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Spatial simulation of malaria transmission and its control by malaria transmission blocking vaccination
International Journal for Parasitology 32 (2002) 1617–1624 www.parasitology-online.com
Invited review
Spatial simulation of malaria transmission and its control by malaria transmission blocking vaccination Richard Carter* Division of Biological Sciences, ICAPB, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, UK Received 18 April 2002; received in revised form 30 July 2002; accepted 13 August 2002
Abstract A simple, visual representation of spatial aspects of malaria transmission in successive snap-shots in time, is presented. The spatial components of the simulation involve (i) the identification of mosquito vector breeding sites of defined shape and area, (ii) the identification of a zone of malaria transmission determined by the shapes and areas of the vector breeding sites and the distance from these sites that the mosquitoes disperse, (iii) a human population dispersed in relation to the malaria transmission zone, (iv) perimeters around each individual human within which his or her infection can be transmitted by the local vector mosquitoes. The intensity of transmission within a malaria transmission zone is given by a number which is the number of new cases of malaria that each existing case will distribute through the human population within the duration of an infection. The simulation has been used here to examine the effects of vaccination against malaria transmission. Different levels of vaccine coverage are represented under endemic and epidemic malaria. The consequences of full or partial coverage of a zone of malaria transmission are also examined. The results are numerically compatible with the predictions of previous simple mathematical simulations of malaria transmission and interventions. The present simulation allows the nature of malaria transmission and the effects of interventions to be communicated easily and directly to an audience. It could have practical value in discussions of malaria control strategies with health planners. q 2002 Published by Elsevier Science Ltd. on behalf of Australian Society for Parasitology Inc. Keywords: Malaria transmission; Spatial simulation; Malaria transmission blocking vaccine
1. Introduction Interventions to prevent or reduce the transmission of malaria are amongst the oldest and most effective public health measures. In Italy in the early 19th century, long before the underlying facts of malaria transmission were known, legislation required that irrigated land be situated at least 500 m from rural habitations and at least 8 km from towns (Carter et al., 2000b). In the 20th century one of the more important and successful interventions in the history of public health was the application of house spraying with residual insecticides to reduce the transmission of malaria (Roberts et al., 1997; Sharma, 1996; Newman, 1965). Both of these approaches operated by reducing the probability that the mosquito vectors of malaria could transmit malarial infection from one human being to another. The first approach simply reduced human/mosquito contact towards zero by ensuring that human populations were beyond the range that the vector mosquitoes could disperse from their aqueous breeding sites. The second, residual insecticide * Tel.: 144-131-650-5558; fax: 144-131-668-3861. E-mail address: [email protected] (R. Carter).
spraying, either repelled the mosquitoes from human contact (Roberts, D., personal communication) or killed them where they came into most frequent human contact – in the home (Pant, 1988). Another approach towards the same end is to reduce the infectivity of the human population itself to mosquitoes. This has been tried in the past through the widespread distribution and use of antimalarial drugs (Hackett, 1937; League of Nations, 1925; World Health Organisation, in press; Yip, 1998). Combined with other measures, such as those described above, it has probably contributed to malaria control in several campaigns. The use of antimalarial drugs for malaria transmission control is, however, by and large not very effective compared with those which directly affect the human/mosquito interaction. The reason is that it is virtually impossible, using drugs alone, to ensure that a malaria-infected individual has received the necessary treatment at the time at which he or she is infectious to mosquitoes (Mendis et al., 2001). In endemic situations drug cover can only be intermittent at best unless permanent drug prophylaxis is employed across an entire endemic human population. This, in most situations, would be neither practical nor affordable.
0020-7519/02/$20.00 q 2002 Published by Elsevier Science Ltd. on behalf of Australian Society for Parasitology Inc. PII: S 0020-751 9(02)00190-X
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There is, however, a potential alternative which could overcome most of the principle problems of using drugs to suppress the infectivity of human populations to mosquitoes. It is the development and deployment of vaccines that were designed to limit the transmission of human malarial infections to mosquitoes - malaria transmission blocking vaccines (TDR, 2000; Carter et al., 2000a). To be effective such a vaccine should have the following properties. It should largely or completely eliminate the infectivity of malaria-infected individuals at all times during the course of a blood infection. This would be from the first moments of the appearance of the infectious sexual stage parasites in the blood, and throughout a subsequent blood infection,
which in the case of malaria can continue intermittently for a year and more. The transmission blocking efficacy of the vaccine should be of at least several years. Such vaccines, the malaria transmission blocking vaccines, are under development for human trials (TDR, 2000; Carter et al., 2000a; Stowers and Carter, 2001). Malaria transmission blocking vaccines are based upon the sexual stage antigens of malaria parasites that are expressed in the mosquito mid gut and which can, therefore, be targeted by antibodies which are ingested by a mosquito during a blood meal. There are two general classes of these target antigens. They are (i) the gamete surface antigens, notably the Ps230 and Ps48/45 families, and (ii) the zygote/ookinete
Fig. 1. Basic set-up for a spatial simulation of malaria transmission (see text). Green spots represent uninfected individuals; red spots represent individuals who have become infected with malaria in the currently represented round of infection and transmission.
