Dynamic aspects of morbidity and acquired immunity in schistosomiasis control

ACTA TROPICA ELSEVIER

Acta Tropica 62 (1996) 105-117

Dynamic aspects of morbidity and acquired immunity in schistosomiasis control M.S. C h a n *, R . M . A n d e r s o n , G . F . M e d l e y 1, D . A . P . B u n d y The Wellcome Trust Centre for the Epidemiology of Infectious Disease, Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, UK Received 1 May 1996;accepted 10 August 1996

Abstract In schistosomiasis control, rational planning of chemotherapy programmes is complicated by the dynamic interactions between treatment and levels of acquired immunity and morbidity in the community. In this paper, mathematical models that address the development of acquired immunity and the prevalence of morbidity are incorporated within an age-structured transmission framework to explore some of the dynamic complexities of long-term chemotherapy programmes. As well as illustrating some of the potential problems inherent in predicting the consequences of control measures, the model provides insights into the dynamics of schistosomiasis transmission and the parameters that need to be measured to further improve the design of community-based control programmes. Keywords: Population Chemotherapy

dynamics;

Helminth

epidemiology;

Immunoepidemiology;

1. Introduction Schistosomiasis causes serious morbidity in many parts of the developing world ( W H O , 1993). In order to reduce morbidity at the community level, regular mass treatment has been advocated as a cost-effective control measure (Savioli et al., 1990; Warren et al., 1993). All three of the main species of schistosomes, namely, Schistosoma mansoni, S. haematobium, and S. japonicum can be effectively treated with a single dose of the drug, praziquantel. Although the strategy for disease control is relatively well defined, the quantification of the benefits of control programmes, and the prediction of trends in the prevalence and mean intensity of infection, is much more problematic. This results * Correspondingauthor. Tel." +44 (1865) 271199;Fax." +44 (1865) 281245. 1Ecosystems Analysis and Management Group, Department of Biological Sciences, University of Warwick, Coventry CV4 7AL, UK. 0001-706X/96/$15.00Copyright© 1996ElsevierScienceB.V. All rights reserved PII S0001-706X(96) 00039-3

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from a relative lack of quantitative understanding of two areas of schistosome biology and of the interactions of the parasite with the human hosts. Firstly, the dynamics of infection at the population level following mass chemotherapy are likely to be related in a complex way to the dynamics of acquired immunity to schistosome infections at the individual level (Anderson and May, 1985a, 1991; Woolhouse, 1992). Acquired immunity to helminth infections in general is not well understood at present (Maizels et al., 1993). The second area concerns the measurement of the burden of disease in the community. Morbidity due to schistosomiasis may not be simply related to the current infection intensity, since chronic schistosomal morbidity develops over many years and is related to the past experience of infection as well as the history of treatment (King et al., 1988; Gryseels, 1989; Medley and Bundy, 1996; Chan et al., 1995; Chan and Bundy, 1996). Both these areas need to be taken into account when predicting or evaluating effects of control programmes. For many infectious diseases, mathematical modelling has proved to be a valuable tool in the prediction of epidemic trends and the design of control programmes (Anderson and Nokes, 1991; Garnett and Anderson, 1995). For schistosomiasis infections, there are models based on describing the dynamics of transmission between man and snails (the intermediate hosts) (Hairston, 1965; Macdonald, 1965; Woolhouse, 1991) and others based on an age structured framework with a direct transmission approximation (Anderson and May, 1985b; Chan et al., 1995). Separate modelling studies have also been carried out on morbidity (Medley and Bundy, 1996; Chan et al., 1996) and acquired immunity (Anderson and May, 1985a; Woolhouse, 1992). The dynamic consequences of chemotherapy for patterns of morbidity have been examined in an earlier paper (Chan and Bundy, 1996). However, to date, acquired immunity has not been combined into the transmission framework to investigate the interaction between herd immunity and morbidity within control programmes. In this paper, the development of a schistosomiasis transmission framework which includes morbidity and immunity is described. The behaviour of this model is explored by simulation of chemotherapy programmes against S. mansoni with special attention given to the influence of immunity and morbidity on the predicted impact of a defined intervention.

2. Model development

2.1. Conceptualframework The model developed is based on the schistosomiasis transmission framework described in Chan et al. (1995) and of mathematical models of acquired immunity (Anderson and May, 1985a). Acquired immunity is added into this framework by making the following three assumptions. Firstly, the acquisition of acquired resistance is assumed to be proportional to the past experience of infection represented as the past integrated worm burden (number of 'worm years' experienced). Secondly, this resistance is assumed to decay such that the immunity acquired is not lifelong.

