PROJECT REPORT: PHASE 1

STRATEGIC PLANNING MODEL FOR PROVISION OF A NATIONAL AMBULANCE SERVICE FOR EMERGENCY MEDICAL SERVICES

November 2002

Prepared By:

Prepared for:

Africon:

Hein Aucamp

Tel : (27 12) 427-2401
Fax: (27 12) 427-2926

Department of Health
Directorate Hospital Services: Disaster Management
Private Bag X828
Pretoria, 0001
Peter Fuhri
Rod Bennett

Project Number

Version

Date

Prepared by

Modification

33310

Draft 1.0

April 02

Hein Aucamp

Original

33310

Draft 1.1

May 02

Hein Aucamp

Helicopter Analysis

33310

Draft1.2

Sept 02

Hein Aucamp

Explanation of capturing

33310

Draft 1.3

Sept 02

Hein Aucamp

Rerun results

33310

Final

Nov 02

Hein Aucamp

Final release

Information Technology Division

PO Box 905, 0001, Pretoria, South Africa

Copyright Ó Africon 2002

All Rights Reserved.

Africon engineering international (PTY) LTD

Table of Contents

1 Introduction

1.1 Background

2 Data Supporting the Analysis

2.1 Datasets Used

2.1.1 Incidents and Base Information from Three Provinces

2.2 Roads Data
2.3 Census Data
2.4 RSA Towns
2.5 Hospitals
2.6 Data Assumptions Made

3 Overview of Analysis Process
4 Capturing of Incidents and Bases

4.1 Qualifications

5 Building of GIS Database and Population Distribution Model
6 Matching of Incidents and Population to Bases
7 Incident Estimation

7.1 Trial Method: Estimation Based on EA Characteristics
7.2 Final Method: Estimation Based on Averages

8 Development of drivetime catchment analysis
9 Satellite Point Catchment Analysis

9.1 Determining Candidate Satellite Points
9.2 Estimating Incidents in EAs
9.3 Determining Population Characteristics of Catchments
9.4 Estimating Incidents in Catchments

10 Hospital Catchment Analysis
11 Round Trip and Incident Capacity Analysis

11.1 General Analysis
11.2 Adjustment for Urban Areas

12 Aircraft Areas
13 Aircraft Analysis
14 Cross Border Analysis
15 Sensitivity Analysis

15.1 Varying the Population Served by Road Ambulances
15.2 Road Ambulance Results by Province
15.3 Inherent Factor of Safety in the Deployment
15.4 Extending the Road Network
15.5 Allowing a 60 minute Response Time

16 Comment on Increasing the Response Time
17 Comment on the possibility of incidents coinciding
18 Accommodating the Seasonal Factor
19 Sample Outputs
20 Appendix A: Bases with Matched Incidents

20.1 KwaZulu-Natal
20.2 Western Cape
20.3 Northern Province

Table of Figures

Figure 1: Explanation of Thiessen Polygons
Figure 2: Demonstration of Thiessen Polygons at Richmond
Figure 3: Enumerator Areas in Richmond
Figure 4: Drive time polygon
Figure 5: Satellite Points
Figure 6: Thinned Satellite Points
Figure 7: Sample drive time catchment polygon
Figure 8: Drive time catchment polygons for kwaZulu-Natal
Figure 9: Enumerator Areas in sample catchment
Figure 10: EA presence in drive time catchments
Figure 11: Estimating incidents in drive time catchments
Figure 12: Effective incidents per drive time catchment
Figure 13: Overlaid drive times for hospitals
Figure 14: Identification of aircraft areas
Figure 15: Establishing incident demand and capacity for aircraft areas
Figure 16: Ranking of polygons for removal during sensitivity analysis
Figure 17: Sample of rankings
Figure 18: Sensitivity analysis plots of ambulance and aircraft variations (linear scale)
Figure 19: Sensitivity analysis plots of ambulance and aircraft variations (logarithmic scale)
Figure 20: Variation of population/ambulance (linear scale)
Figure 21: Variation of population/ambulance (logarithmic scale)
Figure 22: Variation of aircraft/ambulance (linear scale)
Figure 23: Variation of aircraft/ambulance (logarithmic scale)
Figure 24: Investigation of population/ambulance
Figure 25: Extended road network
Figure 26: Response Times
Figure 27: Monthly Call Rates

