Mathematical models for the control of cystic echinococcosis

Parasitology International 55 (2006) S253 – S258 www.elsevier.com/locate/parint

Mathematical models for the control of cystic echinococcosis Paul R. Torgerson * WHO Collaborating Centre for Parasitic Zoonoses Institute of Parasitology, University of Zurich, Winterthurestrasse 266A, 8057 Zurich, Switzerland Available online 20 December 2005

Abstract Cystic echinococcosis (CE) caused by Echinococcus granulosus is a global public health problem. In many areas the disease is being diagnosed in increasing numbers, whilst in other areas it is re-emerging due to the collapse of public health programmes associated with socioeconomic changes. Mathematical models of the transmission dynamics between animals can have an important role to play in developing control options. In particular the parasite is highly endemic in many lower income countries where resources to undertake an intensive control programme that has been successful in wealthy countries, such as New Zealand, are not available. Data from dogs and livestock have been collected and modelled from a number of different countries and regions. In Australia and New Zealand transmission modelling was first developed and these models have been refined using data from the Middle East and central Asia. The model indicates that relatively intense anthelmintic treatment of the dog population will result in a substantial decrease in the parasite population over time and has been supported by the results of control programmes. However, if the newly developed sheep vaccine is included in the control programme, then it should be possible to treat dogs less frequently to achieve the same result. This is due to the potentiating effects of attacking the parasite at two places in its life cycle. This should result in considerable cost savings over the use intensive anthelmintic treatment as the sole method of control. D 2005 Elsevier Ireland Ltd. All rights reserved. Keywords: Echinococcus granulosus; Epidemiology; Mathematical models; Control programme

1. Introduction

2. Age intensity and age prevalence models

Mathematical models have been developed to describe the transmission dynamics of Echinococcus granulosus [1 –3]. To be of practical use models should be able to predict future events given the model and basic information. For example, models could be used to forecast the outcomes of intervention such as periodic anthelmintic prophylaxis in dogs as part of a disease control programme. Furthermore, for them to be useful and widely applicable, they should be simple to understand, but robust under a variety of different systems. Assuming a model is based on theoretical ideas of parasite – host relationships, they can be tested using actual data and departures from the theoretical model can be used to define better models and thus gain a better insight into the parasite biology. To formulate a working model of the transmission dynamics of E. granulosus and other tapeworm species, knowledge of the parasites’ biology, together with observational studies of its epidemiology are required.

Roberts et al. [1,2] derived a model that described the variation of parasite prevalence and abundance with the age of the host. This basic model has been further developed and the model has been parameterised using data from both sheep and dogs [3]. From these models important information about the transmission of the parasite (such as the infection pressure) in the different hosts in the life cycle can be deduced. For example if there is no parasite induced immunity in the definitive host the mean prevalence of infection and mean abundance of parasite asymptotically increases with age producing the type of relationship illustrated in Fig. 1. The exact shape of the curve (i.e. the level asymptotic prevalence or abundance) and the rate at which it approaches the asymptote is only dependent on the prevailing infection pressure and the death rate (or life expectancy) of the parasite. An important property of the model is that it predicts that when there is significant host immunity it allows for a lower prevalence or abundance in old animals compared to young animals (Fig. 1, middle and bottom). A decrease in the prevalence of Echinococcus in old dogs has been observed in Tunisia [4] and indeed was suggested in data reported in

* Tel.: +41 1 63 58535; fax: +41 1 63 58907. E-mail address: [email protected]. 1383-5769/$ - see front matter D 2005 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.parint.2005.11.037

