Useful Tools in

Mosquito Surveillance

DenominatorsInfection Rates

(MIR and MLE’s)

Data Smoothing

Vector Index

Denominator

The denominator is the lower portion of a fraction used to

calculate a rate or ratio.

1512/01# Sand Flies CollectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

1512/01# Sand Flies CollectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

3513/011512/01

# Sand Flies CollectedDate

3513/011512/01

# Sand Flies CollectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

4514/013513/011512/01

# Sand Flies CollectedDate

4514/013513/011512/01

# Sand Flies CollectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

5015/014514/013513/011512/01

# Sand Flies CollectedDate

5015/014514/013513/011512/01

# Sand Flies CollectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

6016/015015/014514/013513/011512/01

# Sand Flies CollectedDate

6016/015015/014514/013513/011512/01

# Sand Flies CollectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

10017/016016/015015/014514/013513/011512/01

# Sand Flies CollectedDate

Human Bait Collection of Lutzomyia Sand Flies in Amazonas State, Brazil, January 13 to 17, 1975

0

20

40

60

80

100

120

12-Jan 13-Jan 14-Jan 15-Jan 16-Jan 17-JanDate

Sand

Flie

s

# flies collected

10017/01

6016/01

5015/01

4514/01

3513/01

1513/01

# collectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

310017/01

36016/01

25015/01

14514/01

13513/01

11513/01

Persons# collectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

2310017/01

136016/01

225015/01

314514/01

213513/01

111513/01

HoursPersons# collectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

2310017/01

136016/01

225015/01

314514/01

213513/01

111513/01

HoursPersons# collectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

XX

X

X

XX

==

=

=

==

62310017/01

3136016/01

4225015/01

3314514/01

2213513/01

1111513/01

Man hrs.HoursPersons# collectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

XX

X

X

XX

==

=

=

==

610017/01

36016/01

45015/01

34514/01

23513/01

11513/01

Man hrs.# collectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

==

=

=

==

16.762310017/01

20.03136016/01

12.54225015/01

15.03314514/01

17.52213513/01

15.01111513/01

Flies/Man HrMan HrsHoursPersons# collectedDate

Human Bait Collection of Lutzomyia Sand Flies

in Amazonas State, Brazil, January 13 to 17, 1975

==

=

=

==

Human Bait Collection of Lutzomyia Sand Flies in Amazonas State, Brazil, January 13 to 17, 1975

0

20

40

60

80

100

120

13-Jan 14-Jan 15-Jan 16-Jan 17-Jan 18-JanDate

Sand

Flie

s

# flies collected / man hr.

# flies collected

5,2804694,995145,4022007

4,7161673,18793,2772006

3,778332,06947,8282005

9232332,15354,1142004

1,1801511,88521,4922003

# Trap Nights

# (+) Pools# Pools

# MosquitoesYear

Trapping Effort, Fairfax County, Trapping Effort, Fairfax County, 20032003--0707

Conclusions

• Numbers can be impressive

• Numbers can be misleading

• Denominators put numbers into perspective

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLEMLE

MLE

MIRMIR

MIR

MIR

MIR or MLE?

That is the Question

Infection Rate

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLEMLE

MLE

MIRMIR

MIR

MIR

Mosquito Infection Rate

MIR – Minimum Infection Rate

MLE – Maximum Likelihood Estimation

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLEMLE

MLE

MIRMIR

MIR

MIR

MIR – Minimum Infection RateAssumes 1 infected mosquito per

pool (sample)

# positive samplestotal # of mosquitoes

tested

X 1,000MIR =

Mosquito Infection Rate

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLE

MLEML

E

MIRMIR

MIRMI

R

MLEMLEMLE

MLE

MIRMIR

MIR

MIR

Mosquito Infection Rate

MLE – Maximum Likelihood EstimationConsiders the possibility of more than 1

positive mosquito per pool and compensates for different sized samples

Calculated with an Excel Add-In

http://www.cdc.gov/ncidod/dvbid/westnile/software.htm

Brad Biggerstaff, CDC

Maximum Likelyhood Estimation of WNV in Culex Mosquitoes Collected in gravid Traps, by Week, Fairfax, Va, 2006

0

5

10

15

20

25

30

35

40

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

EPI Week

Infe

ctio

n ra

te p

er 1

,000

MLE Upper Limitr Lower Limit

WNV Infection Rates in Culex Mosquitoes Collected in Gravid Traps, per Week, Fairfax, Va, 2006

