PCSY-D-25-00086

Vaccination-Dependent Bifurcations in HIV-Mpox Co-infection Dynamics: Synergistic Effects and Endemic Stability

PLOS Complex Systems

Dear Dr. Welu,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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We look forward to receiving your revised manuscript.

Kind regards,

Keith Burghardt, Ph.D.

Academic Editor

PLOS Complex Systems

Keith Burghardt

Academic Editor

PLOS Complex Systems

Hocine Cherifi

Editor-in-Chief

PLOS Complex Systems

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1. We ask that a manuscript source file is provided at Revision. Please upload your manuscript file as a .doc, .docx, .rtf or .tex.

2. If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Additional Editor Comments (if provided):

The reviewers have a wide set of perspectives on this manuscript, however, there are a few points that the authors will need to address:

- Justifying parameters, including values like 1.2 for rho, and sensitivity analysis (R2, R3). The authors will need to do robustness checks to ensure that their results are not sensitive to particular parameters chosen.

- Addressing non-linearities and greater realism (cf. R3)

- Correcting Theorem 3.1

- Model fitting

- Uncertainty quantification

- Improving manuscript clarity.

Also see the many references R3 mentions; these will be important to consider when amending the manuscript.

Overall, I recommend the authors perform a major revision

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Reviewers' Comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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-->2. Has the statistical analysis been performed appropriately and rigorously?-->

Reviewer #1: N/A

Reviewer #2: I don't know

Reviewer #3: No

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-->3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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-->4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: The authors present a mathematical models of HIV-Mpox co-infection model where parameters are obtained from previously published models and publicly available databases. For he formulated model analysis of bifurcations and the stability of its equilibrium points identifies conditions of disease prevalence or containment that are described in theorems with analytical proof. The results presented are of significance. Although based on simulations the co-infection model identify a larger prevalence in the co-infection and the importance of antiretroviral therapy on the outcomes for both diseases and its eventually faster epidemic control. In general better models are always necessary especially when their results are complemented and predictions are compared with experimental or clinical results. I have a couple of comments and suggestions

1. Please revise the manuscript for typos and use justification for you paragraphs.

2. In the abstract there is a typo in the CD4+ result "¡"

3. Figure 6 cuts the combined result please include the complete figure, notice that it goes into negative reproduction number. give a justification for you model to give this result, although it is mention error bands of 5% are possible clarify: is this the reason?

Reviewer #2: 1. General Assessment:

In this manuscript the authors develop a 15-compartment model to study the co-dynamics of HIV and Mpox in an MSM population. Key analytical results include the derivation of R0, stability analysis, and a proof that a backward bifurcation occurs under certain conditions. Numerical simulations illustrate the potential for bistability, the synergy between ART and vaccination, and the temporal dynamics of co-infection. The central claim is that integrated control strategies are more effective than isolated interventions.

This manuscript has good strength points but requires major revisions before meeting publication criteria

2. Strengths:

- The research question is highly relevant following the 2022 global mpox outbreak and its disproportionate impact on MSM communities with high HIV prevalence.

- The model is comprehensive, attempting to capture complex interactions between the two diseases.

- The analytical demonstration of a backward bifurcation caused by HIV co-infection is a significant contribution. This is a non-trivial result with important implications, as it explains why standard "reduce R0 below 1" control logic can fail in syndemic settings.

3. Essential Revisions:

- Parameter justification:

- Some parameters require more careful justification, mainly and essentially the parameter sigma. The core result of this paper (backward bifurcation) relies on sigma exceeding a critical value. The range chosen by the authros references the Mitja2023 study, but as far as I can tell, this study does not prove the increased mpx susceptibilty of HIV+ individuals. They do report a high prevalence of HIV in mpox, but this could be due to increased duration / detectability of infection, or increased exposure risk (behavioral factors), not necessarily increased susceptibililty.

- The assumed value of 1.2 for rho seems arbitrary. Consider providing a justification. (Side note: the name of this parameter is misleading, one can think that starting ART accelerates mpox infection).

- Even the assumed vaccination rate phi (target) should be briefly justified based on actual vaccination rollout data.

- Consider justifying ART related parameters with more recent citations.

- proof of Theorem 3.1: I don’t know if I had a corrupted version of the pdf, but the proof of theorem 3.1 contains missing bits, making it impossible to understand. (lines 92 to 94). Must be fixed.