P.R. Torgerson / Parasitology International 55 (2006) S253 – S258

1 0.8 Proportion susceptible to infection Prevalence

0.6 0.4 0.2 0

0

2

4

6

8

10

1

0.8 Proportion susceptible to infection Prevalence

0.6

0.4

0.2

0 0

2

4

6

8

10

1 Proportion susceptible to infection Prevalence

0.8

3. The intermediate host

0.6 0.4 0.2 0 0

2

4

6

8

likely to be less under conditions of low infection pressure [6]. Thus, in farm dogs in rural Kazakhstan, the model suggested herd immunity is present with an estimated infection pressure of 3000 parasites per dog year compared to just 30 parasites per dog per year in village dogs. In addition the maximum likelihood value of the life expectancy of the parasite given the model and the data was very close to that observed experimentally. The confidence limits were wide, but by rerunning the analysis using prior data that reflect the variation in experimentally observed patency times, it was possible to define the confidence limits of all the parameters in the model more precisely. Recent data from China has also suggested that under conditions of high infection pressure there is a lower mean abundance of parasites in old dogs [7] (Fig. 2). However, in Morocco, the available quantitative data [8] suggest that there are to be greater numbers of parasites in old dogs than young dogs. This would be consistent with a lack of immunity. If the life expectancy of the parasite is around 1 year (as suggested by experimental studies), then the data reported from Morocco would reflect an infection pressure of around about 200 parasites per dogs per year. This is somewhat lower than the farm dogs in Kazakhstan and the infection pressure in China and thus there may be insufficient parasites to stimulate herd immunity.

10

Fig. 1. Variation in prevalence of E. granulosus and the proportion of dogs susceptible to infection with age. Top: 0.44 infections each year and the absence of immunity on exposure. Middle: infection pressure of 2 infections per year with an 80% probability of immunity on exposure and 20% probability of loss of immunity each year. Bottom: 0.44 infections every year with a 0.30 probability of immunity on exposure and 0.02 probability of loss of immunity (MLE estimates of farm dogs from Kazakhstan). All simulations assume a parasite life expectancy of about 1 year.

Roberts et al. [1,2]. Parameterising the full model for the data from Tunisia suggested that the maximum likelihood estimate (MLE) of the infection pressure in Tunisia was 5.3 infections per year and the likelihood of developing immunity on exposure was 0.53. The MLE of the life expectancy of the parasite was 7 months which is biologically reasonable. Attempting to fit the data to the model without immunity gives a poor fit (see [4]). Likewise, data from Kazakhstan [5] (Fig. 1, bottom) indicated that there was likely to be parasiteinduced host immunity under conditions of high infection pressure. However, under conditions of low infection pressure there appeared to be little parasite-induced immunity. This is consistent with E. granulosus stimulating immunity when there is high infection pressure but not in conditions of low infection pressure. The results agree with the idea that herd immunity is

The models derived by Roberts et al. [1,2] to describe the variations of age intensity and prevalence in the intermediate host are essentially the same mathematically as those describing these parameters in the definitive host and also depend on the parameters infection pressure, life expectancy of the parasite, and the rate of acquisition and loss of immunity. In the intermediate host the parasite is assumed to have a greater life expectancy than the definitive host and the assumption is made that, once infected, the intermediate host will be infected for life. Therefore the death rate is 0. Consequently, in the absence of immunity the variation of prevalence with age is only dependent on the infection pressure b. Thus sheep will gradually accumulate hydatid cysts and in the oldest age groups of animals the asymptotic

10000

Mean abundance

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1000 100 E. multilocularis E. granulosus

10 1 0.1 0.01 0 to 5

6 to15

Age (years) Fig. 2. Comparison of E. granulosus and E. multilocularis mean abundance for ages 0 – 5 years and 6 – 15 years, with 95% negative binomial confidence bands for dogs in Shiqu County [7]. The Y-axis (but not the data) has been logtransformed to better illustrate the 95% confidence intervals.

