Title: Controlling The Spread of Epidemics on Networks with Differential Privacy
Venue: NeurIPS 2025
Accepted: yes
Keywords: Differential privacy

network science

computational epidemiology

public health
Abstract: Designing effective strategies for controlling epidemic spread by vaccination is an important question in epidemiology, especially in the early stages when vaccines are limited.
This is a challenging question when the contact network is very heterogeneous, and strategies based on controlling network properties, such as the degree and spectral radius, have been shown to be effective.
Implementation of such strategies requires detailed information on the contact structure, which might be sensitive in many applications.
Our focus here is on choosing effective vaccination strategies when the edges are sensitive and differential privacy guarantees are needed.
Our main contributions are $(\varepsilon,\delta)$-differentially private algorithms for designing vaccination strategies by reducing the maximum degree and spectral radius.
Our key technique is a private algorithm for the multi-set multi-cover problem, which we use for controlling network properties.
We evaluate privacy-utility tradeoffs of our algorithms on multiple synthetic and real-world networks, and show their effectiveness.


Peer reviews:
comments: SUMMARY:
This paper gives a differentially private algorithm for two important problems.

(1) PrivateMaxDeg: Remove the minimum number of nodes such that the remaining graph has maximum degree no larger than a given value $D$.

(2) PrivMinSR: Remove the minimum number of nodes such that the remaining graph has largest eigenvalue no larger than a given value $\Delta$.

The authors give algorithms with theoretical guarantees, give lower bounds to demonstrate that the algorithms are tight, and also give experimental results for the proposed algorithms.

STRENGTHS AND WEAKNESSES:
I think that this paper has a very high potential. Unfortunately, I think that it may need some improvements on the following matters.

(1) The problems addressed in this paper are quite similar to graph coloring problems, and the techniques that the authors introduced are quite similar to theirs. I believe that the authors should have cited the following works and explain the differences between their techniques and the techniques introduced in those papers:

> Private graph colouring with limited defectiveness

> Aleksander B. G. Christiansen, Eva Rotenberg, Teresa Anna Steiner, Juliette Vlieghe

(2) I think the paper misses an explanation at the most important part of the proof that hinders me from understand the proof.
At line 754 of the full paper, I wonder why we can move from the second to the third, and also from the third to the fourth of the equation chain.

QUESTIONS:
I am willing to raise my score if the authors can clarify the derivation at Line 754 and confirm that it is not a typographical error or an omission in explanation.

LIMITATIONS:
yes
TITLE: Official Review
CLARITY: 2
IMPACT: 3
ORIGINALITY: 2
DATE: 2025-06-18

comments: SUMMARY:
This paper studies the problem of epidemic control on networks under edge-differential privacy. It focuses on designing vaccination strategies by minimizing network properties such as the maximum degree (PRIVATEMAXDEG) and the spectral radius (PRIVMINSR). The authors reduce these problems to a differentially private version of the multi-set multi-cover problem (PRIVATEMULSET), and develop both implicit and explicit algorithms using techniques like the exponential mechanism and AboveThreshold. Experimental results are provided on real and synthetic networks to evaluate the trade-off between privacy and utility under different privacy budgets.

STRENGTHS AND WEAKNESSES:
Strengths:
- The paper addresses an important and timely problem of epidemic control under differential privacy.
- It introduces a novel reduction of PRIVATEMAXDEG and PRIVMINSR to a private multi-set multi-cover problem (PRIVATEMULSET), enabling algorithmic design using known private mechanisms.

Weaknesses:
- The connection between PRIVMINSR and PRIVATEMULSET is not clearly demonstrated. A concrete example would help clarify the transformation.
- The use of different privacy parameters (epsilon, epsilon', epsilon_1, delta') across lemmas and algorithms is confusing and lacks clear explanation.
- In the Montgomery County subnet, the private algorithm requires a vaccination budget nearly 10 times higher than the non-private baseline, which raises practical concerns.

QUESTIONS:
- Figure 2 shows an unexpected trend where stronger privacy (lower epsilon) leads to lower vaccination cost. The explanation is brief and needs more justification. The paper does not discuss how to choose an optimal epsilon, nor what happens when epsilon is very small (e.g., < 4) in Figure 2.

LIMITATIONS:
YES
TITLE: Official Review
CLARITY: 3
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-07-08

