Using Mullas Formula to Estimate Percent Control

William K. Reisen

Abstract In California, the endemic mosquito borne encephalitides, including West Nile virus, are contained by special districts using integrated vector management programs. These agencies combine public education, source reduction and proactive larval control to suppress mosquito abundance to the point where tangential transmission of virus to humans is rare or unlikely. However, when these methods in concert fail to prevent enzootic amplification and the risk of human infection becomes eminent or is on-going, emergency adulticide applications of pyrethrin compounds are used to interrupt transmission. The efficacy of these applications has become controversial and some cities have opted to not apply adul-ticides. The current paper describes how a formula developed Dr. Mir Mulla some 40 years ago is still useful in solving contemporary problems of estimating percent control, a statistic useful in evaluating intervention efficacy. This simple but effective equation accounts for changes in both control and treated populations and thereby can be applied in dynamic situations where abundance is not stable. Examples are presented from ground and aerial experimental applications in Riverside County and from emergency interventions in Sacramento County in 2005 and Yolo County in 2006.

Keywords Mulla's formula ■ Mosquito control ■ Encephalitis ■ California

Introduction

The on-going West Nile virus (WNV) epidemic is the largest recorded mosquito-borne encephalitis virus outbreak ever recorded in North America, the largest WNV epidemic documented globally, and has become the leading cause of infectious

Center for Vectorborne Diseases, Department of Pathology, Microbiology and Immunology, School of Veterinary Medicine, University of California, Davis, CA 95616, USA e-mail: [email protected]

P.W. Atkinson (ed.), Vector Biology, Ecology and Control, 127

DOI 10.1007/978-90-481-2458-9_9, © Springer Science+Business Media B.V. 2010

neurological disease during the current decade, with >24,000 laboratory confirmed equine and human cases reported (http://diseasemaps.usgs.gov/). In California alone, there have been 2,045 human cases and 53 deaths reported through 2006, and the outbreak has continued into 2007. The rapid invasion of the New World by this African virus occurred in a very short time period, despite the implementation of emergency control measures augmented by federal funding provided by the Centers for Disease Control and Prevention (CDC). WNV clearly has revealed the inability of the United States public health system to contain an invasive zoonosis (Holloway 2000).

WNV is maintained and amplified within a Culex mosquito and avian host cycle (Komar 2003), with tangential transmission to humans and equines which frequently develop serious disease (Hayes et al. 2005). The transmission cycle showing possible options for intervention is shown in Fig. 1. The primary intervention approach has been Integrated Vector Management (IVM). The removal of avian hosts such as American crows and House sparrows does not meet with conservationist as well as general public approval. Personal protection by either staying indoors in a mosquito free environment after dusk or by applying repellents when outdoors can reduce human cases, but does not affect enzootic transmission leaving those who refuse to alter their behavior at risk (Nasci et al. 2001). Similarly, equine vaccination prevents equine cases but does not alter enzootic transmission patterns, regardless of herd immunity levels (Nielsen et al. 2007b).

Various Virus Infection Alter
Fig. 1 Transmission cycle of West Nile virus, showing the various points for possible intervention

In response to various surveillance indicators (Kramer 2007), integrated vector management programs in California utilize an escalating cascade of suppression approaches in an attempt to maintain mosquito population size below thresholds where the risk of human infection is high (Fig. 2). Initially public education and larval control campaigns attempt to suppress populations through larval control, an effort expected to suppress summer populations (Moon 1976). At this early time point, it is not known if viruses will be active, and surveillance is initiated to detect early season amplification. Once enzootic amplification exceeds detection thresholds, proactive control is initiated, including intensified larval control and adulticiding. If successful, virus amplification is suppressed and does not exceed epidemic thresholds (dashed line in Fig. 2). If unsuccessful, reactive epidemic management commences, usually entailing broad scale adulticiding using aircraft. If this fails and cases continue, then the only approach left is modification of human behavior or the application of effective repellents such as Deet. The time between detection of virus and the onset of human cases depends upon the rate of viral amplification and delineates the "window of opportunity" to implement control to protect the public. During hot midsummer in California when mosquito populations are large, this time "window" may be very short in duration.