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prevalence approaches 1. The model predicts that in the intermediate host, if immunity is absent, then the numbers of hydatid cysts will increase with age in a linear fashion. This is indeed in agreement with a number of observational studies [1,5,9 –13] (Table 1). The terms endemic and hyperendemic were introduced to describe the levels of herd immunity in the intermediate host when infected by taeniid cestodes [1,2]. Essentially the parasite was defined as being endemic if there was no evidence of parasite-induced immunity in the intermediate host. Using this definition, E. granulosus appears to be nearly always in an ‘‘endemic’’ steady state. Other cestodes (e.g. T. hydatigenea) appear to stimulate more readily intermediate host immunity by exposure to natural infections of eggs. With this parasite, the increase in numbers of metacestodes with age is not linear with young animals having similar parasite abundances to older animals. Field observations are consistent with this hypothesis with ovine cysticercosis (see [11,13]). Likewise the asymptotic prevalence is depressed below 1, so even in the oldest age groups of sheep, the prevalence is usually much less than 1. On this definition, hyperendemic cysticercosis has been recorded a number of times (e.g. [2,11,13]), but there have been no convincing accounts of hyperendemic echinococcosis in sheep, cattle, goats or horses. However, a study of E. granulosus infections in yaks in Sichuan province of China suggest an asymptotic prevalence of less than 100%, which might indicate a ‘‘hyperendemic’’ status [3]. Although references have been made to ‘‘hyperendemic’’ echinococcosis, it is important not to confuse reports that have data that support intermediate host immunity rather than the parasite being highly prevalent. Even in China, where Zhang et al. [14] discussed the possibility of a decline in hydatid infections in older sheep in Xingjiang, an evaluation of the original data that was cited from Chi et al. [15] suggests an asymptotic prevalence approaching 1 (96% of sheep age 6 years were infected).

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4. Aggregation In both the intermediate host and particularly the definitive host, there is a large degree of aggregation of parasites. Thus, some hosts harbour a large number of parasites whilst a large proportion of the population harbour few, if any parasites. This can be modelled by a negative binomial distribution. The aggregation of infective stages can explain a large part of the distribution in hosts. Thus eggs in the environment might be expected to be aggregated close to the location of dog faeces. Consequently when sheep (or other intermediate hosts) are infected, an infectious insult may consist of several eggs. In the definitive host infectious stages are always likely to be aggregated as a fertile hydatid cyst can contain large numbers of protoscoleces. When fitting the data to the models described above it is important to ensure that the aggregation is taken into account when calculating the parameters. Thus, the negative binomial function is a suitable model to use as a description of the error variance, together with maximum likelihood techniques to establish the most likely value for the parameters [5,20]. A failure to use such an analytical approach gives an increase in the likelihood statistical errors [21] and can lead to inaccurate estimation of model parameters. 5. Inferences from the models Important epidemiological data can be gained by using these models on data. When data is fitted to the model then the parameters can be estimated. This includes the potential exposure of the hosts to the parasites and thus the infection pressure. This can be combined with data from the biotic potential of the parasite to calculate the numbers of infectious stages of the parasite to which the host is likely to be exposed. For example the numbers of eggs the intermediate host is consuming can be calculated (e.g. [10 – 13]). This can then be used to estimate the level of environmental contamination with

Table 1 Transmission parameters of E. granulosus to intermediate hosts reported from various studies Country

Infection pressure (cysts per year)

Infections per year

Number of cysts per infection

Reference

New Zealand China

1.43a 0.882a 0.997b 1.05 1.66 0.128 0.48 1.98 1.24 0.15 1.03 0.0559 1.27

0.44a 0.436a 0.414b 0.174 0.32 0.06 0.054 0.29 0.23 0.03 0.423 0.0253 0.44

3.25a 2.02a 2.42b 6.03 5.2 2.1 8.9 5.89 5.46 5.70

[1] [10]

Uruguay Jordan (sheep) Jordan (goats) Jordan (donkeys)c Kazakhstan (Almaty Oblast) South Kazakhstan Kazakhstan (cattle) Tunisiad Tunisia (camels) Peru

Transmission is to sheep except where otherwise stated. a Female sheep. b Male sheep. c Possibly the equine strain (or species E. equinus, see [19]). d Liver cysts in sheep only.