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper studies vaccination strategies for epidemic control on contact networks under differential privacy constraints. The authors focus on two key network properties known to influence epidemic spread: maximum degree and spectral radius. Their key technical approach reduces both problems to instances of a \"multi-set multi-cover\" problem, for which they design private algorithms using the exponential mechanism. They provide both implicit solutions (outputting a permutation from which nodes can determine inclusion) and explicit solutions (directly outputting the vaccination set).\n\nSTRENGTHS AND WEAKNESSES:\nStrength -\n1. The lower bound results are impressive and establish the limitations in private cover problems.\n2. The multi-set multi-cover reduction is clever and the approach to providing both implicit and explicit solutions addresses a known challenge in private covering problems.\n3. Contact tracing privacy concerns were a major barrier during COVID-19, making this a practically motivated research direction even if the current results have limitations.\n\nWeaknesses -\n1. The edge-DP model assumes node identities are public while only edge relationships are private. Knowing who exists but not who they contact severely limits the model's applicability.\n2. In covering problems, even the optimal non-private solution often requires vaccinating a significant fraction of nodes (hundreds to thousands). Multiplying this by large approximation factors makes the solution require vaccinating most of the network.\n3. I think generally, the issue is that while logarithmic factors are asymptotically good, the hidden constants and practical parameter values make these bounds. Therefore, I recommend this paper to focus on the theory instead of tying the problem to actual application. If application is still their focus, then they have to first start with answering what is a practically acceptable privacy-utility trade-off and then make a convincing case whether their solution satisfies that.\n\nQUESTIONS:\nMostly around significance and how applicable it is.\n\nLIMITATIONS:\nMore discussion on actual applicability. Their evaluation was on a small network, way smaller than a typical city where such a thing would be used.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 4, "IMPACT": 1, "ORIGINALITY": 3, "DATE": "2025-07-14"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper studies the problem of designing interventions (vaccination or isolation strategies) to control the spread of epidemics through a network. The main challenge arises from having to do the interventions in a privacy-preserving way in order to protect sensitive information like which users share contact (edges of the network). The paper considers interventions that can influence network properties like Max Degree or Spectral Radius. Their main contribution is three-fold: i) developing a private algorithm for the general Multi-Set Multi-cover problem, ii) showing that the problems of minimizing max degree or spectral radius can be reduced to instances of the multi-set multi-cover problem which they already know how to solve privately, and iii) finally, demonstrating effectiveness of their algorithm on real-world and synthetic networks.\n\nSTRENGTHS AND WEAKNESSES:\n*Quality*: Although the reviewer has not checked the mathematical details/proofs, the paper appears to be technically thorough. Technical questions below. \n\n*Significance and originality*: The paper studies a very important problem. Differential privacy has enormous scope in the public health domain. As the paper rightly points out, people are in general concerned about privacy which degrades the efficacy of interventions (for, example, reluctance to provide information to help with contact-tracing during Covid-19). From that point of view, the paper tries to make a meaningful contribution which is both significant and original. \n\n*Clarity*: The paper has serious deficiencies when it comes to clarity. Please find detailed comments and questions below.\n\nQUESTIONS:\nDetailed Comments & Questions: \n\nSection 4:\n\n1. At the start of section 4.1, the authors say that they are discussing the Unweighted case, which according to their Defn 3.4 should try to minimize the number of sets to be chosen from S to achieve the desired coverage for all elements. However, their main result Lemma 4.1 mentions an approximation ratio on the worst case cost which leads the reviewer to think that this is the weighted case ? Can the authors clarify ? \n\n2. What does f mean ? The statement says \"maximum frequency of an element (ignoring multiplicity)\" -- this is not clear. Are the authors talking about the maximum number of sets S_i any element can occur in ? \n\n3. The authors should provide a description of their main algorithm, specifically including where the modifications are due to privacy. The entire description before Lemma 4.1 has no mention of privacy at all. They should at least mention that the sampling is done using the exponential algorithm on the total utility of set S_i.  This is especially important for readability because their other algorithms build on this.\n\n4. The reviewer is not familiar with previous literature on the best achieved approximation ratio for the multi-set problem in the non-private case. Can the authors provide that and discuss how their ratio compares with it. It is expected to be worse due to differential privacy, but by how much? \n\n5. I do not understand the distinction between implicit and explicit solutions in this case. In the normal setting, given a permutation \\pi, we can map it back to a collection of sets {S_u} which can be mapped back to a set of nodes {u} to be treated/removed. Is the mapping hindered by privacy ? This should not be the case because the central planner (who is deciding where to intervene) knows the contact graph fully ? The impression I got from reading the introduction is that the goal is to design the intervention in a privacy-preserving way, but the designer knows the contact graph. Can the authors clarify the privacy model ? \n\n6. I do not understand Lemma 4.5. Why does the privMaxDeg algorithm only achieve partial coverage ? My intuition from the privMultiSet algorithm is that privacy causes us to remove more sets than we actually need to, incurring a larger cost than OPT, but always achieving full coverage. If MaxDeg exactly reduces to MultiSet, why does full coverage break ? \n\n7. Minor typo (Lemma 4.1): The authors probably mean O((ln m)/ϵ + ln q) · |OP T|, not ϵ'.\n\nSection 5:\n1. What is T in Sec 5.1 ? \n\n2. Can the authors comment on the relationship between spectral radius and max degree of a graph? How should we interpret the results in Table 2 ? I ask this because Max Degree of a graph seems to be a much poorer indicator of how connected a graph is/how easily infection spreads over the network. Spectral Radius seems to be a more holistic metric to try and minimize. Can the authors provide examples of graph classes where Max Degree reduction is the better way to go ?  \n\n\nI will be willing to reconsider my score if my questions are answered meaningfully.\n\nLIMITATIONS:\nOverall, the reviewer feels that the paper would benefit greatly from a more streamlined way of presenting results. The paper in its current form is overloaded with technical results without (in many cases) clear explanation of why those results are important to the context. For example, why would a reader care about graph-theoretic connections between the spectral radius and walks of length 4. A lot of these unnecessary technicalities can be removed from the main body.  Lots of notation are introduced on the fly without formal definitions. Several results like runtime complexity can be omitted entirely from the main body or just mentioned in passing.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 1, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-17"}