Method To Estimate Relative Transmission Efficiencies of Anopheles Species (Diptera: Culicidae) in Human Malaria Transmission CHANDANA MENDIS, PUSHPA R. J. HERATH,* JAGATH RAJAKARUNA, SUDATH WEERASINGHE, ASOKA C. GAMAGE-MENDIS, KAMINI N. MENDIS, AND ARJUNA P. K. DE ZOYSA* Malaria Research Unit, Department of Parasitology, Faculty of Medicine, University of Colombo, Kynsey Road, Colombo 8, Sri Lanka
KEY WORDS Insecta, Anopheles spp., malaria, mathematical modeling
Anopheles culicifacies Giles is considered to be the principal vector of human malaria in Sri Lanka (Carter & Jacocks 1929, Wickramasinghe 1981). However, recent studies have incriminated several other anopheline species as vectors of malaria (Herath et al. 1983, Mendis et al. 1990). During an epidemiological study of malaria in Kataragama, a region where predominantly P. vivax is endemic, entomological parameters were monitored for 17 mo through two consecutive transmission seasons (Mendis et al. 1990). Using five adult mosquito sampling techniques (WHO 1975), 10 anopheline species (including An. culicifacies) were found to be prevalent in the study area, eight of which fed on humans. Six of these eight species were found to be infected with sporozoites of either P. vivax or P. falciparum (Mendis et al. 1990), indicating that they contributed to transmission. Transmission of malaria by multiple vectors has been recognized elsewhere (e.g., de Arruda et al. 1986, Baker et al. 1987). When several vectors contribute to malaria transmission, quantification using vectorial ca1 2
Entomology Division, Anti-Malaria Campaign, Sri Lanka. The Open University of Sri Lanka, Nugegoda, Sri Lanka.
pacity formulations (Garrett-Jones 1964) requires knowledge of the human blood index, the duration of the gonotrophic cycle, the mortality rate, and the human-biting rate (HBR) of each species. Some of these properties, in particular mortality and the human blood index of exophilic species, are difficult to measure reliably in the field (Molineaux et al. 1988). Furthermore, vector abundance in Sri Lanka is relatively low (Herath et al. 1986) compared with Africa (Molineaux & Gramiccia 1980, Del Giudice et al. 1987) or Papua New Guinea (Burkot et al. 1988), making it even more difficult to estimate vector population parameters reliably. In addition to the parameters used in the vectorial capacity equation (GarrettJones 1964), there also may be fundamental differences among species in vector competence to support the sporogonic development of the parasite (Macdonald 1957, Collins et al. 1985, De Zoysa et al. 1988, Kasap 1990). Several attempts previously have been made to overcome these problems through indirect estimation of the vectorial capacity of the vectors (Dye 1986, Graves et al. 1990). We have derived a mathematical expression to calculate the relative transmission efficiency of an anopheline species with respect to a standard,
0022-2585/92/0188-0196$02.00/0 © 1992 Entomological Society of America
Downloaded from http://jme.oxfordjournals.org/ by guest on June 9, 2016
J. Med. Entomol. 29(2): 188-196 (1992) ABSTRACT A mathematical expression was derived to estimate the relative malaria transmission efficiency of an anopheline species with respect to a standard well-characterized species for which all vector parameters can be sufficiently determined. The method is particularly useful in situations where multiple anopheline species contribute to human malaria transmission and requires the estimation of the man-biting rate, the sporozoite rate, and the human malaria incidence. Under stable conditions of vector abundance, the average sporozoite rate in a species during a transmission season would by itself reflect its relative transmission efficiency. This "efficiency" then was used to calculate the "effective human-biting rate"; i.e., the human-biting rate of that species if it were to have ecological properties identical to those of the standard species. The standard well-characterized species then could be used with the effective human-biting rate of all species to quantify transmission, thus overcoming the need to measure vector parameters for all anopheline species contributing to transmission. An expression also was derived to calculate the relative contribution made by each species to malaria transmission. The usefulness of this method was illustrated using entomological and epidemiological data from Kataragama, Sri Lanka.