R. Carter / International Journal for Parasitology 32 (2002) 1617–1624
Fig. 2. Infection transmission perimeters showing different Ro values (see text).
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surface antigens, notably the Ps25 and Ps28 families (TDR, 2000; Carter et al., 2000a; Stowers and Carter, 2001). Antigens of the first class are expressed in the gametocytes in the blood circulation. Because of this, antibodies against these antigens are strongly boosted by the blood infection itself (Carter et al., 2000a). This is a great potential advantage to the development of Ps230 and Ps48/45 group antigens for malaria transmission blocking vaccines. The antigens of the second class, Ps25 and Ps28, are expressed in significant amounts only on the mosquito mid gut stages of the parasites. They are, therefore, not available to boost immunity against them during blood infections. Each of these antigen types is under consideration for transmission blocking vaccine (Stowers and Carter, 2001). In trying to predict the likely impact and the epidemiological circumstances under which malaria transmission blocking vaccination could be usefully deployed, it is very important to understand the relevant principles of malaria transmission. Analyses have been developed in the past to address questions related to malaria transmission. These include investigation of the impact of vaccination and trans-
Fig. 3. Spatial simulation of malaria transmission with an Ro of 6 under 99% coverage with a malaria transmission blocking vaccine. Green and red spots are as in Fig. 1. Large spots (green or red) represent those who have not been malaria transmission blocking vaccine (TBV) immunised; small spots represent individuals who have received TBV immunisation.
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mission blocking vaccination (Saul, 1993; Struchiner et al., 1989, 1990; Halloran et al., 1989). One of the most crucial elements in understanding these effects is the spatial one, i.e. how humans and the vectors of malaria relate to each other in terms of their locations and habits of movement and distribution. Although there is a considerable literature on spatial effects in disease and immunity (Werneck and Struchiner, 1997), spatial analysis in malaria seems to have received little attention. Heterogeneity effects in mosquito-bore diseases have been examined mathematically (Hasebeder and Dye, 1988; Woolhouse et al., 1997) and spatial studies have recently been published in relation to the effects of insecticide-treated bed nets and malaria transmission (Binka et al., 1998; Hii et al., 2001). In this article I present an approach to the analysis of the effects of
transmission blocking vaccines by means of a simple simulation of the spatial characteristics of malaria transmission.
2. Method The size and shape of a zone of malaria transmission is determined by the location of mosquito vector breeding sites and by the dispersal range of mosquito vectors. The intensity of malaria transmission within such a zone is determined by the power of the mosquitoes to become infected from one malaria infected-and-infectious human and to reinfect another human. The situation can be represented by a time and space simulation (Fig. 1). The components of the simulation are:
Fig. 4. Spatial simulation of malaria transmission with an Ro of 6 under 85% coverage with a malaria transmission blocking vaccine.
R. Carter / International Journal for Parasitology 32 (2002) 1617–1624
1. A perimeter within which the mosquito vectors have their aqueous breeding sites (the Vector Breeding Perimeter) (Fig. 1) 2. A human population of discrete individuals dispersed in relation to the mosquito breeding sites (Fig. 1) 3. Perimeters around each human individual within which the mosquitoes are able to transmit a malarial infection from the individual to others (the Infection Transmission Perimeters) (Figs. 1 and 2) The superposition of these three types of spatial element produces a Transmission Zone within the perimeter of which malaria transmission takes place (Fig. 1). In its simplest form, the simulation assumes a fixed duration of infectiousness of each infected individual and a fixed number (Ro) of new infections that will be disseminated to other individuals via the prevailing mosquito vector population within the Infection Transmission Perimeters of individual humans (Fig. 2). The simulation is run by allowing the number of new infections derived from an existing infection (Ro) to be distributed randomly in space within the Infection
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Transmission Perimeter around each infected individual. Successive rounds of transmission can be run in this way.
