{"id":"8607c950-fed2-4e8a-b0bd-62141f8d2f2e","arxiv_id":"2509.03374","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":9,"one_line_summary":"Numerical simulations of bi-pathogen reaction-diffusion models on multiplex networks show that hotspot growth depends on extreme parameter choices and that infected-mobility restrictions are the most effective early containment.","lead":"This paper simulates two models of two pathogens spreading on multiplex networks, showing that stationary hotspots can grow into collapse and that restricting infected mobility slows spread. It connects these patterns to real-world COVID/TB and TB/HIV co-infection data.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Hotspot growth/collapse is demonstrated only for hand-picked parameters with negative cross-diffusion and no co-infected mobility; need a robustness scan and a check that collapse is not an artifact of density clipping at 0.","rationale":"The reader's CONDITIONAL verdict is appropriate. The paper's two headline phenomena (stationary hotspot growth and collapse) rely on two worked examples with visibly extreme parameter choices (negative cross-diffusion, very large d33, and no co-infected mobility). The paper itself states that these parameter features are associated with pattern formation, so the central claim is not shown to be generic. My stress-test identifies the weakest load-bearing assumption in the same place as the reader: the examples are hand-selected and not subjected to robustness analysis. I add a sharper technical point: the simulation protocol forces densities to non-negative values, and collapse is declared when densities hit 0, so the numerical floor could artificially stabilize the collapse scenario; the paper gives no check of this. That is a concrete, potentially decisive gap. Independent supporting evidence in the paper (deterministic comparison across WS/BA/lattice topologies, 1000-trial averages in Tables I-II) does not fix this, because those tables measure spread/saturation times rather than the growing-hotspot-to-collapse phenomenon. The agreement is 'agree' because both the reader and I identify the parameter selection/representativeness of Examples 1 and 2 as the central weakness; my added clipping concern strengthens it without changing the verdict. The verdict should remain CONDITIONAL: not ACCEPT (paper lacks a reproducibility check for a strong qualitative claim), not REJECT (the models and simulations are plausible and largely self-consistent), and not UNVERDICTED (the central claim is clearly stated and testable).","tokens_in":20296,"tokens_out":1871,"duration_ms":16468,"concrete_test":"Re-run Examples 1 and 2 with an ODE solver that does not hard-clamp densities at 0, or monitor the unclipped state during solving; if collapse still occurs (same qualitative sequence of hotspot growth and extinction), the claim survives this objection. Then perform a small robustness scan around Example 1, varying d12, d13, and d33 by ±20-50% and, for MBRD-CI, add a nonzero co-infection diffusion term d44 to the C-layer equation; if collapse only occurs at the single hand-tuned point and disappears under perturbation or with co-infected movement, the paper's central claim would need to be rephrased as a conditional, not a general result.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The paper's strongest claim is that stationary hotspots can grow over time and lead to system collapse under MBRD-SI and MBRD-CI. The evidence for this rests on Examples 1 and 2 (§III.B). These use d12=d13=-0.2 (susceptible individuals are attracted to infected regions) and d33=4.8 (fast pathogen-2 diffusion), which the paper itself admits (bullets after §III.C) are ingredients that 'help induce pattern formation'. No parameter sweep is reported around these examples, so the reader cannot tell whether growing hotspots and collapse occur in an open set of parameter space or only at fragile, specially selected points. Likewise, the MBRD-CI model has no edges on the fourth (co-infection) layer by construction (§II), so co-infected individuals cannot diffuse; the claim that co-infection dynamics produce collapse is therefore untested for any regime in which C-mobility is nonzero. A second, more specific concern: the simulations clamp all densities at 0 ('we set 0 as the minimum threshold', §III.A). Since collapse is defined by densities reaching 0, the numerical integration with a hard floor can create an absorbing state that the continuous ODE would not approach the same way. The paper does not report whether collapse times or the growth rates change when the clamp is removed (e.g., by using a positivity-preserving scheme, or by checking whether the same initial perturbation without clipping still crosses the extinction threshold). The absence of confidence intervals means the