March 1992
MENDIS ET AL.: MALARIA TRANSMISSION EFFICIENCIES OF ANOPHELINES
well-characterized species. This method requires data on the HBR, average sporozoite rate, and the human malaria incidence in the locality. Using relative transmission efficiency, we calculated an "effective HBR"; i.e., the HBR of that species if it were to have properties identical to those of a standard species. The properties of the standard, well-characterized species then could be used with the effective MBR of all vector species to estimate a combined vectorial capacity of anopheline useful in quantifying malaria transmission. Materials and Methods
were obtained from fewer cases, stained with Giemsa, and examined (400 microscopic fields) for the presence of malarial parasites. Four mass blood surveys also were carried out at approximately 6-mo intervals to monitor the prevalence of P. vivax and P. falciparum in the study population and to evaluate the sensitivity of the passive case detection program (Mendis et al. 1990). Definition of Relative Transmission Efficiency. Transmission efficiency (eik) was defined as the ability of the i th species to transmit malaria relative to a kth species; i.e., if n{ and nk are the number of expected sporozoite inoculations resulting from a single infectious blood meal of the i th and kth species, respectively, then ik
nk If the vector competence of an i th species, Ct, is the species-specific probability of developing sporozoites from a single infectious bite and a{ and fit are the man-biting habit and mortality rate of the i th species, respectively, and if we assume a constant mortality rate with a daily survival probability of e~M, the number of resulting inoculations will be
and, similarly for the kth species, Ck-ak nk =
then (1) The vectorial capacity expression of GarrettJones (1964) assumes that if a female mosquito takes an infectious blood meal and survives the incubation period of parasite (defined as r), it will in every case develop sporozoites; i.e., the probability of developing sporozoites is always 1, or C{ = e~^r. However, this is unlikely to be the case (Macdonald 1957, Graves et al. 1990). To account for this difference, we assume the more general form
C
— R •s>~lJLT
i - b{e
^ ,
(O\
[1)
where B{ is a species-specific biological competence factor describing the ability of the vector to sustain parasite development independent of its mortality. B{ may be defined strictly as the conditional probability that a vector species i will develop sporozoites from a single infectious bite, given that it survives the subsequent incubation period of the parasite. Mathematical Expression for Efficiency. Because it is difficult to determine accurate values
Downloaded from http://jme.oxfordjournals.org/ by guest on June 9, 2016
Study Area. The study area comprised seven contiguous villages (population size, 3,625) within an area of—10 km2 located at Kataragama, a P. vivax-endemic area in southern Sri Lanka described previously by Mendis et al. (1990). Recently, an epidemic of P. falciparum occurred in this P. tnoax-endemic area (Samarasinghe 1986, 1987). Estimation of HBR. A total of 52 all-night and 204 partial-night human bait collections was made at randomly selected houses (indoors and outdoors) to determine the HBR of anophelines in three representative villages from November 1986 to March 1988. Four humans were employed in collecting mosquitoes on one full night (1800-0600 hours) and four partial nights (18002100 hours, two before and two after the fullnight collection) within 21 d/mo in each village. Mosquitoes attempting to feed on collectors were caught using glass aspirators and flashlights and kept in net-covered paper cups. All anopheline mosquitoes were identified to species and stored frozen at -20°C for later testing for infection by an enzyme-linked immunosorbent assay (ELISA). The HBR was standardized as the number of female mosquitoes collected per man per night. Partial-night collections were standardized using the ratio of collection rates (mosquitoes per hour) from 1800 to 2100 hours to that of from 1800 to 0600 hours of the full-night collection. Enzyme-Linked Immunosorbent Assay (ELISA). The ELISA developed by Burkot et al. (1984) and Wirtz et al. (1985) was used to detect the presence of P. falciparum and P. vivax circumsporozoite antigen in the thoraces of mosquitoes collected at human baits. Laboratory-fed anophelines (glands positive for sporozoites after feeding on P. vivax and P. falciparum gametocyte carriers) and recombinant P. falciparum and P. vivax circumsporozoite peptides (synthetic) were used as positive controls. The ELISA positivity rate was used to estimate sporozoite rates for each species of mosquito. Monitoring Malaria Incidence. Passive case detection was carried out to screen fever patients in the seven villages. Thick- and thin-blood films
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JOURNAL OF MEDICAL ENTOMOLOGY
for Ci} ao and /xt- of each species during a transmission season, we outline here a method to obtain an estimate for eik using parameters that normally are monitored during a malaria epidemic. We made the following assumptions for a transmission season (e.g., wet and dry seasons): (a) the terms ai} ^{, and C{ are relatively constant, (b) the number of mosquitoes infected during a transmission season are much higher than those remaining infected at the end of a season, and (c) sporozoite rates are low Thus, spr{ sprk •
MBRJt)
0(t) [A2]
MBR.
[A4] -*CN.
1
1 B i (t)
[A12]"
(3) R
spr{/sprk .
(4) Estimating Vectorial Capacity Using eik. The number of potential inoculations that arise out of a single infective bite of t th species is C f a,//i,. The daily rate at which potentially new inoculations arise from a single infective human (Ir), therefore, is
1
[A61
[A7]
e 1k U10]
Fig. 1. Schematic diagram of steps involved in the calculation of elk and contribution of different anopheline species, using the MBR, sporozoite rate, and the malaria incidence. Equations are given in the Appendix.
By substituting for terms HBR^t) and spr{(t) with terms in equations A2, A3, and A6 (see Appendix), we can show that and that the percentage contribution of the i th species is x 100.