Table of Tables

Table 1: Summary of captured incidents
Table 2: Incident estimation based on averages
Table 3: Estimated Monthly Incidents
Table 4: Shortest drive time to hospital
Table 5: Round trip analysis parameters
Table 6: Incident capacity and ambulance demand for drive time catchments
Table 7: Parameters for aircraft analysis
Table 8: Current totals of ambulances and aircraft
Table 9: Sensitivity analysis results
Table 10: Ambulances by province in sensitivity analysis
Table 11: Inherent factor of safety in deployments due to roundup
Table 12: Implications of extending the road network
Table 13: Inherent factors of safety after extending the road network
Table 14: Implications of a 60 minute response time
Table 15: Inherent factors of safety if allowing a 60 minute response time
Table 16: Results of theoretical response time analysis

1 Introduction

1.1 Background

Emergency Medical Services are currently based on historic budgets and are unable to adequately service the population equitably or effectively. More specifically, a goal has been set to provide ambulance services to every citizen of South Africa within a time limit of 40 minutes. This goal is not met by the current deployment of equipment and vehicles: a strategy therefore needs to be formulated to achieve this by modifying the distribution of ambulances, and by supplementing such vehicles.

The Department of Health (DoH) requested Africon to propose a study to develop a model for planning the deployment of ambulances, and to develop business cases for achieving the set goals. In particular, it should address the deployment of Emergency Medical Services in South Africa to achieve the appropriate standards of service delivery. The system is hereafter referred to as the EMS.

Although emergency services delivery includes other non-ambulance emergency services (such as the fire or traffic departments), this study excludes those services: the EMS in this case will consist of only ambulance services.

Africon supplied the proposal, which was accepted by the DoH. The DoH secured funding for a part of the proposal. Africon undertook the limited scope of works. Funding to complete the study is being pursued; the outputs of the current scope will support the completion of the project.

This document is a description of the work undertaken for the first phase of the project. It shows the approach and results. Because the first phase is an interim phase in the study, its significance lies as much in the results as in the development of tools to support further phases.

2 Data Supporting the Analysis

2.1 Datasets Used

2.1.1 Incidents and Base Information from Three Provinces

The DoH provided sheets reflecting the actual incidents serviced by ambulance bases in three provinces: kwaZulu-Natal, Western Cape, and Northern Province (Limpopo). The incidents did not cover the provinces entirely, but allowed assessment of incident patterns over a range of population conditions.

The base names were reported with variations of spelling and under a variety of pseudonyms, and Africon performed matching to ensure sensible results. The success in matching incidents to known bases appears in the table below:

Province

Incidents Captured

Incidents Matched

Matching Success

KwaZulu Natal

10687

10670

98.9%

Western Cape

8977

8737

97.3%

Northern Province

1605

1569

97.8%

Table 1: Summary of captured incidents

Appendix A contains lists of the bases with matched incidents.

2.2 Roads Data

The DoH purchased a set of roads data. Africon verified the cleanness of the data to allow network analysis. The data allowed determining of road speeds and connectivity, which was used in producing the drive time service areas.

2.3 Census Data

The DoH made a set of the 1996 Census Data available to Africon for the purposes of this project. The EA polygons and census attributes allowed classification of the population in the service areas, which allowed estimation of the incidents arising in the service areas of the ambulance satellite points.

2.4 RSA Towns

A towns dataset was used to provide background information and to assist with positioning of ambulance bases and hospitals.

2.5 Hospitals

A limited hospital dataset (not an official DoH source) was used to position hospitals, and was augmented by considering towns of sufficient size to contain a hospital.

2.6 Data Assumptions Made

It became apparent that the DoH would not be able to provide comprehensive information about hospital locations and ambulance bases in the remaining provinces. The DoH extended a broad mandate to Africon to allocate points responsibly.

It must be emphasised that the analysis results are virtually insensitive to limited relocation of the satellite points allocated by Africon. Relocation of the satellite points to suitable venues within several kilometres will not materially affect the outcomes. Africon’s allocations will therefore not materially limit the DoH in its deployment strategies.

Africon’s assumption of location of hospitals will likewise not materially affect the outcomes. The roundtrip analysis (described later) depends on average times, and changes in the locations of hospitals of several kilometres will not materially affect the decisions of the DoH based on the results of this project.