2.21 2.89

[11] [13] [16] [5]

[17] [18] [12]

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Table 2 Suggested baseline parameters for sheep and dogs in Kazakhstan Parameter

Value

Infection pressure in sheep Time to maturity of cysts Mean age of sheep population Mean age of dogs Infection pressure to dogs Life expectancy of infection in dogs Probability of dogs acquiring immunity on exposure Probability of dogs losing immunity Initial prevalence in sheep Initial prevalence in dogs

1.98 cyst per year 2 years 2.4 years 3.1 years 0.44 infections per year 0.99 years 0.30 0.02 0.48 0.23

eggs as well as indicate likely control feasibility. The model has also been used on one occasion to demonstrate the lower level of exposure to eggs by goats compared to sheep grazing in the same herds. Torgerson et al. [13] reported that sheep had a greater abundance of hydatid cysts compared to goats but fewer metacestodes of Taenia hydatigena. By modelling the age related distribution it could be shown that the increase in T. hydatigena metacestodes was actually likely to be due to less host immunity resulting in greater numbers of cysts compared to sheep despite a lower infection pressure. Because E. granulosus appeared not to stimulate immunity in either intermediate host then the lower numbers of hydatid cysts was related directly to the infection pressure. This observation was hypothesized to be due to the fact that goats are browsers and thus more likely to consume the extremities of the herbage. Here eggs are likely to be at lower concentrations and have a lower viability due to greater exposure to desiccation and ultraviolet radiation. This was confirmed experimentally by Heath (reported in [3]). Similarly the model has been used to analyse the distribution of ovine cysticercosis in a feral sheep population on a remote Scottish island where there are no carnivores. The conclusion was that the most likely explanation of the infection in these sheep was due to long distance transmission from the Scottish mainland possibly through birds as mechanical carriers of taeniid eggs [22]. 6. Simulation of control programmes Possibly the most important use of modelling is their potential to model control intervention. In the case of cystic echinococcosis, the equations that define transmission reported have been used to develop a spread sheet model that could be utilized to predict the possible outcomes of intervention. This is reported in more detail in [3,23]. A spread sheet model was built round cell entries for prevalence and abundance of the host populations based on the equations reported above. Simulation of control was undertaken by assuming an intervention strategy would change one or more of the base line parameters in the model. Precontrol parameters being first obtained by surveillance data (Table 2) such as that reported from Kazakhstan [5,20]. Once baseline information is obtained for a particular locality, control can be simulated by changing the parameters (Table 3) [23]. For example, if treatment of dogs with

MLE value of best model fit for sheep from Almaty Oblast Suggested from surveillance data Suggested from surveillance data MLE value of best model fit MLE value of best model MLE value of best model MLE value of best model fit Almaty Oblast Farm dog population

anthelmintic is undertaken every 6 weeks (the prepatent period for the G1 strain) then the mean survival time of a patent infection is reduced to 0. However, other less intense (and cheaper) programmes can be modelled such as 3- or 6-monthly anthelmintic treatment. In modelling intervention it must be assumed that 100% compliance is rarely if ever achieved. In China, frequently less than 80% of dogs were treated in a control programme [24] whilst in Turkana Kenya only 59% of dogs could be treated [25]. Less than 100% compliance is modelled by increasing the life expectancy of the parasite to a larger value than would occur if there was 100% anthelmintic treatment. For example, a capture rate of 100% with a treatment interval of 6 weeks would reduce the life expectancy of the parasite in dogs to 0. A capture rate of 50% with 6 weekly treatments would reduce the mean life expectancy of the parasite in dogs to approximately 6 weeks. This is because half the parasite population would have a life expectancy of 0, a further quarter of the population (0.52) a life expectancy of 6 weeks, a further eighth (0.53) a life expectancy of 12 weeks, etc.; up to a maximum assumed life expectancy of 1 year. No parasites would survive greater than 1 year because of natural senescence after 1 year even if the dog has avoided anthelmintics on all occasions. This calculation assumes there is an equal chance of each dog avoiding capture on each occasion. If the same dogs avoided capture each time, then the mean life expectancy of the parasite in dogs would simply be halved to 6 months. Likewise, a capture rate of 60% with 3monthly anthelmintic treatment would reduce the mean life expectancy to approximately 11 weeks (assuming each dog has an equal chance of avoiding capture). Similarly other life expectancies can be calculated based on the anthelmintic treatment interval, the capture rate of dogs and if the same dogs or different dogs evade capture on each occasion. The decrease in parasites in dogs caused by anthelmintic treatment will result in a lowered infection pressure in sheep. In Table 3 Modelling control through changes in the parameters Control intervention