HBR, = Ir. th
Substituting of the f species and the vector properties of the kth standard species (equation 1), for term C,a,//^ with elk, we can show that
M*
(5)
This expression defines an effective HBR of i th species being equal to (e?/tHBR
KEY WORDS Insecta, Anopheles spp., malaria, mathematical modeling
Anopheles culicifacies Giles is considered to be the principal vector of human malaria in Sri Lanka (Carter & Jacocks 1929, Wickramasinghe 1981). However, recent studies have incriminated several other anopheline species as vectors of malaria (Herath et al. 1983, Mendis et al. 1990). During an epidemiological study of malaria in Kataragama, a region where predominantly P. vivax is endemic, entomological parameters were monitored for 17 mo through two consecutive transmission seasons (Mendis et al. 1990). Using five adult mosquito sampling techniques (WHO 1975), 10 anopheline species (including An. culicifacies) were found to be prevalent in the study area, eight of which fed on humans. Six of these eight species were found to be infected with sporozoites of either P. vivax or P. falciparum (Mendis et al. 1990), indicating that they contributed to transmission. Transmission of malaria by multiple vectors has been recognized elsewhere (e.g., de Arruda et al. 1986, Baker et al. 1987). When several vectors contribute to malaria transmission, quantification using vectorial ca1 2
Entomology Division, Anti-Malaria Campaign, Sri Lanka. The Open University of Sri Lanka, Nugegoda, Sri Lanka.
pacity formulations (Garrett-Jones 1964) requires knowledge of the human blood index, the duration of the gonotrophic cycle, the mortality rate, and the human-biting rate (HBR) of each species. Some of these properties, in particular mortality and the human blood index of exophilic species, are difficult to measure reliably in the field (Molineaux et al. 1988). Furthermore, vector abundance in Sri Lanka is relatively low (Herath et al. 1986) compared with Africa (Molineaux & Gramiccia 1980, Del Giudice et al. 1987) or Papua New Guinea (Burkot et al. 1988), making it even more difficult to estimate vector population parameters reliably. In addition to the parameters used in the vectorial capacity equation (GarrettJones 1964), there also may be fundamental differences among species in vector competence to support the sporogonic development of the parasite (Macdonald 1957, Collins et al. 1985, De Zoysa et al. 1988, Kasap 1990). Several attempts previously have been made to overcome these problems through indirect estimation of the vectorial capacity of the vectors (Dye 1986, Graves et al. 1990). We have derived a mathematical expression to calculate the relative transmission efficiency of an anopheline species with respect to a standard,
0022-2585/92/0188-0196$02.00/0 © 1992 Entomological Society of America
Downloaded from http://jme.oxfordjournals.org/ by guest on June 9, 2016
J. Med. Entomol. 29(2): 188-196 (1992) ABSTRACT A mathematical expression was derived to estimate the relative malaria transmission efficiency of an anopheline species with respect to a standard well-characterized species for which all vector parameters can be sufficiently determined. The method is particularly useful in situations where multiple anopheline species contribute to human malaria transmission and requires the estimation of the man-biting rate, the sporozoite rate, and the human malaria incidence. Under stable conditions of vector abundance, the average sporozoite rate in a species during a transmission season would by itself reflect its relative transmission efficiency. This "efficiency" then was used to calculate the "effective human-biting rate"; i.e., the human-biting rate of that species if it were to have ecological properties identical to those of the standard species. The standard well-characterized species then could be used with the effective human-biting rate of all species to quantify transmission, thus overcoming the need to measure vector parameters for all anopheline species contributing to transmission. An expression also was derived to calculate the relative contribution made by each species to malaria transmission. The usefulness of this method was illustrated using entomological and epidemiological data from Kataragama, Sri Lanka.