fitted collapse times and power-law curves (Figures 6, 7, 12-14) may not be stable, but the clipping issue is more directly load-bearing for the central collapse claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents a simulation-based study of two multiplex reaction-diffusion epidemic models introduced in a companion paper: MBRD-SI (superinfection) and MBRD-CI (co-infection). The authors simulate pattern formation, hotspot growth, and point-source outbreaks on lattice, Watts-Strogatz, and Barabási-Albert networks. The main claimed results are that stationary Turing-type hotspots can grow in severity and lead to system collapse under both models; that higher superinfection or co-transmission coefficients accelerate spread; that limiting infected migration is important for containment; and that network topology affects spread, with BA networks producing faster propagation than WS networks. The paper also compares simulated co-infection spatial patterns with COVID-19/tuberculosis data from Recife and HIV/tuberculosis data from Jiangsu, claiming qualitative agreement. The central numerical evidence for the collapse phenomenon is based on two parameter sets (Examples 1 and 2) that include negative cross-diffusion and a large pathogen-2 diffusion coefficient, and the MBRD-CI model has no diffusion on the co-infection layer.","tokens_in":20737,"tokens_out":4123,"duration_ms":47370,"significance":"If the claims are robust, this work could contribute to the understanding of spatial pattern formation in multi-pathogen systems and inform discussions of targeted interventions. The paper has some strengths: it systematically compares several network topologies and degree combinations, reports averages over 1000 trials for the point-source tables, and attempts to connect simulation output to real co-infection data. However, the headline result of growing hotspots and system collapse is demonstrated only for hand-picked parameter sets with no uncertainty quantification or robustness analysis, and the model itself embeds several of the reported effects by construction. The real-world comparisons are descriptive and lack statistical testing. As presented, the paper is better characterized as an exploratory simulation study than as a set of established quantitative findings. The central claims may be salvageable, but they require additional numerical and statistical support.","major_comments":[{"comment":"The central claim that stationary hotspots can grow until system collapse is supported by exactly two parameter sets, both with d12=d13=-0.2 and d33=4.8, parameters that the paper itself (Section III.C) identifies as pattern-inducing. No parameter sweep, continuation, or perturbation study is reported around these examples. Consequently the reader cannot determine whether growing hotspots and collapse occur in an open region of parameter space or only at fragile, specially chosen points. Please provide a systematic scan (e.g., over d12, d13, d33, β1/β2, σ/β12) and report the fraction of parameter combinations exhibiting growth and collapse, with collapse times or growth rates and error bars.","section":"§III.B, Examples 1 and 2 (Eqs. 5-6)"},{"comment":"The text states 'we set 0 as the minimum threshold for all densities.' Since system collapse is identified by densities reaching 0, the hard floor can create an absorbing state that the continuous ODE would not approach in the same way. The paper does not test whether collapse still occurs without clipping or with a positivity-preserving integrator. Please report whether the same initial conditions and parameters lead to densities approaching zero (rather than being reset to zero artificially), and quantify changes in collapse times or growth rates. Also report the numerical integrator, step size, and tolerance used.","section":"§III.A, density floor and collapse definition"},{"comment":"The MBRD-CI model has no edges on the fourth (co-infection) layer, so co-infected individuals cannot diffuse. The claim that co-infection dynamics produce growing hotspots and system collapse is therefore untested for any regime with nonzero co-infected mobility. Because co-infected individuals are often mobile in real populations (e.g., COVID-19/TB co-infected patients can travel), this is a load-bearing limitation. Either extend the model to allow C-layer diffusion and re-run the collapse examples, or explicitly scope all MBRD-CI conclusions to immobile co-infected populations and state that the collapse phenomenon is not shown to persist under C-mobility.","section":"§II, Figure 1; §III.B Example 2"},{"comment":"The comparison with Recife and Jiangsu data is qualitative and lacks statistical testing. For example, the statement that 'for more than 35% of the regions, the absolute difference between the COVID and tuberculosis category numbers are