Change in parameter

Anthelmintic treatment of dogs

Reduction in life expectancy of patent infection Reduction in numbers of cysts in sheep from time of vaccination Reduction of infection pressure to dogs

Vaccination of sheep Education programme

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this model it has assumed that the decreased infection pressure is proportional to the decreased patent period. The numbers of cysts in sheep will begin to decline but not change the infection pressure in dogs for some time because of the longevity of cysts in the older sheep. Thus delay is included in the model to allow time for older sheep with their parasite population to be removed from the system. The length of the delay depends on the time to cysts maturity. In addition some of the parameters relating to immunity were assumed to change as control of the parasite population progressed. For example as the prevalence in dogs becomes lower, the probability of immunity on exposure is decreased. This models the relaxation of herd immunity as a result of lower infection pressure. Data for this concept can be found in [20], where it was demonstrated that herd immunity was significant when the prevalence in the dog population was 23% but absent when the prevalence was only 5.8% in a separate population of dogs. An important recent development in the control of echinococcosis is the development of the sheep vaccine [26,27]. A vaccination campaign can be modelled as a reduction in the numbers of new fertile cysts from the date of vaccination. Thus, sheep that are vaccinated with a 100% effective vaccine will develop no further cysts from continued exposure to Echinococcus eggs. However, infection acquired before vaccination can still be transmitted to dogs, thus there will be some delay until all the cysts disappear from the sheep population. Likewise an education campaign may reduce the rate at which offal is fed to dogs and this can be modelled as a reduction in the infection pressure in dogs. There is significant variability in some of the parameters suggested by different experimental work and in the possible capture rates of dogs in the populations. There will also be additional variability in the base line surveillance data obtained for the precontrol parameters. To model this variability in the simulations, Monte-Carlo routines have also been written into the spreadsheet model to account for this. Thus, variability in the capture rate of dogs between the best case (say 90% treated) and worse case (say 60% treated) can be modelled. This is particularly important in the absence of accurate dog population figures and would give best and worse case scenarios if a target capture rate or compliance rate of 75% was assumed. A number of hypothetical scenarios were investigated using this simulation model. The conclusion was that if anthelmintic treatment is used as the main strategy, then generally a minimum of treatment every 3 months is required assuming at least 60% of the dogs in the population are treated. Vaccination of sheep is effective, provided that a large proportion of the population is vaccinated (over 90%). Interestingly, the most effective intervention was a combination of vaccinating sheep and anthelmintic treatment. Using this strategy it was possible to reduce levels of echinococcosis in both principal life cycle hosts to very low levels. If there is vaccine cover of about 75% of the sheep population, anthelmintic treatment in dogs can be reduced to six monthly intervals. Such a less intensive approach would have advantages in terms of cost, and may also increase compliance. In

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any case, by using an integrated approach, a low level of compliance would still result in acceptable levels of control. 7. Echinococcus multilocularis This model has been utilised to investigate the transmission E. multilocularis in dogs in China [7,28,29]. In a group of nearly 400 dogs there was a different pattern of infection than with E. granulosus. The most obvious observational difference was that old dogs were as heavily infected as young dogs, which was in contrast to E. granulosus which had very few parasites in the older age groups (Fig. 2). This can be explained by hypothesizing that E. multilocularis does not stimulate herd immunity in dogs. This result has a potentially important implication. The hypothesis of E. multilocularis transmission in China is that there is a disturbed life cycle with dogs acting as a conduit of infection to humans. The lack of herd immunity in dogs suggests that significant progress can be made with control without the ‘‘positive’’ feedback effects of herd immunity [7,29]. However important questions remained to be answered. The most important one is if dogs are actively participating in the cycle or becoming infected only as spill over from the natural fox-rodent cycle. If it is the former then any intervention measure to control the parasite will have a greater effect than in the latter. 8. Future developments This review has mainly concentrated on the model originally developed by Roberts et al. [1] and has illustrated some of the potential uses of such modelling techniques to gain insights into the epidemiology of parasite transmission and for intervention strategies. However there still remain significant issues to resolve. For example, the negative binomial distribution has been discussed as a suitable link function for fitting abundance data to the model. However, the use of this function is not a natural product of the mathematical derivation of the model, but rather a convenience to fit highly aggregated data to the models. In the later respect, it has served a very useful function. However there remain significant anomalies to resolve. E. granulosus infections in dogs are highly aggregated as already discussed. Because of this phenomenon, the addition of just a small number or even 1 highly infected animal into a data set, even a large data set can significantly change the results or even the conclusions. For example, a data set of over 600 farm dogs [20] suggested lower abundance rates in old dogs compared to young dogs. However, additional data has been collected [30] and this additional data adds a question mark to the earlier observed distribution. Indeed it is the addition of just one infected dog of age 5 years with an estimated burden of over 200,000 parasites that increases substantially the mean burden in older dogs. A robust modelling system should be more resistant to the effects of individual observations in such a large data set. Therefore new modelling techniques that utilise infinite compartmentalisation of parasites into animals infected with 0, 1, 2, 3, 4, etc., parasites is now underway and it is hoped that such an

