The document proposes using an accessibility model to optimize vector control planning in Huaquillas, Ecuador. It summarizes: 1) Calculating current accessibility to vector control services shows variability across bases. 2) Modeling a new base location found one area improved overall access the most while equalizing administration burden. 3) Distributing workers across bases to meet service thresholds each month maximized coverage, especially during rainy periods. The model provides insights into better targeting limited resources.

1. An access based approach to
vector control planning
James Martin

2. Background
• Vector control is a major aspect of public health
• In urban areas it is especially important for preventing
diseases such as Dengue fever, West Nile, and Zika
• Certain species are well adapted to the city life
• Mosquito control programs have limited budgets
• It is important to make the best use of
limited resources
• Informed planning is essential

3. Introduction
• Accessibility models have been used in many
contexts to measure access across space
• These models take into account the supply of
a resource, the demand in a population, and
the spatial proximity (barriers)
• The two step gravity model is one way of
measuring access
• Proposed in 1982 by Joseph and Bantock

4. Introduction
• Given its flexibility we can modify
the two step gravity model to
answer many questions about
supply and demand
• What would be the best place to
add a supply point?
• What distribution of resources
among supply points maximizes
access?

5. Study site
• Huaquillas is a city in southern
coastal Ecuador (pop: 50,000)
• Borders Peru and the largest
binational hub of commerce
• Rainy tropical climate first half of
the year, dry desert for the last
• Dengue is endemic and mosquitos
are a major concern

8. Our Data: Demand
• Census tracts were used as
population points
Source: Instituto Nacional
de Estadística y Censos (INEC)
• Centroids were created
using building locations
Source: Open Street Map

10. Our Data: Supply
• Mosquito control is under the
administeration of the
Ministerio de Salud Pública
(MSP)
• Locations gathered through
google maps and government
website
• We assume any MSP base can
be used for vector control
efforts

11. Google street view
images

12. Our Data: Barriers
• Road network from Open
Street Map
• Had to be manually cleaned
to calculate network distance

13. • Network distances from each tract center to each base calculated
using the ‘igraph’ package in R, plus some original code to convert
GIS data formats to network objects

14. Our questions
1. What is the accessibility to vector control services?
2. Where could we place a new base to best improve
access
3. How could we distribute workers among the bases
to maximize access

15. Our assumptions
• For questions 1 and 2, we assume workers are distributed
equally among bases
• There are only spatial barriers to service
• The need for services is equal in the population
• Travel time on the network is uniform
• β is 1

16. Our metric
• We consider the accessibility to vector control services the
minutes of service that can be provided each month to
each person
• We assume there are 30 full time workers for the city
• That means 4,800 hours of service a month
• 960 hours for each base, 57,600 minutes
• All workers are equally capable

17. Question One:
Basic Access Scenario

18. Base
Minutes of Service
per person/month

19. Flipping the formula
• Instead of calculating each tracts’
access to services we can
calculate each bases’ access to
population
• This is useful to see how much of
the total population each base
has access to 𝑉
𝑗 =
𝑘
𝑃𝑘
𝑑𝑘𝑗
𝛽
𝐴𝑖 =
𝑗
𝑆𝑗
𝑑𝑖𝑗
𝛽
𝑉
𝑗

20. Flipping the formula
𝑖 is the base
𝑗 is the census tract
𝑆 is the tract population
𝑘 is the base
𝑃 is the supply of service
𝑑 is the distance 𝑉
𝑗 =
𝑘
𝑃𝑘
𝑑𝑘𝑗
𝛽
𝐴𝑖 =
𝑗
𝑆𝑗
𝑑𝑖𝑗
𝛽
𝑉
𝑗

21. Flipping the formula
• Access to population for each base
• Access metric is for each minute of
work, how many people does it
have access to
• Not very intuitive
• Lets try a use the number of
workers instead
Base Access
Binational 0.176
November 18 0.197
La Paz 0.205
Huatulco 0.084
Mercedes 0.167

22. Flipping the formula
Base Access per
Worker
Total Access
Binational 1688 10,126
November 18 1896 11,375
La Paz 1965 11,791
Huatulco 807 4,846
Mercedes 1595 9,568
Total population of Huaquillas: 47,706
• Each base has 6
workers
• This shows how
many people each
worker has access
to

23. Base
Minutes of Service
per person/month

24. Question Two:
Building a New Base

25. Choosing a location for a new base
• Lets say the MSP is interested in building a new base
• No new workers come with this offer
• Each location will now have 5 workers instead of 6
• What locations would increase overall access to services?
• What locations would make the burden of service more
equal among the bases ?

26. Our method
• Use the fishnet tool in ArcMap
to generate 53 equally spaced
points
• Each represents a potential new
base location
• We repeat our calculation of 𝐴𝑖
53 times, each time we include
one of the new points
• Which point increases overall
access the most?

