10  Chapter 10 — Vaccines, R₀ and Herd Immunity

Applied Epidemiology in Aquaculture — Part IV: Interventions

Where this sits — Prevent (primary prevention). Vaccination is the flagship Prevent tool. This chapter measures whether a vaccine works in the field, how fast disease would spread without it (R₀), how much immunity it takes to stop transmission, and — new in this book — whether vaccinating pays.

10.1 Overview

A vaccine that works in a challenge tank may barely move mortality on a farm. This chapter separates efficacy (ideal conditions) from effectiveness (field conditions), measures effectiveness two ways (risk and time-to-event), then asks the population question: given how contagious SRS is, can vaccination alone stop it? The answer — built from your own in-review transmission work — is a resounding not on its own, and it reframes vaccination as one layer among several. We finish with a cost-effectiveness model, because “does it work?” and “is it worth it?” are different questions.

We use srs_vaccine.csv: 60 cages, half vaccinated, with cumulative SRS mortality and time to first outbreak.

10.2 10.1 Preparation

pacman::p_load(rio, here, tidyverse, survival)
vac <- import(here("data", "srs_vaccine.csv"))

10.3 10.2 Vaccine effectiveness from risk

Efficacy is the protection seen in a controlled trial; effectiveness is what you get in the water, where timing, handling, co-infections and strain mismatch all erode it. Effectiveness is one minus the relative risk of disease in vaccinated vs unvaccinated animals:

VE = 1 − RR

vac |>
  group_by(vaccinated) |>
  summarise(deaths = sum(srs_deaths), fish = sum(n_at_risk)) |>
  mutate(risk = deaths / fish)
# vaccinated   7.69% ;  unvaccinated 10.87%
RR <- 0.0769 / 0.1087          # 0.71
VE <- 1 - RR                   # 0.29

So field VE is 29% — squarely in the 22–32% range reported for injectable SRS vaccines (Rozas-Serri, 2026; and the vaccine field studies synthesised in Diethelm-Varela et al., in press). That is real but modest: vaccination here prevents under a third of SRS deaths.

10.4 10.3 Vaccine effectiveness from time-to-event

Mortality risk hides when disease strikes. Survival analysis uses the whole follow-up, handling cages that never had an outbreak (censored). The Kaplan–Meier curve and Cox model compare time to first outbreak:

sf <- survfit(Surv(time_to_outbreak, outbreak) ~ vaccinated, data = vac)
summary(sf)$table[, "median"]        # unvaccinated 11.5 wk ; vaccinated 47 wk
coxph(Surv(time_to_outbreak, outbreak) ~ vaccinated, data = vac)
#   HR (vaccinated vs unvaccinated) = 0.25 (95% CI 0.13–0.47), p < 0.001

The hazard ratio of 0.25 says vaccinated cages have a quarter of the weekly risk of starting an outbreak — and the median onset slips from 11.5 to 47 weeks. This is the key practical value of a modest vaccine: it may not prevent SRS, but it delays the first outbreak, and delaying the first outbreak matters because later outbreaks in a cycle are deadlier (Diethelm-Varela et al., 2025). This is exactly the analysis the national SRS studies used (logistic regression plus Cox models; Jakob and Happold, in Diethelm-Varela et al., in press).

10.5 10.4 How fast does SRS spread? R₀ and herd immunity

To know whether vaccination can ever stop transmission, we need R₀ — the average number of new infections one infected fish causes in a fully susceptible population. A systematic review and meta-analysis of 24 cohabitation trials estimated R₀ for P. salmonis at 4.22 (95% CI 3.64–4.89), with a ~20-day serial interval and a 4-day doubling time (Mardones, Córdova-Bührle, Diethelm-Varela et al., in review).

From R₀ comes the herd-immunity threshold — the fraction that must be immune to push the effective R below 1 and halt spread:

HIT = 1 − 1/R₀ = 1 − 1/4.22 = 76%

R0  <- 4.22
HIT <- 1 - 1/R0        # 0.76

Three-quarters of the population must be immune. That is achievable with a good vaccine — but ours only protects 29%.

10.6 10.5 The stark arithmetic of critical coverage

Immunity achieved by vaccination is coverage × effectiveness, so the critical vaccination coverage needed to reach the herd-immunity threshold is:

Vc = HIT / VE

HIT / 0.29     # 2.61  -> 261%, impossible
HIT / 0.75     # 1.02  -> 102%, still impossible
HIT / 1.00     # 0.76  -> 76%,  only a perfect vaccine could do it

🧮 Epivet Tools — Vaccine effectiveness, R₀ & herd immunity tools.epivet.cl/vaccine-herd — enter vaccinated/unvaccinated risk and R₀ for VE, the herd-immunity threshold and critical coverage (with an “impossible” flag).