- model fitting: the manuscript states the model was calibrated and validated against 2022 co-infection data, but no fitting procedure, goodness-of-fit metrics, or comparison between model output and real-world data are presented.

- In the numerical simulation, the coinfection initial conditions simulate a scenario where both epidemics are introduced simultaneously into a naive population. The real-world situation of the 2022 outbreak was the introduction of Mpox into a population where HIV was already endemic. That is an important distinction to be addressed. Would the results be different?

4. Revisions to consider:

- the results in line 158 (beta_h has a damepening effect) is counterintuitive albeit possible. Maybe explain and justify this result.

- Consider including a state transition diagram to improve readability.

- values in figure 1 for negative influence are not readable

5. Conclusion:

The manuscript identifies a critical gap in the literature and proposes a sophisticated model with a compelling central thesis (the backward bifurcation). The authors have the potential to produce a high-impact paper, but this requires an effort to ground their model in empirical data and to present their results with greater clarity and rigor.

Reviewer #3: SPECIFIC COMMENTS:

The paper is an interesting paper about the first mechanistic model capturing bidirectional HIV-Mpox interactions, incorporating three critical innovations: (1) HIV-induced immunological modulation of Mpox progression, (2) antiretroviral therapy (ART)-dependent transmission rates, and (3) vaccination stratification by HIV status. Results provide a framework for integrated HIV-Mpox control, demonstrating that coordinated testing and prevention campaigns outperform sequential interventions by 21-34\% across epidemiological scenarios.

Specific comments are below.

-- I think you shold discuss what is the generalizability of your results and how the those have universal signatures in common to other ecosystems. You can search the literature for that or compare patterns.

-- I believe Deep Uncertainty must be considered when making these projections. So can you please comment on that considering also the intrinsic assessment into data?

-- in none of the results/figures there is a probabilistic assessment that is performed, where probability density functions (pdfs) characterize the distribution of information (ecosystem variables like HIV-Mpox infections, HIVmInf) and uncertainty, and that can be used for inferring the causal linkages between the ''eco-outcomes'' and socio-env causes.

--in general all sections are very poor and in parrticular the introduction and model presentation. I do not believe the paper is written in a very standard way according to science standards. All is very short and very poorly connected.

Generic comments are provided below to perhaps try to find some sort of generalizabilty and depth of results through quantification, whether possible. Further quantification may be done in the future but the statement of limitations and possibilities is an important aspect of scientific publication.

GENERAL COMMENTS:

(1) Eco-STOCHASTICITY/VARIABILITY of PATTERNS as spatio-temporal probability distributions (useful for eco-variability attribution via systemic uncertainty decomposition or GSUA): To address the model/data Uncertainty-Sensitivity coupling, global sensitivity and uncertainty analysis (GSUA, aka systemic information decomposition) should be done to identify key determinants of model/data variability (HIVmInf) and universal determinants across geographies. You do not quite perform a one-factor-at-a-time sensitivity analysis, nor a non-linear sensitivity analysis to capture the variables' interactions (high-order interactions) that can be predominant in defining patterns' variability (OVER SPACE AND TIME). See Pianosi et al. (2016) for an extensive discussion about this topic and how data should be used for GSUA using a simple variance-based approach. Entropy approaches of GSUA (Li and Convertino, 2021) are also available when the pdfs are too complex to make the variance meaningful.

I also think the paper should pinpoint which sites (and models) has the highest and lowest uncertainty (uncertainty sources and sinks), uncertainty/information baseline and thresholds (regular and anomalous patterns), type of tipping points, and whether the degree of uncertainty is attributable to env determinants. Maximum HIVmInf gradients should have the lowest uncertainty and the highest likelihood of spreading.

(2) ecoNETWORKS=ecoGRAPHY underpinning PATTERNS (information-based causal networks, i.e. causal discovery and/or inference of eco-information propagation): The socioecological-environmental processes you investigate (HIVmInf dynamics) are largely non-linear. Non-linear models such as Convergent Cross Mapping or others (see Sugihara et al 2012, Campo-Bescós, 2013 et al., and Li and Convertino et al. 2021 for instance, that are all generic models which can be applied to any dynamics) can account for variable non-linear interactions (vs. simple correlation that does not imply causality) dependent on dynamical heterogeneity driven by divergence and asynchonicity. These models are also able to capture spatial joint variability (due to eco-environmental networks, such as ecological dependencies like corridors and flows, i.e. teleconnections considering time delays to understand spatial dependencies that are important for the variables considered (and their collective interactions, in this case HIVmInf).

