Ascaris egg viability as a rate process

Chapter 2 exposed Ascaris suum eggs to every reagent used in helminth test methods, for a set of exposure times, then incubated 28 days at 25–27 °C and scored the developmental outcome. Chapter 3 varied the mechanical handling — washing mode, centrifuge speed and time, flotation density — and scored recovery. Together these are a chemical stress series and a mechanical stress series on the same organism.

The developmental chain

The thesis stages development explicitly: one-cell, two-cell, four-cell, eight-cell, sixteen-cell, morula, blastula, gastrula, then the larval egg. Scoring collapses that chain into four potentially-viable categories and three non-viable ones.

Non-viable outcomes — dead, necrotic, infertile — sit off this chain. That structure is exactly a sequential reaction with a competing death pathway, which is why a chemical-engineering treatment is natural rather than imported.

The four chemical experiments

Replication is n = 5 throughout, with a stock of roughly 300 eggs per mL and 1 mL spiked per tube. Those denominators are large enough to support count-based likelihood rather than percentage-based ANOVA.

The thesis reduces each treatment to two numbers: potential viability, scored immediately, and actual viability, scored after incubation. Both are scalars, and a scalar cannot distinguish two quite different things a reagent might do.

• Killing. A fraction of eggs is destroyed outright. The survivors develop at the normal rate and reach the larval stage on schedule.
• Retardation. Nothing is killed, but development is slowed, so at the 28-day count many eggs are still part-way along the chain.

Both reduce actual viability. Tuned to give the same actual viability, they are indistinguishable on that metric — but they produce completely different stage profiles, and Danica already counts the stages.

Why potential viability looked flat

Across all eight wash solutions and all five exposure times, potential viability sat between 81 and 90%. That near-invariance is not a null result — it is a statement about the assay. Immediately after exposure, an undamaged egg and a lethally damaged one are morphologically identical, so potential viability mostly reports the stock's infertile fraction. The 28-day incubation is the step that resolves damage. Potential and actual viability are therefore not two competing metrics but two observation points on one consecutive process:

Modelling the pair as a series reaction extracts k₁ and k₂ separately, and the gap between the two viability measures becomes the quantity being measured rather than a discrepancy to be explained.

The thesis notes "inconsistent fluctuations in actual viability across exposure times" and attributes them to contamination and consequent egg damage. Taking that observation seriously, rather than treating it as a caveat, produces two findings.

Finding one: the time axis contains an artefact

Pooling all eight reagents, mean actual viability by exposure time runs:

Finding two: the reagent ranking may be measuring the wrong property

Grouping by the antimicrobial action the thesis itself identifies:

The two antimicrobial reagents have coefficients of variation of 4.7 and 10.8%. The other six span 26.4 to 58.2%. The groups do not overlap, with a factor of 2.4 between them at the boundary.

A per-tube contamination hazard drawn from a gamma distribution reproduces the observed error structure — roughly 32 ± 18% actual viability across tubes — from a single underlying treatment effect. That variance belongs in the model as a random effect. Left in the residual, it masks the kinetics we are trying to measure.

To model mechanical stress we first need the egg as an object. Taking the thesis's own figure of specific gravity 1.13 and an ellipsoid of roughly 60 × 45 × 45 µm gives an equivalent-volume sphere of 49.5 µm.

The rotor radius can be recovered from the thesis's own numbers: 2500 rpm quoted as 1050 × g and 3000 rpm as 1512 × g both imply r = 150.3 mm. The two independent statements agree exactly, so the stated conditions are internally consistent and can be used as given.

Egg density is the least certain input and it matters: across the reported helminth range of 1.05 to 1.27, the settling velocity varies from 76 to 285 mm/s and the shear stress from 4.6 to 17.3 Pa. Measuring egg density properly is a cheap experiment with high leverage over everything downstream.

Recovery is a separation problem, and speed and time are one variable

Chapter 3 reports that centrifugation time significantly affected recovery (P < 0.001) while speed alone did not (P = 0.540). Read as separation engineering, that is not two findings but one. Capture in a tube centrifuge scales with the group ω²rt. Across the tested range, speed contributes a factor of 1.44 in ω² while time contributes a factor of 3, so time simply spans more of the same variable.

