Salmonella enteritidis infections in France and the United States: characterization by a deterministic model

Salmonella Enteritidis Infections inFrance and the United States:Characterization by a DeterministicModel

Laurence Watier, PhD, Sylvia Richardson, PhD, and Bruno Hubert, MD

IntroductionSalnwnella enteritidis infections are

a new and increasing public health prob-lem in most European countries and inNorth America.' Consumption of raw orinadequately cooked eggs has been foundto be the major source of infection.2 Somecountries, such as the United States, theUnited Kingdom, and France, have re-cently implemented control measures toidentify and slaughter flocks of infectedlaying birds. To evaluate the efficacy ofthese measures, two sources of informa-tion are available: notification of out-breaks and identification of Salmonellaisolates by a national reference center.

We propose a simple deterministiccompartmental model to analyze the dy-namic evolution of the total number of S.enteritidis isolates in a population, and weestimate this model on data from refer-ence centers in France and the UnitedStates. In this model, we distinguish onlytwo groups of individuals, susceptible andinfected, since S. enteritidis is not knownto confer any immunity.3 A time-depen-dent transition rate from susceptible to in-fected is modeled at first in terms of botha baseline transmission rate (Io) from theanimal reservoir to humans and a seasonalmultiplicative factor.

Such a model can help to achieve sev-eral public health objectives. Firstly, the es-timation of P3o for different time periods en-ables us to quantify the increase in cases ofS. enter,iidis observed in recentyears and tocompare the epidemic's development be-tween countries. We show comparative re-sults between France and the Middle Atlan-tic region of the United States.

Secondly, time components in themodeling of the transition rate from sus-ceptible to infected can also be included to

test if the time structure of potential envi-ronmental sources of contamination is re-

flected in the evolution of the indicator.Investigations in France from 1989 to 1990showed that 52% of S. enteritidis out-breaks associated with eggs were due tofree-range eggs from small holdings thatwere noncommercially distributed.4Thus, we included in the transition rate anindicator of the seasonal time pattem ofegg laying of free-range hens.

Finally, model predictions were cal-culated to measure the impact of preven-tive measures taken in France since May1989 and in the United States since Feb-ruary 1990.5

Material and MethodsData

France. The data used in this studycome from the National Salnonella Refer-ence Center at the Pasteur Institute. Thiscenter receives Salmonella isolates fromprivate or public laboratories for serotyp-ing. Monthly notifications of identified S.enteritidis isolates are available dating fromJanuary 1978. The period analyzed in-cludes 156 months of observations fromJanuary 1978 to December 1990. In addi-tion, quarterly data on the number of iso-lates identified in laboratories other thanthe National Reference Center are alsoavailable and are used to check the stabilityof the distribution of isolates between thecenter and other laboratories.

Laurence Watier and Sylvia Richardson arewith the Institut National de la Sante et de laRecherche Medicale, Villejuif, France. BrunoHubert is with the Reseau National de SantePublique, Saint Maurice, France.

Requests for reprints should be sent toLaurence Watier, PhD, Inserm Unite 170, 16,av Paul Vaillant Couturier, 94807 Villejuif, Ce-dex, France.

This paper was accepted June 29, 1993.Editor's Note. See related annotation by

Halloran (p 1667) in this issue.

December 1993, Vol. 83, No. 12

Sabmoneaa Entrdi

Up until the end of 1988, the numberofSabnonella isolates other thanS. enter-iidis and S. tphimwiwn was fairly con-stant (Figure 1); consequently, the ob-served increase in the number of S.entetidis isolates in 1987 and 1988 (Fig-ure 2) probably corresponds to a real in-crease in the incidence rather than to im-proved reporting. The mean-range plotconfirms that the years 1987 and 1988stand out (Figure 3). However, because ofmedia coverage and some reorganizationof laboratory analysis practices, twosources of bias were introduced. First,higher awareness of the dangers of Sal-monella infections is reflected in a 16%increase in the yearly total of Salmonellaisolates of all serotypes other than S. en-te?td and S. tphimwiuin Second, it isknown that in 1989, laboratories outsidethe National Reference Center started toequip themselves with antisera to be ableto identify S. enteitid. Indeed, for eachyear from 1978 to 1988, the center identi-fied apprmately 78% of all reported S.entildiv isolates. The situation changedin 1989, however, and this proportion de-creased to74% and47% for 1989 and 1990,respectively. Hence, model estimation isbased on reference center data only upuntil the end of 1988. Yearly predictionsfor 1989 and 1990 are compared with ob-served yearly numbers after allowing forsome bias corrections.