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approach will not only overcome this problem but will also give a natural mathematical description of parasite distribution in dogs and indeed other animals without the arbitrary use of a convenient mathematical distribution. This in turn should improve the reliability of modelling systems. 9. Conclusions Important advances in the understanding of the transmission dynamics of E. granulosus have been described in this paper. By using mathematical models it is possible to gain a better understanding of the parasite’s biology and the dynamics of transmission. In addition, parameterisation of the models may be helpful in developing simulation models which will indicate the likely success of hypothetical control programmes and thus help in the planning stage of a control programme.

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[15]

[16]

Acknowledgements The author would like to thank INTAS (INTAS 97-401; INTAS 01-500, INTAS 01-505, INTAS 03-51-5661, the NIH (TWO 1565-02) and the National Science Foundation for financial support for undertaking many of the studies reviewed in this article. References [1] Roberts MG, Lawson JR, Gemmell MA. Population dynamics of echinococcosis and cysticercosis: mathematical model of the life cycles of Echinococcus granulosus. Parasitology 1986;92:621 – 41. [2] Roberts MG, Lawson JR, Gemmell MA. Population dynamics of echinococcosis and cysticercosis: mathematical model of the life cycles of Taenia hydatigena and Taenia ovis. Parasitology 1987;94:181 – 97. [3] Torgerson PR, Heath DD. Transmission dynamics and control options for cystic echinococcosis. Parasitology 2003;127:S143 – 58. [4] Lahmar S, Kilani M, Torgerson PR. Frequency distribution of Echinococcus granulosus and other helminths in stray dogs in Tunisia. Ann Trop Med Parasitol 2001;95:69 – 76. [5] Torgerson PR, Shaikenov BS, Rysmukhambetova AT, Abdybekova AM, Usenbayev AE, Baitursinov KK. Modelling the transmission dynamics of Echinococcus granulosus in sheep and cattle in Kazakhstan. Vet Parasitol 2003;114:143 – 53. [6] Anderson RM, May RM. Herd immunity to helminth infections and implications for parasite control. Nature 1985;315:493 – 6. [7] Budke CM, Craig PS, Jiamin Q, Torgerson PR. Modeling of the transmission of Echinococcus multilocularis and Echinococcus granulosus in dogs for a high endemic region of the Tibetan plateau. Int J Parasitol 2005;35:163 – 70. [8] Ouhelli H, Kadiri A, El Hasnaoui M, Kachani M. Prevalence of Echinococcus granulosus in dogs in Morocco and potential role of dogs in transmission of cystic echinococcosis. In: Ouhelli H, Kachani M, editors. Compendium on cystic echinococcosis in Africa and in Middle Eastern countries with special reference to Morocco. Provo’ Brigham Young University;, 1997. p. 145 – 55. [9] Gemmell MA. Australasian contributions to an understanding of the epidemiology and control of hydatid disease caused by Echinococcus granulosus past, present and future. Int J Parasitol 1990;20:431 – 56. [10] Ming R, Tolley HD, Andersen FL, Chai J, Sultan Y. Frequency distribution of Echinococcus granulosus hydatid cysts in sheep popula-

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