greater than 2' is not compared to a null model of independent random categories; similarly, the 'around 87 percent' co-infection-tuberculosis agreement is reported without a test of association or confidence interval. Hotspot/coldspot statements from Wu et al. are also qualitative. Please add formal statistical tests (e.g., permutation tests, chi-square or Fisher exact tests on category counts, spatial correlation measures) before claiming that the simulations are supported by real-world data.","section":"§V, real-world comparison"},{"comment":"Several headline results are direct consequences of the model equations rather than emergent simulation discoveries. For example, higher σ directly increases the superinfection conversion term -σβ2 J_i I_i/(S+I+J) in Eq. (1); higher β12 directly increases co-infection production in Eq. (2); and reducing d22/d33 directly slows spatial spread of infected populations. Presenting these as 'findings' or 'observations' is circular and obscures the genuinely non-obvious results, such as the non-monotonic amplitude response to β12 in Figure 7. Please explicitly distinguish structural consequences from emergent behaviors and reframe the conclusions accordingly.","section":"§III.C, §IV.E, §VI"}],"minor_comments":[{"comment":"The denominators S_i+I_i+J_i-C_i can vanish if all four densities are zero; the paper should state how the reaction terms are handled in that case (e.g., by setting the fraction to zero) to ensure the numerical scheme is well defined.","section":"Equation (2)"},{"comment":"The fitted Fourier coefficients are given as 'a2 = 0.2676, 0.7012'; the second value is presumably b2 and should be labeled. Similarly, in Figure 13's caption, 'where 1 .1382 and b = 227' is missing the coefficient name and has a typo.","section":"Figure 7 caption"},{"comment":"The definition of peak time uses a condition 'δ(t) = δ(t*) ∀ t ∈ {(t*, u] | t ≡ 0 mod n}' where n is not defined. This should be τ, consistent with the initial definition. Also, the phrase 'an smallest integer multiple' should be 'the smallest integer multiple'.","section":"Definition 5"},{"comment":"The caption reads 'LA14-LA4-LA4 (left)' but the text and Section III.D describe only LA4, LA12, and LA24 lattices; LA14 appears to be a typo for LA12-LA4-LA4.","section":"Figure 8 caption"},{"comment":"The tables are described as averages of 1000 trials, but no standard deviations, standard errors, or confidence intervals are reported. Since the WS and BA networks are stochastic, some measure of variability is needed to compare entries across degree combinations.","section":"Tables I and II"},{"comment":"The paper states that 'Turing-Hopf patterns are rarer than Turing patterns' without quantifying this claim or explaining how the two pattern types were distinguished. Please provide a criterion or prevalence measure, or soften the statement.","section":"§III.D and §VI"}],"recommendation":"major_revision","confidential_remarks":"The manuscript leans heavily on a companion paper for model derivation and instability conditions; this work's contribution is primarily the numerical exploration. Before considering publication, the authors should address the robustness and floor-scheme concerns and add statistical rigor to the real-data section. I would also encourage the editor to verify that the manuscript is sufficiently self-contained relative to the companion paper, since several model definitions and parameter meanings are deferred to [10]."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nYou should know before reading: the paper claims stationary hotspots can grow and drive system collapse under both models, but the evidence is two hand-picked parameter sets that the authors themselves say “help induce pattern formation.” So file the headline under “illustrative phenomenon,” not “established generality.”\n\nWhat is actually good: the simulation study is systematic. They use lattice, Watts-Strogatz and Barabasi-Albert networks, define spread indices cleanly, and provide a lot of tables on saturation times. The qualitative comparison with Recife and Jiangsu co-infection data is a nice touch, even if it never goes beyond counting category differences. The observation that co-infection spatial distributions track one pathogen’s distribution more than the other is worth remembering. For a numerical exploration in the companion-model framework, this is solid, careful work.