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Thirdly, the immunity is assumed to protect the host from further establishment of parasites. These assumptions are based on modifications of earlier models (Anderson and May, 1985a, 1991; Woolhouse, 1992). Morbidity is modelled by using the framework established in Chan et al. (1996) and Chan and Bundy (1996). Morbidity due to S. mansoni is divided into early chronic disease (hepatomegaly) and late chronic disease (Symmers fibrosis). The stages of disease are modelled as a progression such that hepatomegaly develops in a manner related to the accumulated past experience of infection and Symmers fibrosis develops from hepatomegaly. Both types of morbidity are assumed to resolve spontaneously, although at different rates. 2.2. Transmission and immunity The age-structured transmission framework used here is developed from the model described in Chan et al. (1995). The basic model structure is the same but is modified to include the effects of acquired immunity. It is assumed that immunity is acquired as a result of exposure to adult worms and is therefore related to the cumulative past exposure (Anderson and May, 1985a). Acquired immunity protects the host against further infection by modulating the rate at which parasite establishment occurs. The immunity is not lifelong but has an average duration given by 1/s where s is the decay rate of acquired immunity (Anderson and May, 1985a). In the absence of detailed data, this decay rate is assumed to be exponential in form. If the mean worm burden experienced at age a and time t is denoted by M(a, t) the average level of acquired immunity I(a, t) at any age and time can be given by: a

I(a, t) = S e- s(a- d)M(a,,t _ a + a')da'

( 1)

0

An exponential function is assumed to relate acquired immunity to the extent of protection offered. The rate of change of mean worm burden can then be described by the following partial differential equation: OM(a,t) ~t

~M(a,t) 4 - -A(a,t)e-~I(a)-#M(a,t) 0a

(2)

where A (a, t) is the rate of infection, 6 is a measure of the protective strength of the immunity, and ~ is the mortality rate of the worms. A(a,t) is given by: #Rop(a)f(M(a,t)) ~ rc(a)~c(a)M(a,t)da A(a,t) = a 7z(a)tc(a)p(a)da

(3)

a

R o is the basic reproductive number which is calculated from the initial age intensity curve specified, f ( M ( a , t ) ) is a density dependent establishment function and 7t(a) represents the proportion of people in each age group. The forms of these two functions and the parameters used are identical to those described in Chan et al. (1995). However, the age-dependent contact (p(a)) and contamination (x(a)) func-

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tions follow the functional forms used in Chan et al. (1996), namely: p(a) = (ae -(aa)2) + c

(4)

where fl and c are constants. The contamination function is of a similar form with the fl being replaced by 0. In this study it is assumed that these two parameters have the same numerical value. The contact function describes the relative rate at which people of different ages are exposed to infection and the contamination function describes the relative rate that these people contaminate the environment with their faeces. The measure of the strength of protective immunity (6) is difficult to correlate with field data or to understand intuitively. We therefore evaluate this parameter by introducing a new parameter (A) which is the percentage resultant reduction in mean worm burden at age 20 as a result of the acquired immunity being present. Note that the value of A depends also on the duration of immune protection. To carry out the simulations, values for the peak intensity and the age at this peak are input and the parameter fl is calculated from this information by an optimisation procedure. The partial differential equations are solved by numerical methods. Egg counts are calculated from mean worm burden by multiplying by a constant factor (el) (Chan et al., 1995).

2.3. M o r b i d i t y

The morbidity framework used is described in Chan et al. (1996) has been incorporated into the dynamic transmission model as described in Chan and Bundy (1996). Early chronic disease is observed primarily in younger people and is exemplified by hepatomegaly in S. mansoni. The prevalence of early chronic disease (De (a,t)) is given by: 3De(a,t) -

-

aa

ODF(a,t) +- = r e m ( a , t ) ( 1 -- OE(a,t) --#DEDe(a,t) Ot

(5)

where re is the development rate of early disease and #oe is its rate of resolution. Late chronic disease progresses from early chronic disease and is generally observed in older people. It is exemplified by Symmers fibrosis of the liver in S. m a n s o n i infections. The prevalence of late chronic disease (DL (a,t)) is given by: aDL(a,t) ~DL(a,t) - + - = rLDe(a,t)( 1 -- DL(a,t) -- ltoLDL(a,t) Oa Ot

(6)

where r L is the development rate of late disease and #oL is its rate of resolution. The structure of the whole model including both the transmission framework with acquired immunity and the morbidity sub-model is illustrated in Fig. 1.