3 Overview of Analysis Process

The analysis appears complex, but each step is a simple addition to the previous step. The process is described in detail in the following text, but an overview appears below:

  1. Capturing of incidents and bases
  2. Building of GIS Database and Population Distribution Model
  3. Matching Incidents and populations to bases
  4. Incident estimation
  5. Development of drive-time catchment analysis
  6. Satellite point catchment analysis
  7. Hospital catchment analysis
  8. Round trip and incident capacity analysis
  9. Aircraft areas
  10. Aircraft analysis
  11. Cross border analysis
  12. Sensitivity analysis

4 Capturing of Incidents and Bases

The DoH provided Africon with raw data on sheets describing the incidents generated for numerous ambulance bases spread across three provinces. Capturing this information allowed Africon to derive statistics about incidents per base, and to incorporate the electronic version of the data into the GIS database and population distribution model.

The project budget allowed R 70 000 for capturing; an amount of approximately R 50 000 was used, reflecting fewer forms than initially envisaged.

Appendix A summarises the captured information.

4.1 Qualifications

It must be emphasised that the captured data contain a degree of uncertainty. Some of the forms were possibly incomplete, and there is also a possibility that some centres did not record all incidents on forms (perhaps because of insufficient forms). The forms were filled in according to a variety of interpretations at the centres, and Africon had to perform interpretation on the captured results, particularly in deciding the centres to which incidents should be allocated (this was often placed in the suburb field of a major centre).

5 Building of GIS Database and Population Distribution Model

This involved collecting the various datasets into to GIS compatible form.

  1. The roads data were already in GIS format, and required verification and rectification to support the network analyses that would follow.
  2. The relevant elements of the census data were collected into attribute tables and linked to the EA polygons to produce a GIS layer allowing determination of the population characteristics of regions. Gender, racial, age, and rural/urban profiles were connected and population totals were attached to each EA. (An EA is an Enumerator Area of the census.)
  3. The towns data were in a GIS format.
  4. The hospital data were in a GIS format.
  5. The base information derived from the capturing was converted to a GIS layer by matching base names with locations.
  6. The bases for which incident totals were known were allocated service areas (see the following section, Matching of Incidents and Populations to Bases), which allowed the population totals and profiles to be analysed per base. This produced a population distribution model for the bases. The significance of the population distribution model is that the population characteristics are known which produce a given number of incidents; this allows estimation of incidents in non-measured areas by considering the population profiles of those areas.

6 Matching of Incidents and Population to Bases

The lists of bases with incident totals are shown in Appendix A. The actual incident totals used to model incidents differ from these totals, because these incident totals include inter-hospital transfers. The analysis undertaken in this project identifies the number of emergency incidents generated to which ambulances must respond.

The first step was to identify the populations served by the bases. This was done using Equal Area Polygons, also called Thiessen Polygons. Thiessen Polygons, are one way of identifying the catchment areas of a point. The method is entirely geometrical, allocating space to a point by halving the distances between alternative points. The following graphic demonstrates this approach.




Base Positions

Equal Area Polygons

Figure 1: Explanation of Thiessen Polygons

This approach was followed for the bases provided. The following graphic demonstrates the process being done on the kwaZulu-Natal bases. (The Thiessen Polygon boundaries were adjusted to coincide with the EA boundaries.)

Figure 2: Demonstration of Thiessen Polygons at Richmond

The thick lines are the original Thiessen Polygon allocation of the area to the base at Richmond. The lightly coloured polygons are the EAs included in the base’s area, and form the new base boundary.

The Thiessen Polygons now identified the total population associated with each base. The populations in each base provided a population profile which allowed incident estimation (described in the next section).

Equal Area Polygons have several characteristics:

Despite these limitations, Thiessen Polygons were the best choice for determining the population in the ambulance base catchments within the certainties of the information supplied.

7 Incident Estimation

The first attempt to estimate incidents was based on the EA characteristics. This did not produce good correlations, so finally an average estimate was used.

7.1 Trial Method: Estimation Based on EA Characteristics

By this stage the populations (their total and age, gender, race, and rural/urban profile) are known for each base. The populations are defined by the characteristics of the EAs underlying each of the base’s Thiessen Polygon catchment areas. The following graphic demonstrates the EA polygons falling into one of the bases’ catchment area.

Figure 3: Enumerator Areas in Richmond

Each EA has a population total and profile, and together the EAs define the population total and profile for the base.