\n\nThe soft spots are real. First, the collapse result rests on Examples 1 and 2: negative cross-diffusion (d12=d13=-0.2) and a very fast pathogen-2 diffusion (d33=4.8). No parameter sweep around these points is reported, so we have no idea whether growing hotspots and collapse happen in an open set of parameters or only at fragile, specially selected values. Second, the MBRD-CI model has no edges in the co-infection layer by construction, so co-infected individuals cannot move; any claim about co-infection-driven collapse is untested for any regime with C-mobility. Third, the simulations clamp all densities at zero. Since collapse is defined by densities reaching zero, the hard floor may itself create an absorbing state. They do not report whether collapse times or growth rates change if you use a positivity-preserving scheme without clipping. That is the load-bearing missing experiment. Fourth, no code or data, and the fitted curves in Figures 6, 7, 12-14 have no error bars. Finally, the real-world comparison uses coarse categorical bins with no statistical test.\n\nTo be clear: I don’t think this is a bad paper. The model-output expectations (stronger pathogen dominates, quarantine works) are confirmed, and some of the spatial findings are genuinely interesting. But the central claim does not yet have the support the abstract implies.\n\nWho is it for? People actively working on reaction-diffusion epidemic models or multiplex contagion, especially those building on the companion paper. It deserves peer review, but the referee should require a parameter robustness scan, a test without the density clamp, and ideally a version with C-mobility. If those come out in the revision, the claim could firm up. As it stands, this is a conditional accept at best.\n\nRecommendation: send it to review, but with clear guidance to the authors on what must be added.","headline":"A thorough simulation study that demonstrates hotspot growth and collapse only in hand-picked, extreme parameter regimes, so the headline claim is not yet shown to be generic.","tokens_in":21174,"tokens_out":3185,"would_cite":false,"duration_ms":30871,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["92D30","35K57"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that stationary infection hotspots can grow in severity over time under both super-infection and co-infection dynamics on multiplex networks, potentially leading to system collapse.","keywords":["epidemic models","reaction-diffusion","Turing patterns","multiplex networks","super-infection","co-infection","bi-virus model","hotspot growth"],"falsifier":"Re-run the MBRD-SI and MBRD-CI simulations on the same networks and Example 1/Example 2 parameters but with non-negative cross-diffusion, with edges added to the co-infection layer so co-infected individuals can diffuse, and with unequal layerwise average degrees. If in any of these settings the stationary hotspots stop growing and no system collapse occurs over long integration times, the paper's central claim—that stationary hotspots can grow to collapse under both dynamics—would be shown to hold only for the specific modeling choices in those examples.","tokens_in":20254,"feed_emoji":"🦠","tokens_out":22047,"duration_ms":180150,"temperature":0.7,"pith_summary":"This paper asks what happens when two pathogens spread through a network of connected regions, each interacting with the other and with human movement between regions. Using numerical experiments with the authors' reaction–diffusion framework on multiplex networks, it claims that under both super-infection and co-infection dynamics, infection hotspots that stay fixed in space can nonetheless grow steadily in severity—eventually driving the susceptible population to vanish across most of the network, a system collapse. It also identifies the conditions that amplify or suppress this behavior: large gaps between the pathogens' transmission and removal rates, negative cross-diffusion, and strong diffusion disparities favor hotspot growth, while varying the network's layerwise connectivity or letting one pathogen dominate inhibits it. Beyond pattern formation, the simulations show that limiting migration of infected individuals is the most effective early containment measure, and that scale-free network topologies spread both pathogens faster than small-world ones—a candidate explanation for holiday-season outbreak surges. If these results hold, they give quantitative signatures for when a two-pathogen epidemic will form stationary, targetable hotspots and when those hotspots will grow toward collapse.","feed_headline":"Stationary infection hotspots can grow until collapse","feed_subtitle":"Two-pathogen network simulations show fixed hotspots growing without bound—and which parameters stop them.","key_machinery":"The engine of the argument is the Multiplex Bi-Virus Reaction–Diffusion (MBRD) framework from the companion paper: coupled reaction–diffusion systems on multilayer metapopulation networks—three layers (susceptible, pathogen 1, pathogen 2) for super-infection, plus a co-infection density layer with no edges for co-infection. The load-bearing mechanism is the Turing instability: small stochastic perturbations of a spatially uniform steady