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~ S. Chan et aL/ Acta Tropica62 (1996) 105-117 F

acquisition

~¢?

Immunity I(a,t)

~!

"",

s loss

///i

~;;J

,

,

MeanWorm Burden,M(a,t)

[

// mortality

Hepatomegaly DE(a,t)

t

L ao,

development

resolution

/ /

Symmers fibrosis,DL(a,t) RL

development

JJ

~ DL resolution

Fig. 1. Flowchartto showthe modelstructure.

3. Simulation of chemotherapy programmes The model is used in this paper to examine some of the complex dynamics which may be observed when the system is 'perturbed' by chemotherapy on a community scale. An important objective of this exercise is to show how the consequences of a control programme may be related to the duration and strength of acquired immunity and the rate of spontaneous resolution of morbidity. The parameters used reflect the biology of S. mansoni since more parameter estimates are available for this species. For consistency, the parameter values are the same as those used for previous analyses (Chan et al., 1995,1996; Chan and Bundy, 1996). For most communities for which chemotherapy programmes are planned the ageintensity profile of infection may be known but not the underlying patterns of morbidity and immunity. This simulation exercise therefore explores different patterns of immunity and morbidity which give the same age-intensity curve. Combinations of two morbidity scenarios and four immunity scenarios are simulated giving seven simulations in total. In an earlier paper on the morbidity framework (Chan et al., 1996), remarkable consistency was observed in the estimated morbidity parameter values for different data sets and even for different species. However, the early morbidity patterns for S. mansoni appear to fall into two variant forms. In one case, which is exemplified by S. mansoni in Africa the prevalence of hepatomegaly usually decreases in the adult age classes indicating fast spontaneous resolution of the condition (Gryseels and Polderman, 1987; Gryseels, 1988). In the other case, reported from Brazil the

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prevalence of hepatomegaly may not decrease with age suggesting that hepatomegaly resolves spontaneously at a very slow rate (Lehman et al., 1976). The two early morbidity scenarios simulated here reflect these 'African' and 'Brazilian' situations. Note that the intention is not to assert that there is a geographical difference in patterns of early morbidity but to explore the dynamic consequences of the two distinct morbidity patterns which have been observed. Acquired immunity is assumed here to depend on two parameters: the strength of the immunity (~) and its duration (l/s). Although there is evidence for the existence of some level of acquired immunity, which is of short duration (years rather than decades) and offers partial protection (Hagan et al., 1991; Butterworth et al., 1992), neither parameter has been quantified for S. mansoni. In the absence of empirical guidance, and in order to provide contrast with the assumption of no immunity, we first assume here a high strength of immunity. Simulations are run to examine the effects on worm burden when the duration of immunity is varied (2, 5 and 10 years, see Table 2). Since the degree of protection is dependent upon both the duration and strength of immunity, these combinations of assumptions are equivalent to a reduction in worm burden (A) of 25%, 46% and 60% at 20 years of age, respectively (Table 2). In order to explore the effect of the strength of immunity on worm burden, simulations are also run assuming two different values of strength (Table 2) at a constant duration of 5 years protection. These combinations of parameters are equivalent to 27% and 46% reduction in worm burden at 20 years of age. Finally, we examine the effects on morbidity ('African' and 'Brazilian' type hepatomegaly and Symmers fibrosis) of assuming a higher strength of immunity which provides 5 years of protection. The high strength of immunity was used in these simulations to provide a contrast with the results obtained under the assumption of no immunity. The same chemotherapy programme was simulated for each parameter set to enable comparison between the simulations. The simulation assumes that children between the ages of 7 and 18 are treated every four years over a 20 year period. This corresponds to a strategy of infrequent targeted treatment of children of school age which has been advocated as a cost effective strategy (Butterworth et al., 1991; Warren et al., 1993). After year 21 the treatment is stopped so that rebound effects can be observed. The simulations are run for 50 years. The parameters used are shown in Table 1Table 2. The results from the simulations for mean egg count, prevalence of hepatomegaly and prevalence of Symmers fibrosis are recorded as 3-dimensional surface plots.