3. Results and discussion In the simulations presented here I have represented a human population of 348 individuals, dispersed over an area of about 45 km 2 within which is an irregular Vector Breeding Perimeter to an area of around 12 km 2 (Fig. 1). Each individual human is at the centre of a circular Infection Transmission Perimeter with a radius of 1 km. Taking account of the Infection Transmission Perimeters around each individual, the simulated malaria Transmission Zone has a total area of about 35 km 2. I have allocated an Ro of 6. By assuming a duration of infectiousness of each infected individual of about 100 days, three rounds of transmission occur in each year according to this simulation. As presented, the simulation represents the progress of a malaria epidemic in a non-immune human population (Fig. 1). It is compatible with the expectations of the
Fig. 5. (a,b) The results of simulations of malaria transmission and malaria transmission blocking coverage as represented in Figs. 2 and 4: (a) under stable malaria transmission at an Ro of 6; (b) with transmission blocking coverage introduced at the start of a malaria epidemic driven by an Ro of 6. (c) The TBV coverages needed to interrupt malaria transmission at different Ros as calculated using the Ross/Macdonald equation (Macdonald, 1957; Carter, 1999; TDR, 2000).
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Ross/Macdonald equation for the transmission of malaria (Macdonald, 1957). The same simulation model can be used to represent the effects of interventions, e.g. immunisation with a malaria transmission blocking vaccine, which reduce the probability that an individual will transmit his or her malarial infection. In the simulation shown here I have represented an intervention which is 100% effective in reducing the infectivity of an infected individual to mosquitoes. In different simulations the intervention is, however, distributed through the population at different levels of coverage, namely 99% (Fig. 3), 95% (simulation not presented) and 85% (Fig. 4). The reductions in incidence under each level of coverage is presented in Fig. 5a. As with the basic simulation itself,
the levels of coverage which are effective in totally interrupting malaria transmission in relation to the assumed Ro value (Fig. 5c), are compatible with the expectations of the Ross/Macdonald equation (Macdonald, 1957). It is noteworthy that at a level of coverage, 85%, which just failed to achieve complete interruption of transmission under the Ro of 6, case incidence persisted indefinitely at a much reduced level, mainly in one small area of the transmission location. This result shows that levels of coverage that fail to achieve complete interruption of malaria transmission can, nevertheless, sustain transmission at levels below, and even far below, those which existed before the intervention. Fig. 5b shows the results of a simulation in which three
Fig. 6. Spatial simulation of malaria transmission with an Ro of 6 under 85% coverage of half of a zone of malaria transmission with a malaria transmission blocking vaccine.
R. Carter / International Journal for Parasitology 32 (2002) 1617–1624
levels of effective transmission blocking vaccine coverage of 99, 95 and 90% were applied at the start of an epidemic of malaria driven by an Ro of 6. At all these coverages the case incidence is held to relatively very low levels and the epidemic is aborted. In the last type of situation explored here (Fig. 6), transmission blocking vaccine coverage was limited only to the population in one half of the transmission zone. A coverage of 85% was used. While there is some ‘flooding in’ of infection from the unvaccinated population into the area covered by the transmission blocking vaccine, it is clear that the transmission blocking intervention is otherwise effective in the area to which coverage is applied. A boundary of 1 km – the simulated transmission dispersal range of the vector mosquitoes – separates the area in which transmission is unaffected from that in which it is completely interrupted. The simulation represents the important fact that interventions, such as transmission blocking vaccines, that aim to prevent the spread of malarial infection, are themselves effective at a strictly local level. Moreover, and crucially, their effectiveness is largely insulated from malaria transmission taking place beyond the area of coverage, except at the interface. Here ‘flood-in’ can take place, but only to a depth corresponding to the malaria transmission dispersal range (the Infection Transmission Perimeter) of the mosquito vectors in an adjacent malaria transmission zone. The biological principles upon which this simulation has been set up, and the justification for choosing the values used for the biological parameters, most notably the range over which mosquitoes effectively transmit malarial infection (the Infection Transmission Perimeter), have been discussed previously (Carter et al., 2000b) as has the biological and theoretical basis of transmission blocking vaccination in the epidemiological situations to which it could apply (Carter et al., 2000a; TDR, 2000). The quantitative and temporal results of this simple