state are amplified into stationary spatial patterns when the diffusion coefficients and cross-diffusion terms (susceptibles migrating toward infected regions) differ strongly across layers. The paper tracks outcomes with a network-wide pattern amplitude—the","core_discovery":"In both the super-infection model (MBRD-SI) and the co-infection model (MBRD-CI), the paper finds that multiplex reaction–diffusion dynamics can produce Turing-instability hotspots that stay pinned in space yet grow steadily in amplitude until the system collapses—susceptible and pathogen-1 densities fall to zero in most nodes. The phenomenon appears in two explicit regimes and is narrow, requiring a large gap between the pathogens' transmission and removal rates, negative cross-diffusion drawing susceptibles toward infected areas, and strong diffusion disparity. It also claims that varying layerwise degrees inhibits pattern formation and that pathogen dominance suppresses hotspot growth.","pith_inferences":["A full parameter-space sweep is the obvious next step: the two worked examples sample one point in the growing-hotspot window each, so mapping the window's boundaries would turn the qualitative claim into a predictive phase diagram for when bi-pathogen systems collapse.","The roughly linear, slope-near-one relationship the paper fits between the β12 threshold and the co-infection removal rate α12 implies a testable control rule: to keep co-infection from becoming endemic, raising co-infection removal must be matched by a nearly equal cut in co-transmission.","The holiday-surge explanation is directly testable: compare spread indices on mobility networks built from travel-season versus off-season movement data; the model predicts faster saturation and higher peaks in the scale-free-like holiday regime.","The same multiplex mechanism should transfer to competing information or malware strains, where 'hotspot growth' would appear as echo-chamber amplification or cascading node takeover—an extension the paper cites as motivation but does not simulate."],"forward_implications":["Stationary hotspots mean targetable outbreaks: because Turing-instability hotspots stay pinned to fixed locations, location-based interventions can be aimed before growth accelerates, whereas moving patterns would be far harder to respond to.","A screening rule emerges for the growing-hotspot window: significant gaps between the two pathogens' transmission and removal rates, negative cross-diffusion, and large diffusion disparities are the signatures that indicate a two-pathogen system is in the regime where hotspots grow toward collapse.","Containment priority is clear: in the early stage of bi-pathogen spread, restricting the migration of infected individuals (quarantine) slows both pathogens far more than restricting susceptible movement.","Topology explains seasonal surges: scale-free network structures spread both pathogens faster than small-world structures, so holiday-season mobility that turns human movement patterns scale-free-like can produce outbreak spikes even under bi-pathogen dynamics.","Co-transmission has a sweet spot: intermediate values of the co-transmission coefficient β12 maximize spatial oscillations, and a threshold relating β12 to the co-infection removal rate α12 controls whether co-infections become endemic or die out."],"supporting_citations":[{"why":"Supplies the MBRD-SI and MBRD-CI model equations and the Turing-instability theory that all simulations in this paper build on.","marker":"[10]"},{"why":"Supplies the small-world network model used as one simulation substrate for human mobility.","marker":"[16]"},{"why":"Supplies the scale-free network model used to represent hub-dominated mobility and to explain faster spread.","marker":"[17]"},{"why":"Provides the multiplex-network Turing-instability and cross-diffusion framework whose parameter signatures the observed patterns are checked against.","marker":"[24]"},{"why":"Establishes Turing patterns for an SI epidemic model with cross-diffusion on complex networks, grounding the diffusion-disparity conditions used here.","marker":"[26]"},{"why":"Prior demonstration that interacting contagions can form persistent spatial patterns; this paper extends that phenomenon to bi-pathogen super- and co-infection dynamics.","marker":"[12]"},{"why":"Links strain competition to growing Turing patterns and system collapse, the collapse phenomenon reproduced in the simulations.","marker":"[25]"},{"why":"Recife COVID-19/tuberculosis co-infection spatial data used to test whether peak–valley anti-correlation and co-infection mirroring appear in real co-circulation.","marker":"[37]"},{"why":"Jiangsu tuberculosis/HIV co-infection hotspot-and-coldspot data used as a second real-world check of the spatial anti-correlation observations.","marker":"[38]"},{"why":"Field