4. Results

For the simulations with the assumption of no immunity, the 3-dimensional surface plots are shown in Fig. 2. Chemotherapy lowers the mean egg count to very low levels in both children and adults by year 20 (Fig. 2a). The mean egg count rises again slowly after the chemotherapy is stopped at year 21 but is still substantially

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Table 1 Default parameter set used for all simulations Parameter

Symbol (units)

Value

Maximum human age Timestep Maximum worm burden Epg per worm Worm lifespan Peak age intensity Peak mean epg (arithmetic) Treatment schedule Coverage Drug efficacy Treated ages

A (years) Years

80 0.05 2000 5.26 4 15 500 Years 1,5,9,13,17,21 80% 95% 7-18

ei l/p epg c e

Table 2 Parameter values for the simulations Simulation number

1

2

3

4

5

6

7

Immunity Morbidity pattern Rate of development early disease (rE) Resolution time early disease (years) (1/#DE) Rate of development late disease (rL) Resolution time late disease (years) ( 1/,ttDL) Strength of immunity (6) % Reduction in worm burden (zJ) Duration of immunity (years) (l/s)

No Africa 0.0071

No Brazil 0.002

Yes NA NA

Yes NA NA

Yes Africa 0.007l

Yes NA NA

Yes Brazil 0.002

1

21

NA

NA

1

NA

21

0.015

NA

NA

NA

0.015

NA

NA

13

NA

NA

NA

13

NA

NA

NA 0

NA 0

0.002 60

0.001 27

0.002 46

0.002 25

0.002 46

NA

NA

10

5

5

2

5

lower at y e a r 50 t h a n the original level (at t = 0 ) . N o t e also t h a t the p e r t u r b a t i o n o f the age profile a n d the benefits o f the p r o g r a m m e , extend b e y o n d the t r e a t e d age groups. ' A f r i c a n - t y p e ' h e p a t o m e g a l y is a s s u m e d to resolve over a time scale o f a p p r o x i m a t e l y one year. Therefore, the p a t t e r n s o f h e p a t o m e g a l y closely reflect the p a t t e r n s o f infection intensity a n d have a similar age profile a n d d y n a m i c s ( c o m p a r e Fig. 2, a a n d b). This suggests t h a t there is an early r e d u c t i o n in ' A f r i c a n - t y p e ' h e p a t o m e g a l y which is s u s t a i n e d after the cessation o f t r e a t m e n t . S y m m e r s fibrosis resolves over a m u c h l o n g e r time scale a n d this is reflected in the p r e d i c t e d p a t t e r n s (Fig. 2c). T h e p e a k prevalence o f S y m m e r s fibrosis occurs at a later age t h a n t h a t o f either the m e a n intensity o f infection or h e p a t o m e g a l y (25 years as o p p o s e d to 15 years).

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Fig. 2. 3-Dimensional surface plots sho~_ng the epidemiological consequences of a chemotherapy programme if it is assumed that there is no acquired immunity. (a) Arithmetic mean egg count. (b) Proportion with hepatomegaly (Africa). (c) Proportion with Symmers fibrosis (Africa). (d) Proportion with hepatomegaly (Brazil).

The response to chemotherapy is also slower such that most of the benefits accrue after the end of the chemotherapy programme (years 20-50). 'Brazilian-type' hepatomegaly is assumed to resolve much more slowly than the 'A•can-type' variant. This results in an age profile which is quite different from the 'African-type' (compare Fig. 2b and d). This result highlights the fact that the effects of a control programme on early disease will be crucially dependent on the rate of resolution of morbidity. Fig. 3 shows the simulated age-intensity profiles under various assumptions of the effects of acquired immunity. It is immediately obvious that the consequences are

M.S. Chan et al./Acta Tropica 62 (1996) 105-117

113

!

Fig. 3. 3-Dimensional surface plots showing the epidemiologicalconsequences of a chemotherapyprogramme if it is assumed that there is acquired immunity. Arithmetic mean egg count is plotted against age and time. The parameter values are varied between simulations. (a) 6 =0.002, l/s= 10. (b) 6 =0.001, l/s=5. (c) ~=0.002, 1/s=5. (d) ~=0.002, 1/s=2. very different from those in the absence of immunity (compare Fig. 2a with Fig. 3). In all the simulations, chemotherapy results in much less marked reduction in intensity, and the cessation of treatment is followed by rapid reinfection. The dynamics are dependent upon the specific values of the strength and duration of protection. The effects of varying strength are explored in Figs. 2 and 3b,c, which represent zero, lower and higher strength respectively assuming a duration of protection of 5 years. These profiles show a graduation of effect, with the benefits of control diminishing with increasing strength of immunity. The effects of varying the duration o f immunity are shown in Figs. 2 and 3a,c,d