spatial simulation are not different from those achieved by other analyses (Saul, 1993; Macdonald, 1957). The approach is valuable, however, in allowing direct visualisation of the events of malaria transmission as and where they occur on the ground. The simulations allow an intuitive appreciation of the properties of malaria transmission and of the effects of interventions against it terms of the spatial relationships involved. This has relevance in conveying how, and in what circumstances, malaria transmission blocking vaccination can be effective. It shows, for example, that the application of such an intervention can be effective upon a quite small and local scale of a few square kilometres either within, or encompassing, a zone of malaria transmission. The simulation, as presented here, is a very simple version and should be viewed as a prototype. It is hoped that it could form the basis of more elaborate and sophisticated spatial simulations of malaria transmission and malaria transmission control. Perhaps the most important
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practical value of this kind of simulation, however, is that it can communicate its message directly and simply to an audience or target group, such as health planners and other policy makers, not to mention the average non mathematical biological scientist, such as myself. References TDR, 2000. Malaria Transmission Blocking Vaccines: An Ideal Public Good. A Special Report of the UNDP/World Bank/WHO Special Programme for Research and Training in Tropical Diseases (TDR). Publication no. TDR/RBM/MAL/VAC/2000.1, TDR, Geneva. Binka, F.N., Indome, F., Smith, T., 1998. Impact of spatial distribution of permethrin-impregnated bed nets on child mortality in rural northern Ghana. Am. J. Trop. Med. Hyg. 59, 80–85. Carter, R., 1999. Epidemiological considerations for malaria reduction by transmission blocking vaccination. Parassitologia 41, 415–20. Carter, R., Mendis, K.N., Miller, L.H., Molineaux, L., Saul, A., 2000. Malaria transmission blocking vaccines – potentially a major public health tool, but how can their development be supported? Nat. Med. 6, 241–4. Carter, R., Mendis, K., Roberts, D.R., 2000. Spatial targeting of interventions against malaria. Bull. WHO 78, 1401–11. Hackett, L.W., 1937. Malaria in Europe; An Ecological Study, Oxford University Press, London. Halloran, M.E., Struchiner, C.J., Spielman, A., 1989. Modeling malaria vaccines. II: Population effects of stage-specific malaria vaccines dependent on natural boosting. Math. Biosci. 94, 115–49. Hasebeder, G., Dye, C., 1988. Population dynamics of mosquito-borne disease: persistence in a completely heterogeneous environment. Theor. Pop. Biol. 33, 31–53. Hii, J.L., Smith, T., Vounatsou, P., Alexander, N., Mai, A., Ibam, E., Alpers, M.P., 2001. Area effects of bednet use in a malaria-endemic area in Papua New Guinea. Trans. R. Soc. Trop. Med. Hyg. 95, 7–13. League of Nations, 1925. Malaria Commission. Report on its Tour of Investigation in Certain European Countries in 1924, League of Nations, Geneva. Macdonald, G., 1957. The Epidemiology and Control of Malaria, Oxford University Press, London. Mendis, K.N., Sina, B.J., Marchesini, P., Carter, R., 2001. The neglected burden of Plasmodium vivax malaria. Am. J. Trop. Med. Hyg. 64 (Suppl), 97–106. Newman, P., 1965. Malaria Eradication and Population Growth: with Special Reference to Ceylon and British Guiana, , Research Series, Bureau of Public Health Economics, School of Public Health, University of Michigan, Ann Arbor, MI. Pant, C.P., 1988. Malaria control: imagociding. In: Wernsdorfer, W., McGregor, I.A. (Eds.). Malaria, Principles and Practice of Malariology, Churchill Livingstone, Edinburgh, pp. 1173–212. Roberts, D.R., Laughlin, L.L., Hshieh, P., Legters, L.J., 1997. DDT, global strategies, and a malaria control crisis in South America. Emerg. Infect. Dis. 3, 295–302. Saul, A., 1993. Minimal efficacy requirements for malarial vaccines to significantly lower transmission in epidemic or seasonal malaria. Acta Trop. 52, 283–96. Sharma, V.P., 1996. Re-emergence of malaria in India. Indian J. Med. Res. 103, 26–45. Stowers, A., Carter, R., 2001. Current developments in malaria transmission blocking vaccines. Expt. Opin. Biol. Ther. 1, 619–28. Struchiner, C.J., Halloran, M.E., Spielman, A., 1989. Modeling malaria vaccines. I: New uses for old ideas. Math. Biosci. 94, 87–113. Struchiner, C.J., Halloran, M.E., Robins, J.M., Spielman, A., 1990. The behaviour of common measures of association used to assess a vaccination programme under complex disease transmission patterns–a computer simulation study of malaria vaccines. Int. J. Epidemiol. 19, 187–96.
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Werneck, G.L., Struchiner, C.J., 1997. Studies on space-time disease clusters: concepts, techniques, and challenges. Cad. Saude Publica 13, 611–24. Woolhouse, M.E., Dye, C., Etard, J.F., Smith, T., Charlwood, J.D., Garnett, G.P., Hagan, P., Hii, J.L., Ndhlovu, P.D., Quinnell, R.J., Watts, C.H., Chandiwana, S.K., Anderson, R.M., 1997. Heterogeneities in the transmission of infectious agents: implications for the design of control programs. Proc. Natl. Acad. Sci. USA 94, 338–42.