United States. The data analyzedcome from the Centers for Disease Con-trol and Prevention in Atlanta and areavailable for the period 1968 to 1990. Thedata are based on a passive laboratory-based Sabnonella surveillance activity.The number of cases reported was foundto represent from 1% to 5% of the realincidence of this infection.6 Ihe MiddleAtlantic region of the United States wasselected for analysis to maximize compa-rability with France data, given that sim-ilar climatic conditions prevail in both re-gions. The increase of reported casesstarted in 1984, providing a long stable pe-riod (Figures 3 and 4).

As in France, the system has inherentbiases. However, Hargrett-Bean et al.7judged the data to be of sufficiently ghquality to allow some insight as to the ef-fectiveness of public health intervention.

The CompartmentalSusceptible-Infected Model

Person-to-person contact is consid-ered of little importance in Sabnonellatnision in contrast to classical infec-tious disease models.8 Mostnew cases arerelated to the animal reservoir through

foodstuffcontamination. The dynamic ev-

olution of Sabnonella infections is ana-

lyzed using a simple deterministic com-

partmental model. The population isdivided into subgroups, the susceptiblesand the infectds, and the flows betweenthese two subgroups per unit of time are

expressed. The model can be representedschematically as follows:

f(t)- ->

I NS(t) I-Y

where S(t) denotes the proportion of in-dividuals not infected but sus-ceptible to contract S. entei-

idis infection at time t;

American Journal of Public Health 1695

5000.sow

4000

36000-20001000-.

78 79 80 81 82 83 4 85 86 37 so 89 90Yea

9The valu for 1989 and 1990 are obtined after allwing for a 16% medbtic incrae.

FIGURE 1-Ye_aly nber of Iokae of Samixnlb In FranxW: all peexceS. NWhand S.antedtlI

Nb of identified cases

4001

3001 Observed values

I- -- One step ahead forecasts

100- 1

JAN78 JAN80 JAN82 JAN84 JAN86 JAN88

Date

5The values or ding to July, August, SepWnber, and Ocober 1984 have been cor-rededbu ey mistkenly incuded some oubrk cases.

bMaOe includes a basene traission rats (s), a seasonal fct (1), and a seasnaisWng effect (N2.

FIGURE 2-Co aron of th o ed value and fitte val of model 2b for S.entedU--- In Franoo fom 1978 to 1968.

December 1993, Vol. 83, No. 12

300-

2SO-

200-

150-R

100-

50.

1987 a 1988 ..

600X

400

to

00 25 50 75 100 125 150

M (Frnc)

' 1989

*19901988

1986.a- 1987

a 1984 a 1985

Dr1. .-:t . I

100 200 300 400

M (United Sta8es)aThe plot of the range against the mean for each seasonal period.

FIGURE 3 plt: mean and range for yealy £ endt In France from1978 to 1988 and In the Middl AUantlc reglan of the United Statua from1968 to 1990.

I(t) denotes the proportion of in-dividuals infected with S. en-teritdis at time t;

Nis the total population size, as-

sumed to be constant; andf(t) andy are the flows per unit of

time between the two sub-groups.

Note that NI(t) represents the numberof cases of the disease at time t.

The following hypotheses are madethroughout:

1. Susceptible individuals become in-fected per unit of time at a rate f(t),which represents a contact between in-dividuals and contaminated foods; and

2. Infected individuals recover andbecomesusceptble at a constant rate y, with l/y

representing the mean infection time.

Assuming a constant population size,these hypotheses lead to linear differentialequations for S(t) or I(t), which can beeasily solved (see Appendix).

Two models are proposed for thetransmission rate f(t). Salmonella multi-plication is facilitated by a temperature of20°C or higher, which explains the in-creased incidence ofinfection during sum-mer months. Thus,

f(t)= o 1 + 1 sin 12 (Model 1),

where 13o is a baseline transmission ratefrom the animal reservoir to humans and13 is a multiplicative seasonal effect ofperiod 12 (Figure 5).

Investigations in France have tendedto incriminate noncommercially distrib-uted free-range eggs from small holdings,even though this category of eggs ac-counts for only 20%o of French produc-tion.4 Cimatic conditions between No-vember and April lead to an interruptionof laying in nonindustrial free-range hens.This suggests a second model, including afurther time component in the tnsmis-sion ratef(t):

/ 2irtf(t)=3o1 +1P sin - +13g(t)\ ~~12/

(Model 2),

whereg(t) is a periodic indicator functionof the laying period and is equal to 1 be-tween April and October, inclusively. Theparameter 2 is referred to as a seasonallaying effect (Figure 6).

