using mathematical modelling. PLOS Medicine 2016; 13

2016
[42]

Latent tuberculosis infection: An overview

Kiazyk S and Ball TB. Latent tuberculosis infection: An overview. Canada Communicable Disease Report 2017; 43

2017
[43]

Ending tuberculosis by 2030: can we do it? International Journal of Tuberculosis and Lung Disease 2016; 20

Suthar AB, Zachariah R, and Harries AD. Ending tuberculosis by 2030: can we do it? International Journal of Tuberculosis and Lung Disease 2016; 20

2030
[44]

Approximate accelerated stochastic simulation of chemically reacting systems

Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of Chemical Physics 2001; 115

2001
[45]

An agent-based modelling approach to investigate the impact of gender on tuberculosis transmission in Uganda

Doran JWG, Mujuni D, Gallagher K, Yates CA, and Bowness R. An agent-based modelling approach to investigate the impact of gender on tuberculosis transmission in Uganda. arXiv preprint arXiv:2601.09813 2026

work page arXiv 2026
[46]

Risk factors for pulmonary cavitation in tuberculosis patients from China

Zhang L, Pang Y, Yu X, Wang Y, Lu J, Gao M, Huang H, and Zhao Y. Risk factors for pulmonary cavitation in tuberculosis patients from China. Emerging microbes & infections 2016; 5

2016
[47]

Systematic review and meta-analysis of sex differences in social contact patterns and implications for tuberculosis transmission and control

Horton KC, Hoey AL, B´ eraud G, Corbett EL, and White RG. Systematic review and meta-analysis of sex differences in social contact patterns and implications for tuberculosis transmission and control. Emerging Infectious Diseases 2020; 26

2020
[48]

Risk factors for infectiousness of patients with tuberculosis: a systematic review and meta-analysis

Melsew YA, Doan TN, Gambhir M, Cheng AC, McBryde E, and Trauer JM. Risk factors for infectiousness of patients with tuberculosis: a systematic review and meta-analysis. Epidemiology & Infection 2018; 146

2018
[49]

Individual-based modeling of tuberculosis in a user-friendly interface: understanding the epidemiological role of population heterogeneity in a city

Prats C, Monta˜ nola-Sales C, Gilabert-Navarro JF, Valls J, Casanovas-Garcia J, Vilaplana C, Cardona PJ, and L´ opez D. Individual-based modeling of tuberculosis in a user-friendly interface: understanding the epidemiological role of population heterogeneity in a city. Frontiers in Microbiology 2016; 6

2016
[50]

Exploratory data analysis

Tukey JW. Exploratory data analysis. Vol. 2. Springer, 1977

1977
[51]

Factors associated with DELAY in diagnosis among tuberculosis patients in Hohoe Municipality, Ghana

Osei E, Akweongo P, and Binka F. Factors associated with DELAY in diagnosis among tuberculosis patients in Hohoe Municipality, Ghana. BMC public health 2015; 15

2015
[52]

Total delay in treatment among smear positive pulmonary tuberculosis patients in five primary health centers, southern Ethiopia: a cross sectional study

Asefa A and Teshome W. Total delay in treatment among smear positive pulmonary tuberculosis patients in five primary health centers, southern Ethiopia: a cross sectional study. PloS one 2014; 9

2014
[53]

Survival of people with untreated TB: effects of time, geography and setting

Rodriguez CA, Leavitt SV, Bouton TC, Horsburgh CR, Zur Wiesch PA, Nichols B, Jenkins HE, and White LF. Survival of people with untreated TB: effects of time, geography and setting. The International Journal of Tuberculosis and Lung Disease 2023; 27

2023
[54]

Treatment of tuberculosis: guidelines

World Health Organization STI(HO. Treatment of tuberculosis: guidelines. World Health Organization, 2010

2010
[55]

Association between tuberculosis in men and social network structure in Kampala, Uganda

Miller PB, Zalwango S, Galiwango R, Kakaire R, Sekandi J, Steinbaum L, Drake JM, Whalen CC, and Kiwanuka N. Association between tuberculosis in men and social network structure in Kampala, Uganda. BMC Infectious Diseases 2021; 21

2021
[56]

Learning surrogate equations for the analysis of an agent-based cancer model

Burrage K, Burrage PM, Kreikemeyer JN, Uhrmacher AM, and Weerasinghe HN. Learning surrogate equations for the analysis of an agent-based cancer model. Frontiers in Applied Mathematics and Statistics 2025; 11

2025
[57]

Synergy between individual TNF-dependent functions determines granuloma performance for controlling Mycobacterium tuberculosis infection

Ray JCJ, Flynn JL, and Kirschner DE. Synergy between individual TNF-dependent functions determines granuloma performance for controlling Mycobacterium tuberculosis infection. The Journal of Immunology 2009; 182 33 Appendix A Comparison of regression methods We used linear regression to infer the learnt equations for the seven cell types. We considered thr...

2009