But free settling cannot explain the time dependence at all

In a centrifugal field the settling velocity is proportional to radius, so the particle position grows exponentially and the transit time follows in closed form. For this egg in water:

An egg in clean water pellets in well under a second. Spins of 5, 10 and 15 minutes are therefore three to four orders of magnitude longer than free settling requires, and the observed dependence of recovery on spin time cannot be egg sedimentation. It must be matrix-controlled: hindered settling in a concentrated suspension, consolidation of the pellet, or entrapment and release of eggs within the solids. That is the real design variable, and a speed–time factorial in clean suspension does not probe it.

Where the mechanical stress actually is

Three candidate stresses, with very different magnitudes and durations:

The literature is broadly consistent with this: we found no published demonstration of shear inactivation of Ascaris eggs, and the nearest analogue studies attribute viability loss during processing to reagent chemistry. Two caveats are worth carrying, though, and both cut against a confident null. Brownell and Nelson report that stirring alone inactivated around 20% of eggs over 75 minutes in their UV work — a mechanical effect at very modest energy input, unexplained and worth pursuing. And Thomas and colleagues published on temperature and shear stress together in this context; we have not yet read it. Neither overturns the calculation, but both suggest the mechanical question is more open than the stress numbers alone imply — which is an argument for the pellet and resuspension experiments rather than against them.

The same particle mechanics answers the environmental question, and connects this work directly to the eThekwini river monitoring programme.

The egg never feels an eddy

Whether a particle experiences turbulent buffeting or smooth viscous shear depends on its size relative to the Kolmogorov microscale.

The Kolmogorov scale stays at or above 56 µm throughout, so a 50 µm egg sits inside the viscous subrange in every realistic river. It is carried in smooth shear, not struck by eddies. The centrifuge imposes roughly 300 times the river stress — but as established above, both are far below anything that threatens a shelled egg.

Eggs travel as washload

The Rouse number compares settling velocity to turbulent lifting. With a gravitational settling velocity of 0.175 mm/s — an egg needs about 1.6 hours to fall through a metre of still water — the Rouse number is 0.004 to 0.085 across any plausible flow, far below the 0.8 threshold for washload.

Three families of rate expression are in use, and the third is the one this work sits inside. All references below were verified against Crossref; where a journal has not deposited an abstract we describe the paper's scope but quote no numbers from it.

The disinfection family

Developed for chemical disinfectants, these carry a concentration term explicitly, which makes them the natural starting point for reagent exposure.

For Danica's data the Hom form is attractive because the flotation and extraction experiments vary concentration through specific gravity, and the formalin incubation series varies it directly at 0.5, 2 and 5%.

The non-log-linear survival family

From thermal food microbiology, where log-linear kill was found to be the exception rather than the rule.

Geeraerd's structural model adds an explicit shoulder length and a residual population floor, and was framed specifically around what a mechanistic model of mild heat treatment must contain. Peleg and Cole's reinterpretation is the conceptual key: a survival curve is the cumulative distribution of the population's resistance, not the trace of a chemical reaction. That framing matters here, as set out below.

The Ascaris-specific literature

This is a small and coherent body of work, dominated by ammonia and temperature.

The temperature literature, and a discrepancy worth a paragraph

Thermal inactivation is the best-quantified route. Harroff and colleagues report first-order rate constants with standard errors from 36 to 45 °C in both aerobic and anaerobic conditions — rising from 0.147 d⁻¹ at 37 °C to 4.71 d⁻¹ at 45 °C. Regressing those against inverse temperature gives an apparent activation energy of roughly 365 kJ/mol over 37–45 °C, equivalent to a z-value near 5 °C, and consistent with protein denaturation as the underlying mechanism.

On the other variables the literature has converged, and the conclusion is useful because it is negative. Senecal and colleagues found no effect on egg viability from pH 10.5 to 12.5 at 27.5 °C or below over more than seventy days; Pecson and Nelson found no pH effect in the absence of ammonia; and Fidjeland's model selection found that pH, carbonate, dry matter and matrix were all statistically significant but practically negligible once free ammonia and temperature were accounted for. Alkaline pH is not itself an inactivating agent for Ascaris — it acts by shifting ammonium to free ammonia. A two-variable model in NH₃ and temperature is defensible on evidence rather than merely on parsimony.

Two published datasets exist that have never been modelled

These matter because they let a stage-structured model be validated against independent data before Danica's own counts are touched.