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which represent zero immunity (Fig. 2a) and a higher strength of immunity with a duration of 2, 5 and 10 years (Fig. 3d,c and a, respectively). Again, there is a graduation of effect, with the benefits of control diminishing with increasing duration of protection. With strong immunity of long duration, there may even be a transient rebound to levels of infection intensity which may exceed those prior to treatment. Fig. 4 shows the simulated effects of treatment on early and late morbidity under the assumption of a high strength of immunity of 5 years duration. All the age profiles suggest that chemotherapy will be much less able to reduce morbidity if there is effective acquired immunity. This holds true whether the morbidity resolves

Fig. 4. 3-Dimensional surface plots showing the morbidity patterns in the presence of acquired immunity using the immunity parameters 6=0.002, l/s=5. (a) Proportion with hepatomegaly (Africa). (b) Proportion with Symmers fibrosis (Africa). (c) Proportion with hepatomegaly (Brazil).

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rapidly, as in 'African-type' hepatomegaly (compare Fig. 2b and 4a) or resolves very slowly, as in 'Brazilian-type' hepatomegaly (compare Figs. 2 and 4c) and Symmers fibrosis (compare Fig. 2c and Fig. 4b). Under certain conditions, it is possible to observe transient rebound effects resulting in morbidity levels higher than those present before treatment.

5. Discussion

In this paper a model has been developed which can simulate the dynamics of infection, immunity and morbidity in a community with endemic schistosomiasis mansoni. The objectives were to describe the conception and construction of the model and to explore the behaviour of the model under different assumptions using parameters which were assumed characteristic of one schistosome species. Extension of the model to the other species and the full exploration of its dynamical behaviour will be the subject of future work. The development of the model included assumptions about the mechanism of acquired immunity. It was assumed that the immunity is acquired as a response to adult worms and acts against further establishment of larvae. Adult worms can also be the target of immune attack but this is not modelled here. A further assumption is that since the shape of the decay function is not known, the simplest assumption that immunity decays exponentially is used. Thirdly, we assume that the processes of acquired immunity and morbidity development do not interact (apart from dependence on infection). However, the hepatic lesion is an immunopathologic response to parasite eggs (WHO, 1989) which may suggest that there is an association between morbidity and resistance. In the absence of empirical data, the simplest assumptions were adopted here. This model predicts that if immunity is an important regulator of schistosome populations then chemotherapy programmes will be less effective. It is assumed here that the initial age-intensity profile is itself a reflection of the effects of immunity. Since all the initial profiles were set to the same value, then simulations which assumed stronger immunity also assumed a higher potential rate of transmission to balance the effect of the immunity. This is reflected in the assumption of a higher R0 (basic reproductive number) in simulations with immunity (Ro up to 4.8) compared with those without immunity (Ro = 1.62). The result of this assumption is that treatment of initially immune populations will reduce the acquisition of immunity and will allow the population to express its intrinsically higher rate of transmission until such time as immunity is again acquired. It is this relationship which explains the more rapid rate of rebound in the simulations which assume the operation of acquired immunity. Given the centrality of this assumption and the uncertainty of the quantitative estimates of the strength and duration of immunity, it is important to be cautious in interpreting the results presented here. It is not known with any degree of certainty whether the simulations are assuming a reasonable magnitude of immune protection. Validation of the model has been done for the initial phase of a control programme (Chan et al., 1995; Butterworth

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et al., 1991) but the behaviour of the model is more dependent on the strength and duration of immunity during the reinfection phase (after the control programme has been discontinued) for which data are currently unavailable. Also, different initial patterns of morbidity, such as the 'African' and 'Brazilian' variants of S. mansoni morbidity would result in different levels of benefit accrued from the control programme. Thus, the successful design of a practical control programme will be dependent upon more precise quantitative understanding of the basic biology of the host-parasite interaction. The expanded model of schistosomiasis control which also incorporates the dynamics of morbidity and immunity is used to demonstrate the complex dynamics which follow a perturbation of the system due to community based chemotherapy. Model simulations emphasize that caution is required when making decisions based on model outputs given uncertainty over the values of key parameters. However, the results highlight the important insights that can be gained by examining schistosomiasis control from a perspective that takes account of the transmission dynamics of the parasite.

Acknowledgements D.A.P.B. and R.M.A. acknowledge the support of the Wellcome Trust. G.F.M. is a Royal Society University Research Fellow. This study was supported by the Edna McConnell Clark Foundation.

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