At field effectiveness (29%), you would need to vaccinate 261% of the population — a physical impossibility. Even a 75%-effective vaccine falls just short at 102%. Only a perfect vaccine, applied to 76% of fish, could stop SRS transmission by vaccination alone. This is the single most important population-level fact about SRS control, and it follows directly from R₀ ≈ 4: vaccination must be combined with density management, biosecurity, lice control and early detection to bring the effective R down — no product does it alone (Mardones et al., in review).

Shrimp aside. Whiteleg shrimp have no adaptive immunity, so there is no AHPND vaccine at all. For Camarones del Golfo, the entire “Prevent” budget goes to biosecurity and post-larvae screening — which is why AHPND control is a Detect-and-Prevent problem, not a vaccination one.

10.7 10.6 Does vaccinating pay? A cost-effectiveness model

Effectiveness is not the same as value. A simple partial-budget model compares the cost of vaccinating against the mortality it averts, per cage:

N  <- 35000; VE <- 0.29; mort_unvacc <- 0.109
deaths_averted <- N * mort_unvacc * VE            # ~1,106 fish per cage
vacc_cost      <- N * 0.20                          # $0.20/dose -> $7,000
break_even     <- vacc_cost / deaths_averted        # $6.33 per averted death

Vaccinating a 35,000-fish cage averts about 1,106 deaths and costs ~$7,000, so it pays on mortality alone whenever a dead fish represents more than ~$6.33 of lost value — usually true from mid-cycle on. And this undervalues the vaccine, because it ignores two things it also buys: a large delay in outbreak onset (HR 0.25) and reduced antibiotic use (a Safeguard benefit, Chapter 11). A full cost-effectiveness analysis (the dampack/heemod tools, and an incremental cost-effectiveness ratio) would add those, and — crucially — run a sensitivity analysis, because the verdict flips with the price of a dose and the value of a fish.

10.8 10.7 Interpretation on the farm

The honest message for a Prevent programme: vaccinate, but do not expect vaccination to carry SRS control on its own. At R₀ ≈ 4 and 29% field effectiveness, its real contributions are delaying and softening outbreaks and cutting antibiotic use, not eradication. Its value is highest combined with the measures that also lower R — lower density, synchronised fallowing, lice control — which is precisely why this book frames prevention as layered defence rather than a single silver bullet.

10.9 10.8 Exercises

Try it yourself (10.1). Compute vaccine effectiveness from the cumulative mortality figures, then fit the Cox model and report the hazard ratio. Which measure better captures the vaccine’s benefit, and why?

10.2 Using HIT = 1 − 1/R₀, compute the herd-immunity threshold if R₀ were 2 instead of 4.22. Then compute the critical vaccination coverage for a 60%-effective vaccine. Is herd immunity reachable now?

10.3 Redo the cost-effectiveness model with a dose cost of $0.10 and a value per averted death of $9. What is the net benefit and the return on investment per cage?

10.4 Explain why a vaccine that prevents only 29% of deaths can still be worth using, citing both the hazard ratio and the Safeguard (antibiotic) argument.

10.10 Summary & what’s next

  • Effectiveness (field) < efficacy (ideal); VE = 1 − RR gave 29% here.
  • Survival analysis (Kaplan–Meier, Cox HR = 0.25) shows the vaccine’s real value: delaying the first outbreak from week 11.5 to week 47.
  • R₀ ≈ 4.22 → herd-immunity threshold 76%; with field VE, critical coverage exceeds 100%, so vaccination alone cannot stop SRS.
  • Vaccination is cost-effective under reasonable assumptions, but the verdict is assumption-sensitive and should include outbreak delay and antibiotic savings.

In Chapter 11 — Antibiotics and AMR Stewardship we move to Respond and Safeguard: measuring treatment effect, reading antibiograms and MICs, tracking resistance, and the stewardship that keeps treatment viable.

10.11 References & further reading

  • Mardones FO, Córdova-Bührle F, Diethelm-Varela B, et al. Transmission of P. salmonis: R₀ from a meta-analysis of cohabitation trials. In review.
  • Diethelm-Varela B, Atero N, Gelcich S, Gallardo A, Mardones FO. Field-based evidence on P. salmonis management: a systematic review. Reviews in Aquaculture, in press. — vaccine field-effectiveness evidence.
  • Diethelm-Varela B, et al., Mardones FO. Epidemiology of SRS. J Fish Dis. 2025;e70097. — later outbreaks are deadlier.
  • Rozas-Serri M. Salmonid rickettsial septicaemia: a review. Reviews in Aquaculture. 2026. — field vaccine effectiveness 22–32%.
  • Dohoo I, Martin W, Stryhn H. Veterinary Epidemiologic Research. 2nd ed. VER Inc.; 2009. — survival analysis.

Files for this chapter: data/srs_vaccine.csv and scripts/make_srs_vaccine.R (new).