study of co-infection in a plant pathogen used to ground the observation that co-infection distributions spatially mirror one pathogen.","marker":"[36]"}],"fun_headline_variants":["Infectious hotspots grow until system collapse","Pinned infection hotspots grow to full collapse","Two-pathogen nets: fixed hotspots collapse the system","Bi-pathogen model: stationary hotspots grow to ruin"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The collapse phenomenon is demonstrated only for hand-selected parameter sets that include negative cross-diffusion and a very large pathogen-2 diffusion, and the co-infection model assumes co-infected individuals never move; if real bi-pathogen systems do not satisfy these conditions, the hotspot-growth and collapse results may not be generic.","fun_headline_variants_meta":{"raw":{"variants":["Infectious hotspots grow until system collapse","Pinned infection hotspots grow to full collapse","Two-pathogen nets: fixed hotspots collapse the system","Bi-pathogen model: stationary hotspots grow to ruin"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000182,"raw_usage":{"total_tokens":1099,"prompt_tokens":645,"completion_tokens":454,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":389,"completion_tokens_details":{"reasoning_tokens":407}},"tokens_in":389,"tokens_out":454,"duration_ms":5898,"temperature":1.0,"reasoning_tokens":407,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T10:56:56.158499+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the MBRD-SI and MBRD-CI simulations on the same networks and Example 1/Example 2 parameters but with non-negative cross-diffusion, with edges added to the co-infection layer so co-infected individuals can diffuse, and with unequal layerwise average degrees. If in any of these settings the stationary hotspots stop growing and no system collapse occurs over long integration times, the paper's central claim—that stationary hotspots can grow to collapse under both dynamics—would be shown to hold only for the specific modeling choices in those examples.","supporting_citations":[{"cited_title":"Spatial Super-Infection and Co-Infection Dynamics in Networks","cited_arxiv_id":"2508.15740","evidence_quote":"Supplies the MBRD-SI and MBRD-CI model equations and the Turing-instability theory that all simulations in this paper build on."},{"cited_title":"Collec- tive dynamics of ˆ a€˜small-worldˆ a€™networks","cited_arxiv_id":null,"evidence_quote":"Supplies the small-world network model used as one simulation substrate for human mobility."},{"cited_title":"Scale-free networks","cited_arxiv_id":null,"evidence_quote":"Supplies the scale-free network model used to represent hub-dominated mobility and to explain faster spread."},{"cited_title":"Navigating epidemic spread through multiplex networks: Unveiling turing in- stability and cross-diffusion dynamics","cited_arxiv_id":null,"evidence_quote":"Provides the multiplex-network Turing-instability and cross-diffusion framework whose parameter signatures the observed patterns are checked against."},{"cited_title":"Turing patterns of an si epidemic model with cross-diffusion on complex networks","cited_arxiv_id":null,"evidence_quote":"Establishes Turing patterns for an SI epidemic model with cross-diffusion on complex networks, grounding the diffusion-disparity conditions used here."},{"cited_title":"Persistent spatial patterns of interacting conta- gions","cited_arxiv_id":null,"evidence_quote":"Prior demonstration that interacting contagions can form persistent spatial patterns; this paper extends that phenomenon to bi-pathogen super- and co-infection dynamics."},{"cited_title":"Competition-exclusion and coexistence in a two-strain SIS epidemic model in patchy environments","cited_arxiv_id":"2308.10348","evidence_quote":"Links strain competition to growing Turing patterns and system collapse, the collapse phenomenon reproduced in the simulations."},{"cited_title":"Co-infection alters population dynamics of infec- tious disease","cited_arxiv_id":null,"evidence_quote":"Recife COVID-19/tuberculosis co-infection spatial data used to test whether peak–valley anti-correlation and co-infection mirroring appear in real co-circulation."},{"cited_title":"Spatial analysis of tuberculosis, covid-19, and tuberculosis/covid-19 coinfection in recife, pe, brazil","cited_arxiv_id":null,"evidence_quote":"Jiangsu tuberculosis/HIV co-infection hotspot-and-coldspot data used as a second real-world check of the spatial anti-correlation observations."},{"cited_title":"Public holidays in- creased the transmission of covid-19 in japan, 2020- 2021: a mathematical modelling study","cited_arxiv_id":null,"evidence_quote":"Field study of co-infection in a plant pathogen used to ground the observation that co-infection distributions spatially mirror one pathogen."}],"review_version":1}