EstimatonTo be able to estimate No0, 13, and,

in some cases, N12 for fitting model 1 or2 to the observed values of the number ofnew isolates 0(t) over a period [to, tl], itis necessary to suppose thatN1o, (3, andNP2 are constant over [to, tlJ. Clearly thisis a reasonable assumption in a stable sit-uation. In a situation in which an epi-demic is developing, the time intervalschosen will be relatively short (say ayear) so that this assumption holds ap-proximately.

In the fitting of model 1, two coeffi-cients-N1o and NC1-are estimatedwith C1 = o130 (see Appendix). To takeinto account possible time autocorrelationofthe regression residuals, the coefficientsN(3o and NC1 are estimated using a re-gression model with autocorrelated errors(procedure Autoreg ofSAS/ETS9) and thevalue of1 is deduced. To obtain the vani-ance of 1,which is a multiple of421/03, thedelta method is used. The fitting of model2 proceeds along similar lines.

1696 American Journal of Public Health

Wader et a.

WbIdiniMumdss

1000

500 O-aed V ai

Onedp _."bMG400

298

100

40 &

Ja8 Jan71 Jan74 Ja77 Juial Jan83 Jan86 Jlan90~ ~ ~ ~ ~ 0

'MoelIncuds a boan branemluaon rat (bU)and aaori ()

FIGURE4-Comparlsonfthe X dvah andtheOn-S-aedfrsecatifromthe finng of model 1 for S.w:dJdis In the Mddle AtlntIc reglan of theUnItd Sta from 198 to 1990.

I

i

December 1993, Vol. 83, No. 12

Sablonela En riidig

PredictionIn France, the stationary structure of

S. enteitdis infections, which prevailsuntil 1987, gives way to substantial in-creases in the following years (Figure 2).The US situation is similar, but the in-crease starts in 1984 (Figure 4). Underthese conditions, forecasting is possibleonly if one is prepared to model the in-crease; with our approach, this entails pre-dictingvalues ofN1o, I andNpi by pro-longing their observed trend.

Predictions are used as benchmarksto assess the impact of preventive mea-sures. The observed values for the yearsafter the start of the preventive measuresare compared with the forecasts.

RmdtQuantification ofthe Increase in theBaseline Transmission Rate inFrance

To confirm that the structure of thedatawas indeed perturbated in 1987, fore-casts for that year were obtained, basedon the previous observations. FromMarch 1987onward, the observed numberof isolates lies well above the one-sided95% upper confidence interval ofthe fore-casts built from the 1978 to 1986 period,indicating that a nonstationary pattern ofincrease started in March 1987. Model 1was thus estimated separately for the sta-ble period of 1978 to 1986 and thenyearbyyear to characterize the increase.

For the stable period, it was neces-sary to introduce autoregressive parame-ters at lags 1, 3, 8, 12, and 24. The auto-correlations at lags 1 and 3 reflect anexpected short-term correlation, whilethose at lags 8, 12, and 24 are related toresidual seasonality not accounted for bythe deterministic part of the model.

All model parameters are clearly sig-nificant (Table 1). The seasonal multipli-cative effect is fairly constant. On theother hand, there is a substantial increaseofthe baseline parameter o, which is firstmultiplied by 2.3 in 1987 and then by4.1 in1988. The sinusoidal shape of Nf(t) inmodel 1 is illustrated in Figure 5 for thestable period, with parameters chosen inaccordance with Table 1.

Quantfication of the Increase in theBaseline Transmission Rate in theUS Middle Atlank Region

The same compartmental model wasestimated separately for the stable period1968 to 1983 and then year by year. Forthe stable period, the residuals were mod-

eled with signficant autoregressive pa-

rameters at lags 1, 3, and 11.The parameterN% is clearly signifi-

cant over the eight periods (Table 2). Theincrease of seems to have diminished in

1990. For the stable period, the seasonalityis less marked than it was for the French

data, but the seasonal parameter , is

nonetheless significant. From 1984 on-

ward, the seasonal effect is strengthened.

American Journal of Public Health 1697December 1993, Vol. 83, No. 12

500__ L56%c

L. - |

1500

50

bt7S8 7Xi7 JostF iaa s M 4, ,in* Uo S a

OA43 and p ha been reqped by lhr setimated vlues (36.1 and -0.8,.