27. Summary of Results
Average access with 1 new base
Min 1st Quantile Mean 3rd Quantile Max
6.04 6.11 6.13 6.15 6.21
Average access with 5 bases: 6.15

29. A second metric
• In addition to increasing access
we would like make
administration more equal
• Which point minimizes the
standard deviation in the bases’
access to population?
• Lets flip the formula once again

30. Summary of Results
Standard deviation with 1 new base
Min 1st Quantile Mean 3rd Quantile Max
396 426 473 507 678
Standard deviation with 5 bases: 463

31. Summary of Results
Base 5 bases 6 bases
(best case)
Binational 10,126 8,643
November 18 11,375 9,315
La Paz 11,791 9,192
Huatulco 4,846 4,013
Mercedes 9,568 8,207
New Base 8,336

33. Mean Accessibility Equality of Administration

34. Mean Accessibility Equality of Administration

35. Base
c
Suitability

36. Base
New Base
c
Minutes of Service
per person/month

37. Question Three:
Best Distribution of Service

38. Choosing the best distribution of workers
• Up until now we assumed the number of workers at each
base was equal
• The gravity model allows us to modify the supply of service
at each base
• What distribution of workers among the bases would
increase overall access to services?
• We will answer this question in two ways, using mean
access and then different thresholds of access

39. Generating different distributions
• There are 30 workers for 5 bases
• Assume that workers come in pairs
• Each base can have one of the
following values:
2, 4, 6, 8, 10, 12, 14, 16,
18, 20, 22, 24, 26, 28, 30
• The five values must sum to 30
• There are 3,876 combinations

40. Generating different distributions
• Multiply each worker by 40 for hours
• Then 4 for weeks
• Then 60 for minutes
• This gives the minutes of labor
available once again
• Now that we have a list of service
distributions lets feed it into our
gravity model
• Loop for each distribution

41. Summary of Results
Other distributions
Min 1st Quantile Mean 3rd Quantile Max
5.85 6.01 6.16 6.27 6.96
Mean access for equal distribution: 6.15

42. Base
c
Minutes of Service
per person/month
Workers

43. Best distribution by mean access
• According to our model to maximize
the mean access in the city, we
should put all of our workers in the
remote northern base
• This doesn’t make much sense in the
real world
• While mean is highest there are huge
inequalities
• More access isn’t necessarily better

44. Using thresholds
• Thresholds are used in vector control to decide whether or
not to treat an area
• This prevents workers from doing unnecessary interventions
• We can think of access in the same way
• There is a threshold of time spent on vector control
• Once met, mosquitos are kept at an accepted abundance
• After it’s met, additional time is spent better somewhere else

45. Using thresholds
• Using thresholds also allows us to plan for varying
circumstances in time
• We know more service will be
required to keep mosquitos
under control during rainy
months
• We can use this method to
find the distribution of
workers that covers the
most people monthly weatherspark.com

46. 14
12
10
8
6
4
2 2 2 2 2 2
Minutes of service per person
required to keep disease risk
from mosquitos low

47. Threshold 8 minutes
Coverage 23.8% 11,334
Improvement + 15.0% + 7,143
January
Base
c
Minutes of Service
per person/month
Workers

48. Threshold 12 minutes
Coverage 11% 5,229
Improvement + 7.1% + 3,401
February
Base
c
Minutes of Service
per person/month
Workers

49. Threshold 14 minutes
Coverage 9.2% 4,396
Improvement + 6.4% + 3,044
March
Base
c
Minutes of Service
per person/month
Workers

50. Threshold 10 minutes
Coverage 13.7% 6,524
Improvement + 9.8% + 3,401
April
Base
c
Minutes of Service
per person/month
Workers

51. Threshold 6 minutes
Coverage 44.4% 21,181
Improvement + 14.1% + 6,750
May
Base
c
Minutes of Service
per person/month
Workers

52. Threshold 2 minutes
Coverage 100% 47,706
Improvement + 0% + 0
June - November
Base
c
Minutes of Service
per person/month
Workers

53. Threshold 4 minutes
Coverage 89.5% 42,682
Improvement + 8.6% + 4,091
December
Base
c
Minutes of Service
per person/month
Workers

54. 0
1000
2000
3000
4000
5000
6000
7000
8000
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Improvement Over Equal Distribution by Month
Additional
Population
Coverage

55. Conclusions
• Accessibility models have applications in
planning vector control services
• There are many ways access can be
optimized using these models
• How access is defined matters
• There is plenty of room for improvement
• Aspatial barriers
• Population demand
• Using ground knowledge
• Considering costs

56. Minutes of Service
per person/month
Base
At Threshold
≤1.7 ≤9.6 ≤28.2 ≤67.9 ≤331.6
6 kilometers
2 Minutes 4 Minutes 6 Minutes 8 Minutes
10 Minutes 12 Minutes 14 Minutes