pith. sign in

arxiv: 2606.21481 · v1 · pith:WNOMWLMOnew · submitted 2026-06-19 · 🧬 q-bio.QM

Mechanistic mathematical model of the in vitro infection dynamics of Bunyamwera and Batai viruses including MOI-dependent shortening of the eclipse phase

Bevelynn Whaler , Eleanor Todd , Amelia B. Shaw , John N. Barr , Catherine A. A. Beauchemin , Grant Lythe , Carmen Molina-Paris , Martin Lopez-Garcia This is my paper

Pith reviewed 2026-06-26 12:38 UTC · model grok-4.3

classification 🧬 q-bio.QM
keywords Bunyamwera virusBatai viruseclipse phasemathematical modelinfection dynamicsre-infectionin vitroviral kinetics
0
0 comments X

The pith

Bunyamwera virus has longer eclipse and infectious periods than Batai virus, with re-infection shortening the eclipse phase more strongly for BUNV.

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

The paper develops a deterministic mathematical model to describe the infection of A549 cells by Bunyamwera virus and Batai virus. The model includes cell division and death, ongoing virion entry into infected cells, and a shortening of the eclipse phase that depends on the multiplicity of infection. Parameters are estimated from viral decay experiments, growth curves at two inoculum levels, and genome copy data using Markov chain Monte Carlo sampling. The fitted model shows clear differences: BUNV takes longer to exit the eclipse phase and stays infectious longer, while BATV produces more virus particles per cell. Re-infection accelerates the start of production for both, but the acceleration is much greater for BUNV.

Core claim

BUNV exhibited substantially longer eclipse and infectious periods than BATV, while BATV showed a higher per-cell virus production rate. Re-infection was predicted to shorten the eclipse phase for both viruses, but the effect was markedly stronger for BUNV. These results come from a model fit to decay data, growth curves, and genome copy measurements that quantifies the distinct in vitro viral kinetics of the two viruses.

What carries the argument

The deterministic model structure that incorporates MOI-dependent shortening of the eclipse phase due to re-infection, fitted via MCMC to constrain the per-infectious-unit infection rate.

If this is right

  • BUNV has substantially longer eclipse and infectious periods than BATV.
  • BATV produces virus at a higher rate per infected cell than BUNV.
  • Re-infection shortens the eclipse phase more strongly for BUNV than for BATV.
  • Genome copy measurements are essential to constrain the infection rate parameter for BUNV.
  • The model distinguishes the replication dynamics of the two viruses quantitatively.

Where Pith is reading between the lines

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

  • Differences in eclipse phase response to re-infection may affect how each virus spreads in insect vectors or mammalian hosts.
  • Similar modeling could help compare kinetics of other bunyaviruses or related arboviruses.
  • Direct measurement of eclipse phase at different MOIs could test the shortening prediction experimentally.
  • The approach might inform models of within-host viral dynamics for these or similar pathogens.

Load-bearing premise

The MOI-dependent shortening of the eclipse phase is a genuine biological effect that the model structure can represent accurately.

What would settle it

Measuring the eclipse phase duration in cells infected at low MOI versus high MOI and finding no shortening for BUNV would falsify the re-infection effect.

Figures

Figures reproduced from arXiv: 2606.21481 by Amelia B. Shaw, Bevelynn Whaler, Carmen Molina-Paris, Catherine A. A. Beauchemin, Eleanor Todd, Grant Lythe, John N. Barr, Martin Lopez-Garcia.