World Health Organisation, 2002p. A Message to Share: The Fight Against Malaria in Vietnam. Prepared by C. Schuftan, WHO Western Pacific Regional Office. Yip, K., 1998. Antimalarial work in China: a historical perspective. Parassitologia 40, 29–38.
Invited review
Spatial simulation of malaria transmission and its control by malaria transmission blocking vaccination Richard Carter* Division of Biological Sciences, ICAPB, University of Edinburgh, West Mains Road, Edinburgh EH9 3JT, UK Received 18 April 2002; received in revised form 30 July 2002; accepted 13 August 2002
Abstract A simple, visual representation of spatial aspects of malaria transmission in successive snap-shots in time, is presented. The spatial components of the simulation involve (i) the identification of mosquito vector breeding sites of defined shape and area, (ii) the identification of a zone of malaria transmission determined by the shapes and areas of the vector breeding sites and the distance from these sites that the mosquitoes disperse, (iii) a human population dispersed in relation to the malaria transmission zone, (iv) perimeters around each individual human within which his or her infection can be transmitted by the local vector mosquitoes. The intensity of transmission within a malaria transmission zone is given by a number which is the number of new cases of malaria that each existing case will distribute through the human population within the duration of an infection. The simulation has been used here to examine the effects of vaccination against malaria transmission. Different levels of vaccine coverage are represented under endemic and epidemic malaria. The consequences of full or partial coverage of a zone of malaria transmission are also examined. The results are numerically compatible with the predictions of previous simple mathematical simulations of malaria transmission and interventions. The present simulation allows the nature of malaria transmission and the effects of interventions to be communicated easily and directly to an audience. It could have practical value in discussions of malaria control strategies with health planners. q 2002 Published by Elsevier Science Ltd. on behalf of Australian Society for Parasitology Inc. Keywords: Malaria transmission; Spatial simulation; Malaria transmission blocking vaccine
1. Introduction Interventions to prevent or reduce the transmission of malaria are amongst the oldest and most effective public health measures. In Italy in the early 19th century, long before the underlying facts of malaria transmission were known, legislation required that irrigated land be situated at least 500 m from rural habitations and at least 8 km from towns (Carter et al., 2000b). In the 20th century one of the more important and successful interventions in the history of public health was the application of house spraying with residual insecticides to reduce the transmission of malaria (Roberts et al., 1997; Sharma, 1996; Newman, 1965). Both of these approaches operated by reducing the probability that the mosquito vectors of malaria could transmit malarial infection from one human being to another. The first approach simply reduced human/mosquito contact towards zero by ensuring that human populations were beyond the range that the vector mosquitoes could disperse from their aqueous breeding sites. The second, residual insecticide * Tel.: 144-131-650-5558; fax: 144-131-668-3861. E-mail address: [email protected] (R. Carter).
spraying, either repelled the mosquitoes from human contact (Roberts, D., personal communication) or killed them where they came into most frequent human contact – in the home (Pant, 1988). Another approach towards the same end is to reduce the infectivity of the human population itself to mosquitoes. This has been tried in the past through the widespread distribution and use of antimalarial drugs (Hackett, 1937; League of Nations, 1925; World Health Organisation, in press; Yip, 1998). Combined with other measures, such as those described above, it has probably contributed to malaria control in several campaigns. The use of antimalarial drugs for malaria transmission control is, however, by and large not very effective compared with those which directly affect the human/mosquito interaction. The reason is that it is virtually impossible, using drugs alone, to ensure that a malaria-infected individual has received the necessary treatment at the time at which he or she is infectious to mosquitoes (Mendis et al., 2001). In endemic situations drug cover can only be intermittent at best unless permanent drug prophylaxis is employed across an entire endemic human population. This, in most situations, would be neither practical nor affordable.