0

5

10

15

20

25

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41EPI Week

Infe

ctio

n ra

te p

er 1

,000

MLE MIR

Difference Between MIR and MLE

Difference Between MIR and MLEWNV Infection Rates in Culex Mosquitoes Collected in Gravid Traps, Fairfax, Va, 2003

0

10

20

30

40

50

60

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40EPI Week

Infe

ctio

n ra

te p

er 1

.000

MLE MIR

Conclusions

• MIR does not stand for Mosquito Infection Rate

• You can use either MIR or MLE when IR is < 20, but you should use the MLE when IR is > 20

• Use either MIR of MLE but not both

• MIR’s and MLE’s have to be calculated weekly

• Seasonal MIR’s and MLE’s don’t mean anything, these shouldn’t be used

25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data Smoothing

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,

34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data Smoothing

Data Smoothing is a form of low pass filtering = It blocks out the high

frequency components in order to emphasize the low frequency ones (longer trends)

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data Smoothing

The running mean or moving average

The exponential weighted average

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data Smoothing

1yk = yk-1 + ---- (xk – xk-n)n

yk = new set of smoothed dataxk = original set of data

n = the size of the set of number

The running mean (1) or moving average

1yk = yk-1 + ---- (xk – xk-n)

nyk = new set of smoothed dataxk = original set of data

n = the size of the set of number

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data Smoothing

SUM(xk : xk-n)yk = --------------------n

yk = new set of smoothed dataxk = original set of data

n = the size of the set of number

The running mean (2) or moving average

SUM(xk : xk-n)yk = --------------------

nyk = new set of smoothed dataxk = original set of datan = the size of the set of number

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data Smoothing

yk = (1-b)xk + byk-1

The exponential weighted average

yk = new set of smoothed dataxk = original set of data

b = the fraction of the number that is used

yk = (1-b)xk + byk-1yk = new set of smoothed dataxk = original set of datab = the fraction of the number that is used

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data SmoothingFairfax Temperature, 2007

0102030405060708090

100

Jan

Feb Mar Apr May Jun Ju

lAug Sep Oct Nov Dec

Month

O F

Block out high frequency components in order to emphasize longer trends

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Fairfax Tempreature, 2007

0102030405060708090

100

Jan Feb MarAprMay Jun JulAug Sep O ct NovDec

Month

o F

25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

25, 35, 44, 24, 36, 34, 42, 52, 44, 34,

Fairfax Temperature, 2007

0

20

40

60

80

100

Jan Feb Mar Apr May Jun Jul

Aug Sep Oct Nov DecMonth

O F

It blocks out the high frequency componentsemphasize low frequency components (TRENDS)

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data SmoothingDifferent Data Smoothing Strategies

0

10

20

30

40

50

60

70

80

90

100

Jan

Feb Mar Apr May Jun Ju

lAug Sep Oct Nov DecMonth

o F

Ex. Weight Run. mean (1) Run. mean (2)

25, 35, 44, 24, 36, 34, 42, 52, 44, 34, 25,34,

24,

44,36,

35, 34,42,

52,

34,

44,

22,35,

Data Smoothing

Lutzomyia shannoni collected in light traps, Fairfax, VA, 2005

0

2

4

6

8

10

1 7 13 19 23 24 25 25 30 31 32 33 34 35 36 37 39 43 49

EPI Week

Flie

s pe

r tra

pLutzomyia shannoni collected in light traps,

Fairfax, VA, 2005

0

1

2

3

4

51 7 13 19 23 24 25 25 30 31 32 33 34 35 36 37 39 43 49

EPI Week

Flie

s pe

r tra

p

SUM(xk : xk-n)yk = --------------------n

The running mean (2) or moving average

n = 4

Conclusions

• It blocks out the high frequency components

• It emphasizes the low frequency components emphasizing longer trends

• Shows trends more clearly

• Use carefully

Vector Index (VI)

speciesi

ii P̂N Vectorial Indice Vector Index

Roger Nasci, CDC

Vector Index (VI)

• Estimate of the number of infected mosquitoes collected per trap night

• In a meaningful spatial and temporal sampling unit

• Summed for key mosquito species

• Quantitatively related to human risk (cases)

speciesi

ii P̂N Index Vector

VI uses data from existing mosquito-based surveillance

Proportion infectedIncidence of the disease agent in the vector population

Infection Rate

Key vector or indicator species

Relative abundance of species in terms of trapping effort

Information provided

Speciesi

Number collected per trap nightPopulation Density

UnitsParameter

iN

P̂

2141SD3974Average per trap night233442Total57316124253112044913936342221681

Cx. pipiensAe. albopictusTrap Site1. Calculate mosquito density

VECTOR INDEX (VI)

iN

VECTOR INDEX (VI)