Figure 1
Figure 1. Figure 1: Diagram of the in vitro BUNV or BATV infection MM. Uninfected cells, T, and eclipse phase cells, E, divide at rate λR, where R(t) represents the availability of resources for cell division in the media, which are assumed to be used up at a constant rate per cell. The time-dependent rate of natural cell death is given by δN (t), which is the hazard function of an Erlang-distributed random variable. We consi… view at source ↗
Figure 2
Figure 2. Figure 2: Modelling a reduction in the length of the eclipse phase due to re-infection. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Posterior MM predictions compared with the cell number and viral titre data used in the MCMC for [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Posterior MM predictions for the number of RNA copies of each [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Posterior MM predictions for the BUNV (left) and BATV (right) viral decay experiments, compared [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Marginal posterior distributions of model parameters for BUNV (blue) and BATV (orange). [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Posterior distributions of relevant parameter combinations for each virus. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Two-dimensional histograms showing the relationship between the [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the predicted in vitro infection dynamics of BUNV (blue) and BATV (orange) across MOIs. Initial conditions used were T(0) = 106 cells/well and either a low MOI of VSIN(0) = 105 SIN/well for each virus (solid lines) or a high MOI of VSIN(0) = 7 × 106 SIN/well for each virus (dashed lines). (A) Predicted number of cells in the uninfected state; (B) Predicted number of cells in the eclipse state… view at source ↗
Figure 10
Figure 10. Figure 10: Posterior MM predictions for cell division and natural death, [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
read the original abstract

We develop a deterministic mathematical model to quantify the distinct in vitro infection dynamics of Bunyamwera virus (BUNV) and Batai virus (BATV) in A549 cells, incorporating cell division and natural death, continued entry of virions into already-infected cells, and shortening of the eclipse phase driven by re-infection. The model parameters were estimated making use of viral decay data, growth curves at two different inoculum concentrations, and extra-cellular genome copy measurements (for BUNV) via Markov chain Monte Carlo. Genome copy measurements were essential for constraining estimates of the number of cells that can become infected per unit of infectious virus for BUNV. We found that BUNV exhibited substantially longer eclipse and infectious periods than BATV, while BATV showed a higher per-cell virus production rate. Re-infection was predicted to shorten the eclipse phase for both viruses, but the effect was markedly stronger for BUNV. Together, these results provide a quantitative comparison of the in vitro viral kinetics of BUNV and BATV and reveal substantial differences in their replication dynamics.

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.

Referee Report

3 major / 2 minor

Summary. The paper develops a deterministic ODE model of in vitro BUNV and BATV infection in A549 cells that incorporates cell division and death, continued virion entry into infected cells, and linear shortening of the eclipse phase with cumulative re-infection events. Parameters are fit by MCMC to viral decay curves, growth curves at two MOIs, and (for BUNV only) extracellular genome-copy time series. The central claims are that BUNV has substantially longer eclipse and infectious periods than BATV, BATV has a higher per-cell production rate, and re-infection shortens the eclipse phase (more strongly for BUNV).

Significance. If the shortening term proves identifiable and necessary, the work supplies a quantitative, data-constrained comparison of two related bunyaviruses and demonstrates how re-infection can modulate eclipse duration in a virus-specific manner. The explicit use of genome-copy data to break a key degeneracy for BUNV is a methodological strength.

major comments (3)
  1. [Abstract] Abstract and Results: the reported shortening of the eclipse phase is an output of the MCMC fit to the same data used to estimate all other parameters rather than an independent prediction; consequently the claim that re-infection 'was predicted to shorten' the phase and that the effect is 'markedly stronger for BUNV' is circular and its magnitude is not falsifiable within the present analysis.
  2. [Methods] Methods/Results: no model-comparison statistics, Bayes factors, or profile-likelihood traces are shown to establish that the MOI-dependent shortening term is required by the data rather than being absorbed by compensatory changes in production rate or infectious-period length.
  3. [Results] Results: for BATV the degeneracy between the per-infectious-unit infection rate and eclipse duration is not broken by genome-copy data; without additional constraints or sensitivity analysis this undermines the reliability of the cross-virus comparison of eclipse-phase lengths.
minor comments (2)
  1. The full set of model equations, initial conditions, and the precise functional form of the eclipse-shortening term should be stated explicitly in the main text (or a dedicated supplementary section) rather than referenced only by name.
  2. Predictive-check figures should indicate which data types (decay, growth at MOI 1, growth at MOI 10, genome copies) are shown in each panel to allow readers to assess fit quality per data source.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment below and indicate where revisions will be made to strengthen the presentation and analysis.