FIGURE 5-S.wWs In France from 1978 to 1986: tIme plot of N1(t), where f(t) Isthetm n cosponding to model I with is 95%c_nidne Iha

Nb ofidentified cases

200-

Observed valuesModel lSeasonal laying effectModel 2

150

1001

50'

JAN78 JAN80 JAN82 JAN84 JAN86

Date

a1, l,andam have be replaed by their estimated values (32.9, -0.9, and 6.1,resPebvely).

FIGURE 6-S. ntds In France from 1978 to 1986: IOme plot of NO(t), wher f(t) Isthe transmIsson rte c ponding to model 2 (t ter with it twocompo )

m

-Mi

Wader et dL

It is noteworthy that the ratios Ro,which characterize the pattem of increaseof 0, are very similar between Frenchand US data for the first 2 years of theepidemic. However, seasonal pattems aresomewhat different between the two re-gions, with France exhiibiting a more sta-ble seasonal pattem.

Linkng the Time Pattem of S.enteritidis Infection to That ofaSeasonal Laying Effect ofFree-Range Hens

In France, the involvement of flocksfrom small holdings in the epidemic can betested by using model 2. This model wasestimated on the stable period (with au-toregressive parameters for the residualsat lags 1, 3, 8, 12, and 24) and then sepa-rately in 1987 and 1988. All parameters areclearly significant except forN02, which isnonsignificant in 1987 and only marginalysignificant in 1988 (Table 3). The seasonalmultiplicative effect appears reasonablyconstant.

Comparison of Tables 1 and 3 showsthat there is a fairly linear increase of thebaseline parameter I3 for the years 1987and 1988 at a similar rate for both com-partmental models. As expected, the ad-dition ofa parameter in model 2 resulted ina smaller value for the baseline rate N3o.For the stable period, model 2 gives a sig-nificant improvement over model 1

(XI2 = 4.04, P = .04), and the seasonallaying effect parameterN12 is significant.In 1987, N,B2 is not significant, and thestandard error of , is increased. As seenin Figure 2, the increase in 1987 is ex-tremely brutal, and neither model 1 nor 2

fits well. On the other hand, Nfr2 is againsignificant in 1988. Overall, model 2 givesa reasonable fit.

To better visualize the two compo-nents ofmodel 2-the sinusoidal part cor-responding to model 1 and that relating tothe seasonal laying effect (g[t] in theappendix)-these components, as well astheir sum for the stable period, are repre-sented separately in Figure 6, with param-eters chosen in accordance with Table 3.

Model 2 gave a poorer fit than model1 for the stable period with the US data;consequently, the seasonal laying hypoth-esis does not seem appropriate for theUnited States.

Impact ofPreventive MeasuresFrance. Since May 1989, eggs from

flocks found to be infected have been di-verted to pasteurization plants or the flockhas been destroyed. In 1989, for example,eggs were diverted to pasteurizationplants for six flocks while three flocks

were destroyed. To try to combat theemergence of S. entetdi and reduce thenumber of infected birds, a working partycomposed of health officials and egg pro-ducers was set up. Specific recommenda-tions concerning hygiene and poultryhealth checks were made during 1990. Aconvention was signed between theFrench state and the egg producers,whereby the state will compensate theproducers for the eradiction of infectedflocks and will reimburse costs for bacte-riological analyses made in this context.

We have based our evaluation ofpre-ventive measures solely on the yearly to-tals for 1989 and 1990 since they can beglobally corrected for bias.

Yearly forecasts of infected cases (aswell as their standard errors) were com-puted with model 2with parameter valuesreplaced by their respective predictions.The parameter predictions were calcu-lated under the assumption that the linearincrease of the baseline rate observed for1987 and 1988 was continuing. Precisely,predictions for parametersNto, NC1, andN12 in 1989 and 1990 were obtained usingequations corresponding to weighted re-

gression of the estimated values of thoseparameters for three time periods: the sta-ble period, 1987, and 1988. As expected,the parameter Ih was stable for bothyears, and the standard errors ofN,O andNp2 increased between 1989 and 1990.

December 1993, Vol. 83, No. 121698 American Journal of Public Health

Salmonella Ente,its

The observed and bias-correctednumbers of isolates in the National Ref-erence Center for 1989 and 1990 are givenin Table 4. The bias-corrected figureswereobtained after first allowing for a 16% in-crease in the total number of isolates ob-served (National Reference Center andlaboratories) and then taking 78% of theseisolates (see "Material and Methods"above).