Both have only ever been described narratively. Fitting a chain model to them is a self-contained piece of work that establishes the method before it is applied to new data, and the chain length is identifiable directly from the stage occupancies — a claim no existing Ascaris model can make.

One last gap worth recording: egg density rests on a single 1982 measurement, and no direct stiffness measurement of the eggshell appears in the indexed literature, so the shell modulus in the pellet-contact calculation remains an assumed range.

A stage-structured population balance, fitted to counts rather than percentages.

Stress enters through two distinct routes, which is the whole point of separating them:

• Fit by multinomial likelihood. The readout is counts across seven mutually exclusive categories from a finite number of eggs examined. That is a multinomial observation, and fitting it as one uses every counted egg instead of collapsing to a single percentage.
• Contamination as a random effect. A per-tube hazard, not a residual, for the reasons set out in section 3.
• One-step fitting. When the temperature series exists, embed the Arrhenius term and fit all conditions simultaneously rather than fitting constants per condition and regressing those. Re-centre on a reference temperature so that the pre-exponential factor and the activation energy are not almost perfectly correlated.
• Discriminate on AICc, with confidence intervals from profile likelihood or a bootstrap over the five replicates. R² is not a model-selection statistic for non-linear models.

Two known traps are worth naming now. Separating stage-transition rates from stage-specific mortality is a classic identifiability problem in stage-structured populations, and it bites hardest when the absorbing dead state is only observed in aggregate — which is our situation, since dead, necrotic and infertile are scored but the stage at which death occurred is not. Recording the developmental stage of dead eggs, where morphology still permits it, would substantially strengthen identifiability at no extra cost. Second, if the eventual aim includes fluctuating temperature, the model must be integrated as an ODE system rather than evaluated in closed form; the shoulder-and-tail structural models handle this correctly whereas the empirical time-exponent forms do not.

Three tiers, in increasing cost. The first needs no laboratory work at all.

Tier A depends almost entirely on what was recorded. These are the things that decide what is possible.

All DOIs below were resolved through Crossref. Items marked with a dagger had no abstract deposited, so their scope is described from title and bibliographic record only and no numerical values are quoted from them here.

1. Cerf, O. (1977). A review: tailing of survival curves of bacterial spores. Journal of Applied Bacteriology 42. 10.1111/j.1365-2672.1977.tb00665.x
2. David, E. D. & Lindquist, W. D. (1982). Determination of the specific gravity of certain helminth eggs using sucrose density gradient centrifugation. Journal of Parasitology 68:916. 10.2307/3281005 † — the source of the 1.13 specific gravity used throughout section 4.
3. Fidjeland, J., Nordin, A., Pecson, B. M., Nelson, K. L. & Vinnerås, B. (2015). Modeling the inactivation of Ascaris eggs as a function of ammonia concentration and temperature. Water Research 83:153–160. 10.1016/j.watres.2015.06.030 † (see also the 2016 corrigendum, 10.1016/j.watres.2016.02.019)
4. Fidjeland, J., Nordin, A. & Vinnerås, B. (2016). Inactivation of Ascaris eggs and Salmonella spp. in fecal sludge by treatment with urea and ammonia solution. Journal of Water, Sanitation and Hygiene for Development 6. 10.2166/washdev.2016.017
5. Geeraerd, A. H., Herremans, C. H. & Van Impe, J. F. (2000). Structural model requirements to describe microbial inactivation during a mild heat treatment. International Journal of Food Microbiology 59:185–209. 10.1016/S0168-1605(00)00362-7 †
6. Hom, L. W. (1972). Kinetics of chlorine disinfection in an ecosystem. Journal of the Sanitary Engineering Division. 10.1061/JSEDAI.0001370 †
7. Mafart, P., Couvert, O., Gaillard, S. & Leguerinel, I. (2002). On calculating sterility in thermal preservation methods: application of the Weibull frequency distribution model. International Journal of Food Microbiology 72:107–113. 10.1016/S0168-1605(01)00624-9 †
8. Naidoo, D. & Archer, C. E. (2024). Ascaris suum egg recovery from sludge samples after phase extraction. Journal of Parasitology 110. 10.1645/22-57 † — Chapter 4 of the thesis, published.
9. Naidoo, D. & Septien, S. (2019). Drying of faecal sludge: helminth inactivation by drying for the purposes of thermal process design. FSM5 workshop. 10.21955/gatesopenres.1115721.1
10. Nordin, A., Nyberg, K. & Vinnerås, B. (2009). Inactivation of Ascaris eggs in source-separated urine and feces by ammonia at ambient temperatures. Applied and Environmental Microbiology 75:662–667. 10.1128/AEM.01250-08
11. Paulsrud, B., Gjerde, B. & Lundar, A. (2004). Full scale validation of helminth ova (Ascaris suum) inactivation by different sludge treatment processes. Water Science and Technology 49:139–146. 10.2166/wst.2004.0628
12. Pecson, B. M., Barrios, J. A., Jiménez, B. E. & Nelson, K. L. (2007). The effects of temperature, pH, and ammonia concentration on the inactivation of Ascaris eggs in sewage sludge. Water Research 41:2893–2902. 10.1016/j.watres.2007.03.040 †
13. Peleg, M. & Cole, M. B. (1998). Reinterpretation of microbial survival curves. Critical Reviews in Food Science and Nutrition 38. 10.1080/10408699891274246
14. Sengupta, M. E., Thamsborg, S. M., Andersen, T. J., Olsen, A. & Dalsgaard, A. (2011). Sedimentation of helminth eggs in water. Water Research 45:4651–4660. 10.1016/j.watres.2011.06.017 † — the calibration reference for measured settling velocities in section 4.