0020-7519/02/$20.00 q 2002 Published by Elsevier Science Ltd. on behalf of Australian Society for Parasitology Inc. PII: S 0020-751 9(02)00190-X
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R. Carter / International Journal for Parasitology 32 (2002) 1617–1624
There is, however, a potential alternative which could overcome most of the principle problems of using drugs to suppress the infectivity of human populations to mosquitoes. It is the development and deployment of vaccines that were designed to limit the transmission of human malarial infections to mosquitoes - malaria transmission blocking vaccines (TDR, 2000; Carter et al., 2000a). To be effective such a vaccine should have the following properties. It should largely or completely eliminate the infectivity of malaria-infected individuals at all times during the course of a blood infection. This would be from the first moments of the appearance of the infectious sexual stage parasites in the blood, and throughout a subsequent blood infection,
which in the case of malaria can continue intermittently for a year and more. The transmission blocking efficacy of the vaccine should be of at least several years. Such vaccines, the malaria transmission blocking vaccines, are under development for human trials (TDR, 2000; Carter et al., 2000a; Stowers and Carter, 2001). Malaria transmission blocking vaccines are based upon the sexual stage antigens of malaria parasites that are expressed in the mosquito mid gut and which can, therefore, be targeted by antibodies which are ingested by a mosquito during a blood meal. There are two general classes of these target antigens. They are (i) the gamete surface antigens, notably the Ps230 and Ps48/45 families, and (ii) the zygote/ookinete
Fig. 1. Basic set-up for a spatial simulation of malaria transmission (see text). Green spots represent uninfected individuals; red spots represent individuals who have become infected with malaria in the currently represented round of infection and transmission.
R. Carter / International Journal for Parasitology 32 (2002) 1617–1624
Fig. 2. Infection transmission perimeters showing different Ro values (see text).
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surface antigens, notably the Ps25 and Ps28 families (TDR, 2000; Carter et al., 2000a; Stowers and Carter, 2001). Antigens of the first class are expressed in the gametocytes in the blood circulation. Because of this, antibodies against these antigens are strongly boosted by the blood infection itself (Carter et al., 2000a). This is a great potential advantage to the development of Ps230 and Ps48/45 group antigens for malaria transmission blocking vaccines. The antigens of the second class, Ps25 and Ps28, are expressed in significant amounts only on the mosquito mid gut stages of the parasites. They are, therefore, not available to boost immunity against them during blood infections. Each of these antigen types is under consideration for transmission blocking vaccine (Stowers and Carter, 2001). In trying to predict the likely impact and the epidemiological circumstances under which malaria transmission blocking vaccination could be usefully deployed, it is very important to understand the relevant principles of malaria transmission. Analyses have been developed in the past to address questions related to malaria transmission. These include investigation of the impact of vaccination and trans-
Fig. 3. Spatial simulation of malaria transmission with an Ro of 6 under 99% coverage with a malaria transmission blocking vaccine. Green and red spots are as in Fig. 1. Large spots (green or red) represent those who have not been malaria transmission blocking vaccine (TBV) immunised; small spots represent individuals who have received TBV immunisation.
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mission blocking vaccination (Saul, 1993; Struchiner et al., 1989, 1990; Halloran et al., 1989). One of the most crucial elements in understanding these effects is the spatial one, i.e. how humans and the vectors of malaria relate to each other in terms of their locations and habits of movement and distribution. Although there is a considerable literature on spatial effects in disease and immunity (Werneck and Struchiner, 1997), spatial analysis in malaria seems to have received little attention. Heterogeneity effects in mosquito-bore diseases have been examined mathematically (Hasebeder and Dye, 1988; Woolhouse et al., 1997) and spatial studies have recently been published in relation to the effects of insecticide-treated bed nets and malaria transmission (Binka et al., 1998; Hii et al., 2001). In this article I present an approach to the analysis of the effects of
transmission blocking vaccines by means of a simple simulation of the spatial characteristics of malaria transmission.
2. Method The size and shape of a zone of malaria transmission is determined by the location of mosquito vector breeding sites and by the dispersal range of mosquito vectors. The intensity of malaria transmission within such a zone is determined by the power of the mosquitoes to become infected from one malaria infected-and-infectious human and to reinfect another human. The situation can be represented by a time and space simulation (Fig. 1). The components of the simulation are:
Fig. 4. Spatial simulation of malaria transmission with an Ro of 6 under 85% coverage with a malaria transmission blocking vaccine.
R. Carter / International Journal for Parasitology 32 (2002) 1617–1624
1. A perimeter within which the mosquito vectors have their aqueous breeding sites (the Vector Breeding Perimeter) (Fig. 1) 2. A human population of discrete individuals dispersed in relation to the mosquito breeding sites (Fig. 1) 3. Perimeters around each human individual within which the mosquitoes are able to transmit a malarial infection from the individual to others (the Infection Transmission Perimeters) (Figs. 1 and 2) The superposition of these three types of spatial element produces a Transmission Zone within the perimeter of which malaria transmission takes place (Fig. 1). In its simplest form, the simulation assumes a fixed duration of infectiousness of each infected individual and a fixed number (Ro) of new infections that will be disseminated to other individuals via the prevailing mosquito vector population within the Infection Transmission Perimeters of individual humans (Fig. 2). The simulation is run by allowing the number of new infections derived from an existing infection (Ro) to be distributed randomly in space within the Infection
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Transmission Perimeter around each infected individual. Successive rounds of transmission can be run in this way.