Fig. 2 Diagram depicting the surveillance and intervention paradigm during arbovirus seasonal amplification. Dashed line shows the attenuation of amplification following intervention, whereas the solid line show continued amplification above the threshold where human infection is likely

Recent outbreaks in California and the remainder of the US have triggered the widespread use of adulticides to interrupt epidemic transmission, in accordance with local (Kramer 2007) and national (Gubler et al. 2000) guidelines for arbovirus outbreak response. These applications have met with public resistance, especially in California, and concerns about pollution (Amweg et al. 2006), necessitating the careful evaluation of application efficacy. To demonstrate the effectiveness of aerial applications on target mosquito populations, calculations must account for changes in abundance in sprayed target areas and unsprayed comparison areas during pre and post application periods. Four methods have appeared in the literature to analyze these types of data (http://www.ehabsoft.com/ldpline/onlinecontrol.htm); however, with the exception of the Henderson-Tilton formula (Henderson and Tilton 1955), these methods do not account for changes in both sprayed and unsprayed populations during pre and post spray periods. Confronted with the same difficulties in analyzing control of chironomid midges in recreational lakes (Mulla et al. 1971), Dr. Mir Mulla developed a simple, but effective, formula that accounts for changes in the abundance of the target species population in sprayed and unsprayed areas pre and post spray. The current paper given in honor of the long career of Dr. Mulla in vector control focuses on the utility of his formula in estimating percent control during experimental and epidemic adulticide applications in California, using examples taken from our recent research.

"Mulla's Formula"

In this formula, percent control or reduction (R) is calculated as: %R = 100 - [(C1/T1) x (T2/C2)] x 100

where Ci = pretreatment measure of target species abundance in unsprayed control area, C2 = post treatment unsprayed control, T1 = pretreatment treated or sprayed area, and T2 = post treatment sprayed area. This formula is based on several basic assumptions:

1. Counts at individual traps are independent measures of relative abundance.

2. Ratio of abundance at traps in control and treated areas is consistent over time.

3. Changes in this ratio are due to treatment effects.

Although developed for estimates of insect larval abundance, this method of estimating percent reduction can be applied to any standardized measure in treated and control areas.

Examples

During April 2005 the Coachella Valley Mosquito and Vector Control District (CVMVCD) experimentally attempted to suppress Culex tarsalis abundance in a 1 m2 area of the Coachella Valley in Riverside County, California, using three replicate ground applications of a ULV formulation of AquaReslin (Lothrop et al. 2007a). Relative abundance measured by 4-8 replicate traps within 5 strata was variable and significantly correlated over time among abundance measures within strata in the treated area, but not with abundance measured within two unsprayed control strata (Fig. 3). When calculated using Mulla's formula, percent reduction or control was acceptable, ranging from 65 to 85%. However, even with this high level of estimated percent reduction, adult abundance rebounded rapidly and continued to increase post spray, most likely due to rapid recruitment by emergence or immigration.

Correlation analysis

Core

Mid

Edge

In-ContOut-Cont

Core

1.000

Mid

0.942

1.000

Edge

0.933

0.986

1.000

In-Cont

0.352

0.517

0.565

1.000

Out-Con

0.495

0.668

0.695

0.676 1.000

Fig. 3 Relative abundance of Cx. tarsalis at traps deployed within 5 strata in rural Coachella Valley during April 2005 showing the impact of replicated ground ULV application using AquaReslin. Core, mid and edge progress from the center to edge of the sprayed zone, whereas inner and outer controls were not sprayed. Shown are correlations among mean abundance per zone over time (r > 0.67 significant at P = 0.05, df = 7) and percent control estimated by Mulla's formula for traps in the core and mid zones compared with traps in the outer control zone. Data from Lothrop et al. (2007a)

Fig. 3 Relative abundance of Cx. tarsalis at traps deployed within 5 strata in rural Coachella Valley during April 2005 showing the impact of replicated ground ULV application using AquaReslin. Core, mid and edge progress from the center to edge of the sprayed zone, whereas inner and outer controls were not sprayed. Shown are correlations among mean abundance per zone over time (r > 0.67 significant at P = 0.05, df = 7) and percent control estimated by Mulla's formula for traps in the core and mid zones compared with traps in the outer control zone. Data from Lothrop et al. (2007a)

During September 2005, a 1 mi2 area of managed wetlands recently flooded for waterfowl was treated on three alternate nights by air using a ULV formulation of Pyrenone 25:5 mixed in a 1:2 formulation with BVA oil (Lothrop et al. 2007b). The Cx. tarsalis population in this area was rapidly increasing and abundance estimated within 4 of the 5 strata were significantly correlated (Fig. 4). When compared to abundance measured at outer control traps, percent reduction calculated for abundance in the core of the sprayed zone ranged from 2 to -120%, indicating that the spray did not effectively reduce abundance within the target area. This was unexpected, because kill of sentinel mosquitoes exposed in bioassay cages (Townzen and

Natvig 1973) was similar to the April 2005 ground application. These data emphasized the importance of measuring abundance in unsprayed control and sprayed areas as well as assessing spray efficacy using sentinels.