Thermal inactivation and the activation-energy question

1. Harroff, L. A., Liotta, J. L., Bowman, D. D. & Angenent, L. T. (2019). Inactivation of Ascaris eggs in anaerobic digestion. Water Research X 5:100036. 10.1016/j.wroa.2019.100036 — rate constants with standard errors, 36–45 °C, aerobic and anaerobic; the source of the ~365 kJ/mol figure derived in section 7.
2. Popat, S. C., Yates, M. V. & Deshusses, M. A. (2010). Kinetics of inactivation of indicator pathogens during thermophilic anaerobic digestion. Water Research 44:5965–5972. 10.1016/j.watres.2010.07.045 — the only published E_a for A. suum, 105 kJ/mol over 51–56 °C.
3. Naidoo, D., Archer, C. E., Septien, S., Appleton, C. C. & Buckley, C. A. (2020). Inactivation of Ascaris suum eggs by heat and desiccation. Journal of Water, Sanitation and Hygiene for Development 10:209–218. 10.2166/washdev.2020.119 — 40–80 °C across moisture levels; analysed by ANOVA, no kinetic model fitted.
4. Naidoo, D. & Foutch, G. L. (2017). Inactivation of Ascaris eggs at elevated temperatures. Journal of Water, Sanitation and Hygiene for Development 8:123–126. 10.2166/washdev.2017.102 — 60–80 °C at short times; notes that below 45 °C a new relationship is needed.
5. Senecal, J., Nordin, A. & Vinnerås, B. (2020). Fate of Ascaris at various pH, temperature and moisture levels. Journal of Water and Health 18:375–382. 10.2166/wh.2020.264 — the negative result on alkaline pH.
6. Pecson, B. M. & Nelson, K. L. (2005). Inactivation of Ascaris suum eggs by ammonia. Environmental Science & Technology 39:7909–7914. 10.1021/es050659a — pH has no effect in the absence of ammonia.
7. Maya, C., Torner-Morales, F. J., Lucario, E. S., Hernández, E. & Jiménez, B. (2012). Viability of six species of larval and non-larval helminth eggs for different conditions of temperature, pH and dryness. Water Research 46:4770–4782. 10.1016/j.watres.2012.06.014 — one of the few papers to state that developmental stage must be taken into account.
8. Musaazi, I., McLoughlin, S., Murphy, H. M., Rose, J. B., Hofstra, N., Tumwebaze, I. K. & Verbyla, M. E. (2023). Modelling pathogen decay in onsite sanitation systems. Water Research X 18:100171. 10.1016/j.wroa.2023.100171 — meta-analysis; shouldering outperformed log-linear for Ascaris in 15 of 18 experiments.
9. Brownell, S. A. & Nelson, K. L. (2006). Inactivation of single-celled Ascaris suum eggs by low-pressure UV radiation. Applied and Environmental Microbiology 72:2178–2184. 10.1128/AEM.72.3.2178-2184.2006 — also the source of the unexplained stirring effect noted in section 5.