3. Results and discussion In the simulations presented here I have represented a human population of 348 individuals, dispersed over an area of about 45 km 2 within which is an irregular Vector Breeding Perimeter to an area of around 12 km 2 (Fig. 1). Each individual human is at the centre of a circular Infection Transmission Perimeter with a radius of 1 km. Taking account of the Infection Transmission Perimeters around each individual, the simulated malaria Transmission Zone has a total area of about 35 km 2. I have allocated an Ro of 6. By assuming a duration of infectiousness of each infected individual of about 100 days, three rounds of transmission occur in each year according to this simulation. As presented, the simulation represents the progress of a malaria epidemic in a non-immune human population (Fig. 1). It is compatible with the expectations of the
Fig. 5. (a,b) The results of simulations of malaria transmission and malaria transmission blocking coverage as represented in Figs. 2 and 4: (a) under stable malaria transmission at an Ro of 6; (b) with transmission blocking coverage introduced at the start of a malaria epidemic driven by an Ro of 6. (c) The TBV coverages needed to interrupt malaria transmission at different Ros as calculated using the Ross/Macdonald equation (Macdonald, 1957; Carter, 1999; TDR, 2000).
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Ross/Macdonald equation for the transmission of malaria (Macdonald, 1957). The same simulation model can be used to represent the effects of interventions, e.g. immunisation with a malaria transmission blocking vaccine, which reduce the probability that an individual will transmit his or her malarial infection. In the simulation shown here I have represented an intervention which is 100% effective in reducing the infectivity of an infected individual to mosquitoes. In different simulations the intervention is, however, distributed through the population at different levels of coverage, namely 99% (Fig. 3), 95% (simulation not presented) and 85% (Fig. 4). The reductions in incidence under each level of coverage is presented in Fig. 5a. As with the basic simulation itself,
the levels of coverage which are effective in totally interrupting malaria transmission in relation to the assumed Ro value (Fig. 5c), are compatible with the expectations of the Ross/Macdonald equation (Macdonald, 1957). It is noteworthy that at a level of coverage, 85%, which just failed to achieve complete interruption of transmission under the Ro of 6, case incidence persisted indefinitely at a much reduced level, mainly in one small area of the transmission location. This result shows that levels of coverage that fail to achieve complete interruption of malaria transmission can, nevertheless, sustain transmission at levels below, and even far below, those which existed before the intervention. Fig. 5b shows the results of a simulation in which three
Fig. 6. Spatial simulation of malaria transmission with an Ro of 6 under 85% coverage of half of a zone of malaria transmission with a malaria transmission blocking vaccine.
R. Carter / International Journal for Parasitology 32 (2002) 1617–1624
levels of effective transmission blocking vaccine coverage of 99, 95 and 90% were applied at the start of an epidemic of malaria driven by an Ro of 6. At all these coverages the case incidence is held to relatively very low levels and the epidemic is aborted. In the last type of situation explored here (Fig. 6), transmission blocking vaccine coverage was limited only to the population in one half of the transmission zone. A coverage of 85% was used. While there is some ‘flooding in’ of infection from the unvaccinated population into the area covered by the transmission blocking vaccine, it is clear that the transmission blocking intervention is otherwise effective in the area to which coverage is applied. A boundary of 1 km – the simulated transmission dispersal range of the vector mosquitoes – separates the area in which transmission is unaffected from that in which it is completely interrupted. The simulation represents the important fact that interventions, such as transmission blocking vaccines, that aim to prevent the spread of malarial infection, are themselves effective at a strictly local level. Moreover, and crucially, their effectiveness is largely insulated from malaria transmission taking place beyond the area of coverage, except at the interface. Here ‘flood-in’ can take place, but only to a depth corresponding to the malaria transmission dispersal range (the Infection Transmission Perimeter) of the mosquito vectors in an adjacent malaria transmission zone. The biological principles upon which this simulation has been set up, and the justification for choosing the values used for the biological parameters, most notably the range over which mosquitoes effectively transmit malarial infection (the Infection Transmission Perimeter), have been discussed previously (Carter et