Fig. 4 Relative abundance of Cx. tarsalis at traps deployed within 5 strata in rural Coachella Valley during September 2005 showing the impact of replicated aerial ULV applications using Pyrenone 25:5 mixted 2:1 by volume in BVA oil. Core, mid and edge progress from the center to edge of the sprayed zone, whereas inner and outer controls were not sprayed. Shown are correlations among mean abundance per zone over time (r >0.71 significant at P = 0.05, df = 6). Data from Lothrop et al. (2007b)

Fig. 4 Relative abundance of Cx. tarsalis at traps deployed within 5 strata in rural Coachella Valley during September 2005 showing the impact of replicated aerial ULV applications using Pyrenone 25:5 mixted 2:1 by volume in BVA oil. Core, mid and edge progress from the center to edge of the sprayed zone, whereas inner and outer controls were not sprayed. Shown are correlations among mean abundance per zone over time (r >0.71 significant at P = 0.05, df = 6). Data from Lothrop et al. (2007b)

In July 2005, enzootic surveillance measures determined that epidemic WNV amplification was underway in Sacramento, California (Elnaimen et al. 2006). The distribution of the ensuing epiornitic was delineated by the locations of dead birds (mostly corvids, American crows, Western scrub-jays, Yellowbilled magpies) reported to the California Dead Bird Program (Fig. 5). In response to reports of the first indications of tangential transmission to humans within urban Sacramento, the Sacramento-Yolo MVCD treated 120,000 acres on 3 occasions by air using a ULV formulation of the pyrethrin compound EverGreen®. Measures of mosquito abundance, mosquito infection rates, reported dead birds and laboratory confirmed human cases during pre and post spray intervals in the northern Sacramento area were compared to comparable unsprayed areas using Mulla's formula (Fig. 6). Although the decrease in host-seeking Culex abundance was 76%, the associated minimum infection rate in Culex females decreased from 24 to 3 per 1,000 females tested. These data indicated that the adulticide application may have altered the population age structure and disproportionately eliminated the old infected females. In

Fig. 5 Plot of reported dead birds in Sacramento and Yolo counties during July 2005. Data from Elnaimen et al. (2006)

Fig. 5 Plot of reported dead birds in Sacramento and Yolo counties during July 2005. Data from Elnaimen et al. (2006)

C1 I C2 Unpsray

30 25

5 15

E 10

30 25

5 15

E 10

1 1 ,-, 1-1

T1 | T2 N Sac

C1 C2 Unpsray

Unpsray

Unspray

Fig. 6 Changes in host-seeking female Culex per trap night, female Culex infection rate per 1,000 tested, dead bird reports per week and human cases reported from north Sacramento sprayed and unsprayed control areas during pre and post spray period. Included are estimates of percent control using Mulla's formula. Data from unpublished reports by the Sacramento-Yolo MVCD

N Sac

cp 30

E 200

z 10

N Sac

N Sac agreement, the numbers of dead birds reported by the public per week decreased from 537 to 235 in the sprayed zone, while the numbers remained similar in the control zone increasing slightly from 516 to 670 per week. In contrast to the dead bird reports, the numbers of human cases markedly declined in both sprayed and unsprayed areas; however, the rate of decrease in the sprayed area (45-5 cases) was disproportionately greater than in the control zone (33-15 cases), yielding a 76% reduction. Collectively, these data indicated that the marked reduction in infected Culex arrested both epiornitic and epidemic transmission.

During 2006 an outbreak consisting of 15 human cases occurred in Davis, California (Nielsen et al. 2007a). The rising numbers of laboratory confirmed WNV-infected dead birds and human cases during July resulted in the SYMVCD applying a ULV formulation of EverGreen by air on 8-9 Aug 06, even though the abundance of both Cx. tarsalis and Cx. pipiens were low at this time (Fig. 7). Efficacy assessed by sentinel cages was variable, ranging from 0% mortality for cages protected under canopy or wind shadows to 100% for cages positioned in the open. Percent reduction of the target population estimated by Mulla's formula was 26% for Cx. tarsalis questing at dry ice baited traps and 75% for Cx. pipiens collected by gravid female traps. Differences in percent reduction were attributed to mosquito distribution within Davis, with Cx. tarsalis immigrating from larval sources in the surrounding agroecosystem and Cx. pipiens emerging from sources in peridomestic habitats within Davis. The spray did appear to interrupt the outbreak, because there was only a single human case, one WNV positive dead bird report and only one positive Cx. pipiens pool documented after August 20th. Termination of the epidemic most likely also was enabled by the onset of cool weather, where the minimum temperatures remained below 14°C for the remainder of theyear.