Stage-structured development: the datasets and the formalism

1. Cruz, L. M., Allanson, M., Kwa, B., Azizan, A. & Izurieta, R. (2012). Morphological changes of Ascaris spp. eggs during their development outside the host. Journal of Parasitology 98:63–68. 10.1645/GE-2821.1 — twelve stages, daily, 28 °C; cited in the thesis.
2. Kim, M. K., Pyo, K. H., Hwang, Y. S., Park, K. H., Hwang, I. G., Chai, J. Y. & Shin, E. H. (2012). Effect of temperature on embryonation of Ascaris suum eggs in an environmental chamber. Korean Journal of Parasitology 50:239–242. 10.3347/kjp.2012.50.3.239 — the only temperature-resolved stage-profile dataset; open access.
3. Cooper, A. J. & Hollingsworth, T. D. (2018). The impact of seasonality on the dynamics and control of Ascaris lumbricoides infections. Journal of Theoretical Biology 453:96–107. 10.1016/j.jtbi.2018.05.025 — the one model with an explicit egg compartment, and the one to position against.
4. Hurtado, P. J. & Richards, C. (2021). Building mean field ODE models using the generalized linear chain trick. Journal of Biological Dynamics 15(sup1):S248–S272. 10.1080/17513758.2021.1912418 — the formal basis for the chain used in section 8.
5. Rossini, L., Contarini, M., Severini, M. & Speranza, S. (2020). Reformulation of the distributed delay model to describe insect pest populations using count variables. Ecological Modelling 436:109286. 10.1016/j.ecolmodel.2020.109286 † — the closest published match to fitting stage counts.
6. Nisbet, R. M. & Gurney, W. S. C. (1983). The systematic formulation of population models for insects with dynamically varying instar duration. Theoretical Population Biology 23:114–135. 10.1016/0040-5809(83)90008-4 † — stage duration varying with an environmental driver.
7. Truscott, J. E., Hollingsworth, T. D., Brooker, S. J. & Anderson, R. M. (2014). Can chemotherapy alone eliminate the transmission of soil transmitted helminths? Parasites & Vectors 7:266. 10.1186/1756-3305-7-266 — states the single-reservoir convention, and so the gap.

Supporting hydrodynamics and cell-damage literature

1. Born, C., Zhang, Z., Al-Rubeai, M. & Thomas, C. R. (1992). Estimation of disruption of animal cells by laminar shear stress. Biotechnology and Bioengineering 40. 10.1002/bit.260400903 — the 600 Pa lysis benchmark in Figure 2.
2. Cherry, R. S. & Papoutsakis, E. T. (1988). Physical mechanisms of cell damage in microcarrier cell culture bioreactors. Biotechnology and Bioengineering 32:1001–1014. 10.1002/bit.260320808 — separates eddy, collision and wall mechanisms.
3. Croughan, M. S., Hamel, J.-F. & Wang, D. I. C. (1987). Hydrodynamic effects on animal cells grown in microcarrier cultures. Biotechnology and Bioengineering 29:130–141. 10.1002/bit.260290117 — the Kolmogorov-scale criterion used in section 6.
4. Ma, N., Koelling, K. W. & Chalmers, J. J. (2002). Fabrication and use of a transient contractional flow device to quantify the sensitivity of mammalian and insect cells to hydrodynamic forces. Biotechnology and Bioengineering 80. 10.1002/bit.10387 — cell tolerance of 10⁷–10⁸ W/m³.
5. Shenkman, R. M., Godoy-Silva, R., Papas, K. K. & Chalmers, J. J. (2009). Effects of energy dissipation rate on islets of Langerhans. Biotechnology and Bioengineering 103. 10.1002/bit.22241 — the nearest size-matched damage threshold.
6. Amoah, I. D., Reddy, P. & Stenström, T. A. (2017). Effect of reagents used during detection and quantification of Ascaris suum in environmental samples on egg viability. Water Science and Technology 76:2389–2400. 10.2166/wst.2017.324 — the closest analogue to Chapter 2, and cited in the thesis.
7. Nezu, I. & Nakagawa, H. Turbulence in Open-Channel Flows. 10.1201/9780203734902 † — source of the open-channel dissipation relations in section 6.