read point-by-point responses

  1. Referee: [Abstract] Abstract and Results: the reported shortening of the eclipse phase is an output of the MCMC fit to the same data used to estimate all other parameters rather than an independent prediction; consequently the claim that re-infection 'was predicted to shorten' the phase and that the effect is 'markedly stronger for BUNV' is circular and its magnitude is not falsifiable within the present analysis.

    Authors: We agree that the shortening effect is inferred from the MCMC posterior rather than constituting an independent prediction. The shortening term was included in the model on the basis of a mechanistic hypothesis regarding re-infection, and the data determine its estimated magnitude. To remove any implication of an out-of-sample prediction, we will revise the abstract and results sections to state that the model 'infers' or 'estimates' that re-infection shortens the eclipse phase (with a stronger effect for BUNV). This change makes the inferential nature of the result explicit. revision: yes

  2. Referee: [Methods] Methods/Results: no model-comparison statistics, Bayes factors, or profile-likelihood traces are shown to establish that the MOI-dependent shortening term is required by the data rather than being absorbed by compensatory changes in production rate or infectious-period length.

    Authors: The referee correctly notes the absence of formal model-comparison statistics. In the revised manuscript we will add a comparison of the full model against a reduced model lacking the MOI-dependent shortening term, reporting the deviance information criterion (DIC) from the MCMC runs and, where feasible, approximate Bayes factors. We will also inspect the joint posterior and profile likelihoods to confirm that the shortening parameter remains identifiable and is not fully compensated by adjustments in production rate or infectious period. revision: yes

  3. Referee: [Results] Results: for BATV the degeneracy between the per-infectious-unit infection rate and eclipse duration is not broken by genome-copy data; without additional constraints or sensitivity analysis this undermines the reliability of the cross-virus comparison of eclipse-phase lengths.

    Authors: We acknowledge that genome-copy data are available only for BUNV and that this leaves a potential degeneracy for BATV between infection rate and eclipse duration. The two-MOI growth curves supply some constraint via the timing of viral output, yet we agree that explicit sensitivity analysis is needed. We will add a sensitivity study for BATV in which the infection-rate parameter is varied over a plausible range while monitoring the resulting eclipse-duration posterior; the results will be reported to allow readers to assess the robustness of the cross-virus comparison. revision: partial

Circularity Check

1 steps flagged

Fitted re-infection shortening term presented as model prediction

specific steps
  1. fitted input called prediction [Abstract]
    "Re-infection was predicted to shorten the eclipse phase for both viruses, but the effect was markedly stronger for BUNV."

    The model structure incorporates 'shortening of the eclipse phase driven by re-infection' as an explicit term whose coefficient is estimated from the same viral growth and genome-copy datasets used to produce all other results. The reported shortening effect size is therefore the direct numerical output of that fitted coefficient rather than an independent prediction.

full rationale

The paper constructs a deterministic ODE model that explicitly includes an MOI-dependent shortening term for the eclipse phase, estimates all parameters (including the shortening coefficient) via MCMC on the growth curves and genome-copy data, and then reports the shortening as a 'prediction.' This is a fitted model feature rather than an out-of-sample or first-principles result, but the remaining parameter estimates (eclipse duration, infectious period, production rate) retain independent content from the data and are not forced by construction. No self-citation chains or definitional loops are present. The degeneracy noted by the skeptic is a statistical-identifiability issue, not circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

Model rests on several free parameters estimated from data and standard assumptions of deterministic ODE viral kinetics; no new entities introduced.