al., 2000b) as has the biological and theoretical basis of transmission blocking vaccination in the epidemiological situations to which it could apply (Carter et al., 2000a; TDR, 2000). The quantitative and temporal results of this simple spatial simulation are not different from those achieved by other analyses (Saul, 1993; Macdonald, 1957). The approach is valuable, however, in allowing direct visualisation of the events of malaria transmission as and where they occur on the ground. The simulations allow an intuitive appreciation of the properties of malaria transmission and of the effects of interventions against it terms of the spatial relationships involved. This has relevance in conveying how, and in what circumstances, malaria transmission blocking vaccination can be effective. It shows, for example, that the application of such an intervention can be effective upon a quite small and local scale of a few square kilometres either within, or encompassing, a zone of malaria transmission. The simulation, as presented here, is a very simple version and should be viewed as a prototype. It is hoped that it could form the basis of more elaborate and sophisticated spatial simulations of malaria transmission and malaria transmission control. Perhaps the most important
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practical value of this kind of simulation, however, is that it can communicate its message directly and simply to an audience or target group, such as health planners and other policy makers, not to mention the average non mathematical biological scientist, such as myself. References TDR, 2000. Malaria Transmission Blocking Vaccines: An Ideal Public Good. A Special Report of the UNDP/World Bank/WHO Special Programme for Research and Training in Tropical Diseases (TDR). Publication no. TDR/RBM/MAL/VAC/2000.1, TDR, Geneva. Binka, F.N., Indome, F., Smith, T., 1998. Impact of spatial distribution of permethrin-impregnated bed nets on child mortality in rural northern Ghana. Am. J. Trop. Med. Hyg. 59, 80–85. Carter, R., 1999. Epidemiological considerations for malaria reduction by transmission blocking vaccination. Parassitologia 41, 415–20. Carter, R., Mendis, K.N., Miller, L.H., Molineaux, L., Saul, A., 2000. Malaria transmission blocking vaccines – potentially a major public health tool, but how can their development be supported? Nat. Med. 6, 241–4. Carter, R., Mendis, K., Roberts, D.R., 2000. Spatial targeting of interventions against malaria. Bull. WHO 78, 1401–11. Hackett, L.W., 1937. Malaria in Europe; An Ecological Study, Oxford University Press, London. Halloran, M.E., Struchiner, C.J., Spielman, A., 1989. Modeling malaria vaccines. II: Population effects of stage-specific malaria vaccines dependent on natural boosting. Math. Biosci. 94, 115–49. Hasebeder, G., Dye, C., 1988. Population dynamics of mosquito-borne disease: persistence in a completely heterogeneous environment. Theor. Pop. Biol. 33, 31–53. Hii, J.L., Smith, T., Vounatsou, P., Alexander, N., Mai, A., Ibam, E., Alpers, M.P., 2001. Area effects of bednet use in a malaria-endemic area in Papua New Guinea. Trans. R. Soc. Trop. Med. Hyg. 95, 7–13. League of Nations, 1925. Malaria Commission. Report on its Tour of Investigation in Certain European Countries in 1924, League of Nations, Geneva. Macdonald, G., 1957. The Epidemiology and Control of Malaria, Oxford University Press, London. Mendis, K.N., Sina, B.J., Marchesini, P., Carter, R., 2001. The neglected burden of Plasmodium vivax malaria. Am. J. Trop. Med. Hyg. 64 (Suppl), 97–106. Newman, P., 1965. Malaria Eradication and Population Growth: with Special Reference to Ceylon and British Guiana, , Research Series, Bureau of Public Health Economics, School of Public Health, University of Michigan, Ann Arbor, MI. Pant, C.P., 1988. Malaria control: imagociding. In: Wernsdorfer, W., McGregor, I.A. (Eds.). Malaria, Principles and Practice of Malariology, Churchill Livingstone, Edinburgh, pp. 1173–212. Roberts, D.R., Laughlin, L.L., Hshieh, P., Legters, L.J., 1997. DDT, global strategies, and a malaria control crisis in South America. Emerg. Infect. Dis. 3, 295–302. Saul, A., 1993. Minimal efficacy requirements for malarial vaccines to significantly lower transmission in epidemic or seasonal malaria. Acta Trop. 52, 283–96. Sharma, V.P., 1996. Re-emergence of malaria in India. Indian J. Med. Res. 103, 26–45. Stowers, A., Carter, R., 2001. Current developments in malaria transmission blocking vaccines. Expt. Opin. Biol. Ther. 1, 619–28. Struchiner, C.J., Halloran, M.E., Spielman, A., 1989. Modeling malaria vaccines. I: New uses for old ideas. Math. Biosci. 94, 87–113. Struchiner, C.J., Halloran, M.E., Robins, J.M., Spielman, A., 1990. The behaviour of common measures of association used to assess a vaccination programme under complex disease transmission patterns–a computer simulation study of malaria vaccines. Int. J. Epidemiol. 19, 187–96.
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