In 1989, the bias-corrected numberofisolates was higher than the predictedlevel, assuming a linear increase, and wasclose to the latter's upper 95% confidenceinterval. This seems to indicate that S. en-tetids contamination was accelerating.However, this acceleration did not appearto continue in 1990, as the predicted totalwas nearly identical to the bias-correctedvalue for that year. This points to a limitedimpact of preventive measures, but thereis no evidence that the linear rate of in-crease was diminishing.

United States. In the United States, avoluntary state quality assurance programfor S. enteritidis in flocks was imple-mented in February 1990.5 Forecasts ofNpo were calculated for the year 1990 un-der the assumption of a linear increase inthe baseline parameter (Table 5). In 1990the estimated value of NoO is below thelower 95% confidence interval for the pre-dicted N,o, and there is little overlap be-tween their respective 95% confidence in-tervals. This indicates a potential effect ofthe preventive measures.

DiscusionThe value of the model used here,

which relies on strongly simplifying hy-potheses, is that it summarizes the ob-served phenomenon with some easilyinterpretable parameters. A time periodi-cal function similar to ours has been usedin a measles transmission study.10 By at-tempting to represent the underlyingphenomenon, deterministic models leadto predictions that are based on explicithypotheses. An alternative way to makepredictions would be to use time seriesmodeling, as was done for Salmonella bo-vismorbificans.1l However, this purelystatistical approach was found to perfornless satisfactorily, and it permits neithertime effects such as seasonal laying to betested nor comparison with other datasources to be made.

Since the French data were reportedthrough a system of passive surveillance,they represent only a fraction of all Sal-monella infections. This surveillance sys-tem is understandably sensitive to any

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these flocks' rearing conditions ensure anuninterrupted laying throughout the yearsimilar to industrial laying. The S. ente.-tii increase could be due to the impor-tation of infected birds, which are mainlyintroduced into nonindustrial flocks.From 1987, diversification of strains ofhens corresponding to an increase in im-ports from other European countries wasobserved. Nevertheless, it is important topoint out that, in common with any sea-sonal effect, this seasonal laying effectcould be interpreted as a summer ampli-tude correction independent of a directlink with hen laying. It would thus be in-teresting to see whether this particulartime pattern is also present in the structureof indicators of S. entetitidis infections inother countries where, as in France, free-range hens in small holdings contribute tosome extent to the egg production. Ol

AcknowledgentsThis studywas supported inpart by the FrenchMinistry of Health.

The authors wish to thank P. A. D. Gri-mont and P. Bouvet of the Pasteur Institute inParis for providing the French data, and R. V.Tauxe and N. Bean of the Centers for DiseaseControl and Prevention in Atlanta for providingthe US data. This article has benefited fromconstructive comments made by M. E. Hallo-ran and anonymous referees, whose help isgratefully acknowledged.

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December 1993, Vol. 83, No. 12 American Journal of Public Health 1699

Wade et aL

nellosis. JAMA 1988;14:2103-2107.3. MandellJL.Princ@lesandPracticesofIn-

fectious Diseases. New York, NY: JohnWiley and Sons; 1985.

4. Hubert B. Surveillance et prevention dessalmonelioses en France. MedMal Infect.1992;22(special issue):325-330.

5. Outbreak of Salmonella enteris infec-tion associated with consumption of rawshell eggs, 1991.MMWR 1992;41:369-372.Editorial.

6. ChalkerRB, BlaserMJ.Areviewofhumansalmonellosis: Il. magnitude of salmonellainfection in the United States. Rev InfectDis. 1988;10:111-124.

7. Hargrett-Bean NT, Pavia AT, Tauxe RV.Salnonella isolates from humans in theUnited States, 1984-1986. AMMWR 1988;37:25-31.

8. Anderson RM, May RM. Infectious Dis-easesofHwnan. Oxford, England: OxfordUniversity Press; 1991.

9. SAS/ETSs User's Guide, Version 6. 1stedition. Cary, NC: SAS Institute, Inc;1988.

10. Aron J. Multiple attractors in the responseto a vaccination program. Theor PopulBioL 1990;38:58-67.

11. Watier L, Richardson S, Hubert B. A timeseries construction of an alert thresh-old with application to S. bovismorbii-cans in France. Stat Med. 1991;10:1493-1509.

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