free parameters (4)
  • eclipse phase length
    Fitted via MCMC to growth and decay data
  • infectious period length
    Fitted via MCMC
  • virus production rate per cell
    Fitted via MCMC
  • cells infected per infectious virion
    Constrained by genome copy data for BUNV
axioms (2)
  • standard math Infection dynamics follow deterministic ordinary differential equations
    Core modeling framework stated in abstract
  • domain assumption Cell division and natural death occur at constant rates in culture
    Explicitly included in model description

pith-pipeline@v0.9.1-grok · 5765 in / 1326 out tokens · 28556 ms · 2026-06-26T12:38:26.866784+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

32 extracted references · 1 canonical work pages

  1. [1]

    Mechanisms of bunyavirus morphogenesis and egress

    Barker J, daSilva LL, Crump CM. Mechanisms of bunyavirus morphogenesis and egress. J Gen Virol. 2023;104(4):001845

    2023

  2. [2]

    Recent advances in the molecular and cellular biology of bunyaviruses

    Walter CT, Barr JN. Recent advances in the molecular and cellular biology of bunyaviruses. J Gen Virol. 2011;92(11):2467–2484

    2011

  3. [3]

    Attenuation of bunyavirus replication by rearrangement of viral coding and noncoding sequences

    Lowen AC, Boyd A, Fazakerley JK, Elliott RM. Attenuation of bunyavirus replication by rearrangement of viral coding and noncoding sequences. J Virol. 2005;79(11):6940–6946

    2005

  4. [4]

    Visualizing the replication cycle of bunyamwera orthobunyavirus expressing fluorescent protein-tagged Gc glycoprotein

    Shi X, van Mierlo JT, French A, Elliott RM. Visualizing the replication cycle of bunyamwera orthobunyavirus expressing fluorescent protein-tagged Gc glycoprotein. J Virol. 2010;84(17):8460–8469

    2010

  5. [5]

    Key Golgi factors for structural and functional maturation of bunyamwera virus

    Novoa RR, Calderita G, Cabezas P, Elliott RM, Risco C. Key Golgi factors for structural and functional maturation of bunyamwera virus. J Virol. 2005;79(17):10852–10863

    2005

  6. [6]

    Requirement of the N-terminal region of orthobunyavirus nonstructural protein NSm for virus assembly and morphogenesis

    Shi X, Kohl A, L´ eonard VH, Li P, McLees A, Elliott RM. Requirement of the N-terminal region of orthobunyavirus nonstructural protein NSm for virus assembly and morphogenesis. J Virol. 2006;80(16):8089–8099

    2006

  7. [7]

    NSm is a critical determinant for bunyavirus transmission between vertebrate and mosquito hosts

    Terhzaz S, Kerrigan D, Almire F, Szemiel AM, Hughes J, Parvy JP, et al. NSm is a critical determinant for bunyavirus transmission between vertebrate and mosquito hosts. Nat Commun. 2025;16(1):1214

    2025

  8. [8]

    Innate Immune Response Against Batai Virus, Bunyamwera Virus, and Their Reassortants

    Z¨ oller DD, S¨ aurich J, Metzger J, Jung K, Lepenies B, Becker SC. Innate Immune Response Against Batai Virus, Bunyamwera Virus, and Their Reassortants. Viruses. 2024;16(12):1833. June 23, 2026 24/26

    2024

  9. [9]

    It’s in the mix: Reassortment of segmented viral genomes

    Lowen AC. It’s in the mix: Reassortment of segmented viral genomes. PLOS Pathog. 2018;14(9):e1007200

    2018

  10. [10]

    Batai and Ngari viruses: M segment reassortment and association with severe febrile disease outbreaks in East Africa

    Briese T, Bird B, Kapoor V, Nichol ST, Lipkin WI. Batai and Ngari viruses: M segment reassortment and association with severe febrile disease outbreaks in East Africa. J Virol. 2006;80(11):5627–5630

    2006

  11. [11]