Fig. 7 Changes in mean numbers of Cx. tarsalis at dry ice baited traps and Cx. pipiens at gravid traps per night in sprayed treated zone (T) and unsprayed control zone (C) during pre (1) and post (2) spray. Data from Nielsen et al. (2007a)

Fig. 7 Changes in mean numbers of Cx. tarsalis at dry ice baited traps and Cx. pipiens at gravid traps per night in sprayed treated zone (T) and unsprayed control zone (C) during pre (1) and post (2) spray. Data from Nielsen et al. (2007a)

Summary

Evaluation of the impact of ULV adulticiding on target mosquito populations has proven to be difficult and confounded by several factors.

• Treatment and control sites are not always independent. For example, in Coachella Valley unsprayed control traps frequently varied in a similar fashion to traps within the treated spray zones, indicating that the impact of the spray was minimal or that the spray impacted the general population in the area. The latter would seem to be the case based on the assessment of widespread control applications, such as was done in Sacramento during 2005.

• Treatment and control sites are affected differently. For example, in Davis Cx. tarsalis were produced in rural agricultural sources out of the spray zone, immigrated into the city, were most abundant at peripheral monitoring sites, and were minimally impacted by aerial spray over Davis. In contrast, Cx. pipiens were produced within the city and control of this population was similar to that observed in Sacramento during 2005.

• Weather. Variation in weather has a major impact on the application processes as well as the evaluation. In the desert habitats in Coachella Valley, hot and very dry conditions required us to formulate adulticides using BVA oil to ensure that droplets would descend from air craft and kill sentinel mosquitoes at ground level (Lothrop et al. 2007b). In addition, heat radiation off the ground can drive ground applications upwards and out of the target area. In Davis, cool weather following the aerial application most likely contributed to the termination of virus activity (Nielsen et al. 2007a).

• Avian herd immunity. Although minimally discussed in the current paper, the increase in the seroprevalence rate within the peridomestic passerine community appears to markedly dampen virus transmission. Interestingly, the 2004 WNV epidemic in Los Angeles appeared to end abruptly in September, even though no emergency adulticiding was done. Here, as soon as passerine herd immunity exceeded 25%, the epidemic ended and few further human cases or dead birds were detected (Wilson et al. 2005). Considering the elevated mortality among experimentally infected House finches and House sparrows (Komar et al. 2003; Reisen et al. 2005), 25% seroprevalence indicates that there was considerable associated depopulation and that more than 80% of the population may have been infected.

• Diapause. During the fall after the critical photoperiod for the induction of diapause, Cx. tarsalis (Nelson 1964; Reisen et al. 1986) and presumably Cx. pipiens populations, bifurcate into older parous host-seeking females not destined for diapause and non-host-seeking females destined for winter diapause. Therefore, sampling late season populations measured by dry ice baited traps will naturally decrease in abundance regardless of control efficacy.

The evaluation of intervention will remain difficult because of the volatility of mosquito population dynamics and the interplay of multiple interacting and confounding factors. Mulla's formula is useful, because it accounts for mosquito population dynamics in both sprayed and unsprayed areas, pre and post spray, is easy to use and can be applied to other quantifiable measures such as infection rates, dead bird and counts of human cases. The formula may be useful in evaluating surveillance measures providing the control sites are similar to and independent from the treated sites.

Acknowledgements I especially thank Hugh and Branka Lothrop, Donald Gomsi and the staff of the Coachella Valley MVCD who conducted the ground and aerial evaluation studies in Coachella Valley, Dave Brown and staff at the Sacramento-Yolo MVCD who applied and evaluated the emergency applications done in Sacramento and Davis. Carrie Nielsen participated in the evaluation of the Davis application. This research was funded, in part, by grants from the National Institutes of Allergy and Infectious Diseases, NIH, and the Coachella Valley and Sacramento-Yolo MVCDs.

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