0.950.01690.00020.0033ConfidenceUpper LimitLower LimitInfection Rate

Proportion Infected050Ae. albopictus6050Ae. albopictus5050Ae. albopictus4150Ae. albopictus3050Ae. albopictus2050Ae. albopictus1

Positives# in poolSpeciesPool NumberPools tested for virus

2. Calculate infection rate as proportion (Ae. albopictus)

iP̂

VECTOR INDEX (VI)

0.950.02060.00020.0040ConfidenceUpper LimitLower LimitInfection Rate

Proportion Infected050Cx pipiens5050Cx pipiens4050Cx pipiens3050Cx pipiens2150Cx pipiens1

PositivesNumber in poolSpeciesPool Number

Pools tested for virus

2. Calculate infection rate as proportion (Cx pipiens)

iP̂

VECTOR INDEX (VI)

speciesi

ii P̂N

0.40VI=∑ (Ae. albopictus & Cx. pipiens)

0.160.24VI (individual species)

0.0040.0033Proportion Infected

3974Avg/trap night

Cx. pipiensAe. albopictusVector Index Calculation

3. Calculate individual and combined VI

iN

VECTOR INDEX (VI)

speciesi

ii P̂N

0.40VI=∑ (Ae. albopictus & Cx. pipiens)

0.160.24VI (individual species)

0.0040.0033Proportion Infected

3974Avg/trap night

Cx. pipiensAe. albopictusVector Index Calculation

3. Calculate individual and combined VI

iP̂

VECTOR INDEX (VI)

speciesi

ii P̂N

0.40VI=∑ (Ae. albopictus & Cx. pipiens)

0.160.24VI (individual species)

0.0040.0033Proportion Infected

3974Avg/trap night

Cx. pipiensAe. albopictusVector Index Calculation

3. Calculate individual and combined VI

ii P̂N

VECTOR INDEX (VI)

speciesi

ii P̂N

0.40VI=∑ (Ae. albopictus & Cx. pipiens)

0.160.24VI (individual species)

0.0040.0033Proportion Infected

3974Avg/trap night

Cx. pipiensAe. albopictusVector Index Calculation

3. Calculate individual and combined VI

speciesi

ii P̂N

Vector Density

0

50

100

150

200

250

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

EPI Week

No.

/ Tra

p N

ight

0

10

20

30

40

50

60

Cases

Cases Cx. pipiens+sp Ae. albopictus

.00

.01

.02

.03

.04

.05

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

EPI Week

Prop

ortio

n In

fect

ed

0

10

20

30

40

50

60

Cases

Cases Cx. pipiens+sp Ae. albopictus

Infection Rate (Proportion)

0.00.51.01.52.02.53.03.54.04.55.0

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

EPI Week

Vect

or In

dex

0

10

20

30

40

50

60

Cases

Cases Cx. pipiens+sp Ae. albopictus Combined

Vector Index

VECTOR INDEX (VI)

• Combine data from epidemic and non-epidemic years, look for significant correlation.

• Determine if it can predict cases 2, 3, and 4 weeks later.

Conclusions

•Quantifiable association between VI and cases with onset two weeks later

•VI can be used as a threshold for launching epidemic response (adulticide applications) to stem epidemic transmission.

•VI can be used as a method to determine maximum tolerable adult densities, as a guide for larval management programs

•Has to be calculated weekly, seasonal VI is worthless

Acknowledgements

Dr. Roger Nasci & Dr. Brad Biggerstaff CDC for sharing slides on Vector Index and for the MLE Add-In.

Lutzomyia shannoni collected in light traps, Fairfax, VA, 2005

0

1

2

3

4

5

1 7 13 19 23 24 25 25 30 31 32 33 34 35 36 37 39 43 49

EPI Week

Flie

s pe

r tra

p

WNV Infection Rates in Culex Mosquitoes Collected in Gravid Traps, per Week, Fairfax, Va, 2006

0

5

10

15

20

25

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41EPI Week

Infe

ctio

n ra

te p

er 1

.000

MLE MIR

Thank You

Human Bait Collection of Lutzomyia Sand Flies in Amazonas State, Brazil, January 13 to 17, 1975

0

20

40

60

80

100

120

13-Jan 14-Jan 15-Jan 16-Jan 17-Jan 18-JanDate

Sand

Flie

s

0.00.51.01.52.02.53.03.54.04.55.0

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

EPI Week

Vect

or In

dex

0

10

20

30

40

50

60

Cases

Cases Cx. pipiens+sp Ae. albopictus Combined

Vector Index

MIR - MLE Data Smoothing

Denominator