    Comparative characterization of the reassortant Orthobunyavirus Ngari with putative parental viruses, Bunyamwera and Batai: in vitro characterization and ex vivo stability

    Dutuze MF, Mayton EH, Macaluso JD, Christofferson RC. Comparative characterization of the reassortant Orthobunyavirus Ngari with putative parental viruses, Bunyamwera and Batai: in vitro characterization and ex vivo stability. J Gen Virol. 2021;102(2):001523

    2021

  12. [12]

    Mammals preferred: Reassortment of Batai and Bunyamwera orthobunyavirus occurs in mammalian but not insect cells

    Heitmann A, Gusmag F, Rathjens MG, Maurer M, Frankze K, Schicht S, et al. Mammals preferred: Reassortment of Batai and Bunyamwera orthobunyavirus occurs in mammalian but not insect cells. Viruses. 2021;13(9):1702

    2021

  13. [13]

    Probing orthobunyavirus reassortment using Bunyamwera and Batai viruses as models

    Bowen JM, Gunter K, Lunel AM, Omoga DC, Jones JE, Giesel H, et al. Probing orthobunyavirus reassortment using Bunyamwera and Batai viruses as models. PLOS Negl Trop Dis. 2025;19(5):e0013120

    2025

  14. [14]

    Impact of the H275Y and I223V mutations in the neuraminidase of the 2009 pandemic influenza virus in vitro and evaluating experimental reproducibility

    Paradis EG, Pinilla LT, Holder BP, Abed Y, Boivin G, Beauchemin CA. Impact of the H275Y and I223V mutations in the neuraminidase of the 2009 pandemic influenza virus in vitro and evaluating experimental reproducibility. PLOS One. 2015;10(5):e0126115

    2009

  15. [15]

    (In)validating experimentally derived knowledge about influenza A defective interfering particles

    Liao LE, Iwami S, Beauchemin CA. (In)validating experimentally derived knowledge about influenza A defective interfering particles. J R Soc Interface. 2016;13(124):20160412

    2016

  16. [16]

    Uncovering critical properties of the human respiratory syncytial virus by combining in vitro assays and in silico analyses

    Beauchemin CA, Kim YI, Yu Q, Ciaramella G, DeVincenzo JP. Uncovering critical properties of the human respiratory syncytial virus by combining in vitro assays and in silico analyses. PLOS One. 2019;14(4):e0214708

    2019

  17. [17]

    Quantification of Ebola virus replication kinetics in vitro

    Liao LE, Carruthers J, Smither SJ, Team CV, Weller SA, Williamson D, et al. Quantification of Ebola virus replication kinetics in vitro. PLOS Comput Biol. 2020;16(11):e1008375

    2020

  18. [18]

    Time to revisit the endpoint dilution assay and to replace the TCID 50 as a measure of a virus sample’s infection concentration

    Cresta D, Warren DC, Quirouette C, Smith AP, Lane LC, Smith AM, et al. Time to revisit the endpoint dilution assay and to replace the TCID 50 as a measure of a virus sample’s infection concentration. PLOS Comput Biol. 2021;17(10):e1009480. doi:10.1371/journal.pcbi.1009480

    work page doi:10.1371/journal.pcbi.1009480 2021

  19. [19]

    Quirouette C, Thevakumaran R, Adachi K, Beauchemin CA. Does the random nature of cell-virus interactions during in vitro infections affect TCID 50 measurements and parameter estimation by mathematical models? arXiv preprint arXiv:241212960. 2024

    2024

  20. [20]

    Incomplete bunyavirus particles can cooperatively support virus infection and spread

    Berm´ udez-M´ endez E, Bronsvoort KF, Zwart MP, van de Water S, C´ ardenas-Rey I, Vloet RP, et al. Incomplete bunyavirus particles can cooperatively support virus infection and spread. PLOS Biol. 2022;20(11):e3001870

    2022

  21. [21]