March 1992
MENDIS ET AL.: MALARIA TRANSMISSION EFFICIENCIES OF ANOPHELINES
well-characterized species. This method requires data on the HBR, average sporozoite rate, and the human malaria incidence in the locality. Using relative transmission efficiency, we calculated an "effective HBR"; i.e., the HBR of that species if it were to have properties identical to those of a standard species. The properties of the standard, well-characterized species then could be used with the effective MBR of all vector species to estimate a combined vectorial capacity of anopheline useful in quantifying malaria transmission. Materials and Methods
were obtained from fewer cases, stained with Giemsa, and examined (400 microscopic fields) for the presence of malarial parasites. Four mass blood surveys also were carried out at approximately 6-mo intervals to monitor the prevalence of P. vivax and P. falciparum in the study population and to evaluate the sensitivity of the passive case detection program (Mendis et al. 1990). Definition of Relative Transmission Efficiency. Transmission efficiency (eik) was defined as the ability of the i th species to transmit malaria relative to a kth species; i.e., if n{ and nk are the number of expected sporozoite inoculations resulting from a single infectious blood meal of the i th and kth species, respectively, then ik
nk If the vector competence of an i th species, Ct, is the species-specific probability of developing sporozoites from a single infectious bite and a{ and fit are the man-biting habit and mortality rate of the i th species, respectively, and if we assume a constant mortality rate with a daily survival probability of e~M, the number of resulting inoculations will be
and, similarly for the kth species, Ck-ak nk =
then (1) The vectorial capacity expression of GarrettJones (1964) assumes that if a female mosquito takes an infectious blood meal and survives the incubation period of parasite (defined as r), it will in every case develop sporozoites; i.e., the probability of developing sporozoites is always 1, or C{ = e~^r. However, this is unlikely to be the case (Macdonald 1957, Graves et al. 1990). To account for this difference, we assume the more general form
C
— R •s>~lJLT
i - b{e
^ ,
(O\
[1)
where B{ is a species-specific biological competence factor describing the ability of the vector to sustain parasite development independent of its mortality. B{ may be defined strictly as the conditional probability that a vector species i will develop sporozoites from a single infectious bite, given that it survives the subsequent incubation period of the parasite. Mathematical Expression for Efficiency. Because it is difficult to determine accurate values
Downloaded from http://jme.oxfordjournals.org/ by guest on June 9, 2016
Study Area. The study area comprised seven contiguous villages (population size, 3,625) within an area of—10 km2 located at Kataragama, a P. vivax-endemic area in southern Sri Lanka described previously by Mendis et al. (1990). Recently, an epidemic of P. falciparum occurred in this P. tnoax-endemic area (Samarasinghe 1986, 1987). Estimation of HBR. A total of 52 all-night and 204 partial-night human bait collections was made at randomly selected houses (indoors and outdoors) to determine the HBR of anophelines in three representative villages from November 1986 to March 1988. Four humans were employed in collecting mosquitoes on one full night (1800-0600 hours) and four partial nights (18002100 hours, two before and two after the fullnight collection) within 21 d/mo in each village. Mosquitoes attempting to feed on collectors were caught using glass aspirators and flashlights and kept in net-covered paper cups. All anopheline mosquitoes were identified to species and stored frozen at -20°C for later testing for infection by an enzyme-linked immunosorbent assay (ELISA). The HBR was standardized as the number of female mosquitoes collected per man per night. Partial-night collections were standardized using the ratio of collection rates (mosquitoes per hour) from 1800 to 2100 hours to that of from 1800 to 0600 hours of the full-night collection. Enzyme-Linked Immunosorbent Assay (ELISA). The ELISA developed by Burkot et al. (1984) and Wirtz et al. (1985) was used to detect the presence of P. falciparum and P. vivax circumsporozoite antigen in the thoraces of mosquitoes collected at human baits. Laboratory-fed anophelines (glands positive for sporozoites after feeding on P. vivax and P. falciparum gametocyte carriers) and recombinant P. falciparum and P. vivax circumsporozoite peptides (synthetic) were used as positive controls. The ELISA positivity rate was used to estimate sporozoite rates for each species of mosquito. Monitoring Malaria Incidence. Passive case detection was carried out to screen fever patients in the seven villages. Thick- and thin-blood films
189
190
Vol. 29, no. 2
JOURNAL OF MEDICAL ENTOMOLOGY
for Ci} ao and /xt- of each species during a transmission season, we outline here a method to obtain an estimate for eik using parameters that normally are monitored during a malaria epidemic. We made the following assumptions for a transmission season (e.g., wet and dry seasons): (a) the terms ai} ^{, and C{ are relatively constant, (b) the number of mosquitoes infected during a transmission season are much higher than those remaining infected at the end of a season, and (c) sporozoite rates are low Thus, spr{ sprk •
MBRJt)
0(t) [A2]
MBR.
[A4] -*CN.
1
1 B i (t)
[A12]"
(3) R
spr{/sprk .
(4) Estimating Vectorial Capacity Using eik. The number of potential inoculations that arise out of a single infective bite of t th species is C f a,//i,. The daily rate at which potentially new inoculations arise from a single infective human (Ir), therefore, is
1
[A61
[A7]
e 1k U10]
Fig. 1. Schematic diagram of steps involved in the calculation of elk and contribution of different anopheline species, using the MBR, sporozoite rate, and the malaria incidence. Equations are given in the Appendix.
By substituting for terms HBR^t) and spr{(t) with terms in equations A2, A3, and A6 (see Appendix), we can show that and that the percentage contribution of the i th species is x 100.
HBR, = Ir. th
Substituting of the f species and the vector properties of the kth standard species (equation 1), for term C,a,//^ with elk, we can show that
M*
(5)
This expression defines an effective HBR of i th species being equal to (e?/tHBR