Also, if the HIVmInf pattern (or networks, like networks of species traits, envirome or both) is analyzed over time (or topologically over space) the potential eco-stress (or performance change, e.g. HIVmInf level) can be calculated based on the departure from an ideally organized network configurations, and flows, and its relation with environmental networks such as water/hydrological networks as the major blueprint of ecosystem function.

(3) eco-STABILITY and eco-CONTROLS (=ECOFOLIO) via OPTIMAL Network CORE (useful for the detection of optimal causal controls): How indicators/predicted variables (i.e.HIVmInfpattern/network indicators) change over space and/or time, conditional to optimal or desired outcomes (e.g. related to HIVmInf optimal ranges that are not identified in your paper), is critical for mapping site-/time-specific and universal patterns and shifts (Sugihara G et al (2012)), and more importantly environment-ecological controls that are Pareto-optimal (Shoval, O. et al, 2012 and ParTi model), such as FLOWS (water, nutrients, species, etc) and NETWORKS. The stability (and universality) of ecological patterns (Riva et al (2023)) over predictors' gradients and their critical change, should be quantified because that can define potential stable states over which the predictands (causal env factors) are relatively stable or approaching a transition (ecoshifts and optimal eco-controls). These calculations can be done by doing inverse modeling via MonteCarlo filtering over the pdfs of HIVmInf.

RECOMMENDATION:

I suggest Rejecting the paper. The paper is potentially interesting, but I think the findings and models are not presented in a sufficient way. My comments are like for a Major revision but this would take too much time.

REFERENCES:

Li J, Convertino M (2021) Temperature increase drives critical slowing down of fish ecosystems. PLoS ONE 16(10): e0246222. https://doi.org/10.1371/journal.pone.0246222

Campo-Bescós MA, Muñoz-Carpena R, Kaplan DA, Southworth J, Zhu L, Waylen PR (2013) Beyond Precipitation: Physiographic Gradients Dictate the Relative Importance of Environmental Drivers on Savanna Vegetation. PLoS ONE 8(8): e72348. https://doi.org/10.1371/journal.pone.0072348

Pianosi et al. (2016)

Sensitivity analysis of environmental models: A systematic review with practical workflow

Environmental Modelling & Software

Volume 79, May 2016, Pages 214-232

Packages for GSUA

https://safetoolbox.github.io/Documentation.html

Riva et al (2023)

Toward a cohesive understanding of ecological complexity

https://www.science.org/doi/10.1126/sciadv.abq4207

Sugihara G et al (2012)

Detecting Causality in Complex Ecosystems

https://www.science.org/doi/10.1126/science.1227079

Shoval, O. et al. Evolutionary trade-offs, Pareto optimality, and the geometry of phenotype space. Science 336(6085), 1157–1160 (2012).

Pareto Task Inference (ParTI) https://www.weizmann.ac.il/mcb/alon/download/pareto-task-inference-parti-method

--- as for Deep Uncertainty papers see here

https://www.nature.com/articles/s41467-025-57897-1

https://www.science.org/doi/10.1126/sciadv.add7082

https://www.nature.com/articles/s44304-025-00072-9

https://agupubs.onlinelibrary.wiley.com/doi/am-pdf/10.1029/2021EF002322

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Vaccination-Dependent Bifurcations in HIV-Mpox Co-infection Dynamics: Synergistic Effects and Endemic Stability

PCSY-D-25-00086R1

Dear Dr. Welu,

We're pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you'll receive an e-mail detailing the required amendments. When these have been addressed, you'll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

Keith Burghardt, Ph.D.

Academic Editor

PLOS Complex Systems

Additional Editor Comments (optional):

We thank the authors for their updated manuscript. All reviewers agree that the paper is ready for submission. Congratulations!

Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

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-->2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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-->3. Has the statistical analysis been performed appropriately and rigorously?-->

Reviewer #1: I don't know

Reviewer #2: Yes

Reviewer #3: Yes

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-->4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

--------------------

-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

--------------------

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: The authors prepared a revised manuscript that addressed the comments and suggestions from the previous revision. I consider the revision adequate, and the authors have incorporated my previous comments and suggestions. I have only a minor comment: section 2.4 may not be necessary, as it consists only of a bullet list; consider incorporating it into the previous section. Also, the words in the legend of Figure 1 are too light; please consider a darker colour.

Reviewer #2: All comments have been addressed

Reviewer #3: the paper can be accepted for publication

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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