    Emerging infectious diseases: the Bunyaviridae

    Soldan SS, Gonz´ alez-Scarano F. Emerging infectious diseases: the Bunyaviridae. Journal of neurovirology. 2005;11(5):412–423

    2005

  22. [22]

    Tick-borne Bunyaviruses: an emerging public health threat; 2025

    Hawman DW, Appelberg S, Duscher GG. Tick-borne Bunyaviruses: an emerging public health threat; 2025. June 23, 2026 25/26

    2025

  23. [23]

    Oropouche virus: an emerging orthobunyavirus

    Tilston-Lunel NL. Oropouche virus: an emerging orthobunyavirus. Journal of General Virology. 2024;105(10):002027

    2024

  24. [24]

    Bunyamwera virus nonstructural protein NSs counteracts interferon regulatory factor 3-mediated induction of early cell death

    Kohl A, Clayton RF, Weber F, Bridgen A, Randall RE, Elliott RM. Bunyamwera virus nonstructural protein NSs counteracts interferon regulatory factor 3-mediated induction of early cell death. J Virol. 2003;77(14):7999–8008

    2003

  25. [25]

    Interaction of Bunyamwera Orthobunyavirus NSs protein with mediator protein MED8: a mechanism for inhibiting the interferon response

    L´ eonard VH, Kohl A, Hart TJ, Elliott RM. Interaction of Bunyamwera Orthobunyavirus NSs protein with mediator protein MED8: a mechanism for inhibiting the interferon response. J Virol. 2006;80(19):9667–9675

    2006

  26. [26]

    Lymphocytic choriomeningitis arenavirus utilises intercellular connections for cell to cell spread

    Byford O, Shaw AB, Tse HN, Moon-Walker A, Saphire EO, Whelan SP, et al. Lymphocytic choriomeningitis arenavirus utilises intercellular connections for cell to cell spread. Sci Rep. 2024;14(1):28961

    2024

  27. [27]

    Hepatitis C virus cell-cell transmission in hepatoma cells in the presence of neutralizing antibodies

    Timpe JM, Stamataki Z, Jennings A, Hu K, Farquhar MJ, Harris HJ, et al. Hepatitis C virus cell-cell transmission in hepatoma cells in the presence of neutralizing antibodies. Hepatol. 2008;47(1):17–24

    2008

  28. [28]

    Neutralizing antibody-resistant hepatitis C virus cell-to-cell transmission

    Brimacombe CL, Grove J, Meredith LW, Hu K, Syder AJ, Flores MV, et al. Neutralizing antibody-resistant hepatitis C virus cell-to-cell transmission. J Virol. 2011;85(1):596–605

    2011

  29. [29]

    Modulation of potassium channels inhibits bunyavirus infection

    Hover S, King B, Hall B, Loundras EA, Taqi H, Daly J, et al. Modulation of potassium channels inhibits bunyavirus infection. J Biol Chem. 2016;291(7):3411–3422

    2016

  30. [30]

    Bunyamwera orthobunyavirus glycoprotein precursor is processed by cellular signal peptidase and signal peptide peptidase

    Shi X, Botting CH, Li P, Niglas M, Brennan B, Shirran SL, et al. Bunyamwera orthobunyavirus glycoprotein precursor is processed by cellular signal peptidase and signal peptide peptidase. Proc Natl Acad Sci. 2016;113(31):8825–8830

    2016

  31. [31]

    Bunyaviruses: from transmission by arthropods to virus entry into the mammalian host first-target cells

    L´ eger P, Lozach PY. Bunyaviruses: from transmission by arthropods to virus entry into the mammalian host first-target cells. Future Virol. 2015;10(7):859–881

    2015

  32. [32]

    phymcmc: A convenient wrapper for emcee; 2019

    Beauchemin CAA. phymcmc: A convenient wrapper for emcee; 2019. https://github.com/cbeauc/phymcmc. June 23, 2026 26/26

    2019