The non-referred incidents (i.e. the incidents reflecting emergency calls as opposed to those generated by hospital transfers) were assigned to the EAs proportionally to the populationa. The reasoning was that an EA with a higher population will generate proportionally more incidents than an EA with a lower population.

For each EA falling into a base provided by the DoH, the following were now known:

  1. Population total
  2. Incidents generated
  3. Racial profile
  4. Gender profile
  5. Age profile
  6. Rural/urban profile

This information produced an incident estimating model that was applied to the EAs in South Africa that did not fall in bases and have incidents determined by the DoH. For any given EA, its population profile could be matched against an EA that did fall into a base, and its incidents per 1000 population determined. The total population of the EA gave the estimated incidents per month.

The incident estimation process therefore transferred information from the sections of population where the incidents were known to those sections of the population where the incidents were not known, allowing an incident profile to be generated for the entire South Africa.

The estimations arising from this process had unacceptably high standard deviations, so the method was discarded after being used for the first run.

7.2 Final Method: Estimation Based on Averages

Tot. Incidents

Tot. Population

Av inc/1000

Min inc/1000

Max inc/1000

KwaZulu Natal

10367

3017429

3.435706358

0.010629

35.25561

Northern Province

1370

1165863

1.175095187

0.028962

10.27799

Western Cape

7553

1930511

3.912435619

0.032477

19.85309

Total

19290

6113803

3.155155637

0.010629

35.25561

Table 2: Incident estimation based on averages

The final method was to use 3.155 incidents per month per 1000 population. A peak factor was applied, as described in Section 11.

8 Development of drivetime catchment analysis

Instead of using Thiessen Polygons to determine the catchment service areas of the ambulances, a different technique was used: drivetime analysis. By analysing catchments based on road accessibility, many of the limitations of Thiessen Polygons are overcome:

Africon developed a custom application to perform drive time analysis. A screen capture of the application appears below. It is written in Microsoft Visual Basic and uses ESRI MapObjects as a GIS engine. It performs network analysis on a road layer to compute the drive time contour.

Figure 4: Drive time polygon

To the knowledge of Africon’s developer, this application offers unique benefits in comparison to commercial packages that perform similar analyses:

  1. The commercial packages are application driven in that they demand that the road network conform to the expectations of the package. Africon’s application is data driven because it can accommodate any road network that satisfies the minimum of connectivity requirements.
  2. Africon’s application produces a polygon which allows population falling in the catchment to be determined and profiled.

The application produces ESRI shape files which can be imported into standard GIS packages and analysed in conjunction with other GIS layers.

A large part of the work undertaken in this project consisted of GIS analysis of drive time contours in combination with other GIS data layers.

9 Satellite Point Catchment Analysis

9.1 Determining Candidate Satellite Points

Ambulance satellite points are the points at which the ambulances wait for incidents. For the purpose of this high level study, potential ambulance satellite points were chosen from the intersection of major roads. The following graphic demonstrates the road network and satellite points chosen for kwaZulu-Natal.

Figure 5: Satellite Points

It became apparent that some of the points were too closely positioned. The drive time polygons would overlap to an unacceptable extent. A thinning process produced sets of the type shown in the following graphic (again for kwaZulu-Natal).

Figure 6: Thinned Satellite Points

Forty minute drive time catchments were performed for each of the thinned points. A sample drive time catchment appears below.

Figure 7: Sample drive time catchment polygon

The drive time catchment shows the area accessible to the satellite point within 40 minutes, which is the required response time of the ambulances.

It is important to realise that the results of the analysis are practically insensitive to local repositioning of the satellite points. Shifting a satellite point by several kilometres will not affect the analysis materially. This is in part due to the high level nature of the analysis, and in part due to the high degree of overlap that occurs, even after thinning of satellite points. The following graphic shows the results of all the points for kwaZulu-Natal.

Figure 8: Drive time catchment polygons for kwaZulu-Natal

9.2 Estimating Incidents in EAs

As described in Section 7, initially the population profiles of the EAs were used to estimate the incidents per month that would occur in the EA. The following table is a sample of the national table produced by incident matching for individual EAs. The INCIDENT column contains the estimated monthly incident rate.

POLYGONID

INCIDENT

POP96

5130010

2.470365

783

5150006

0.9465

300

5220041

0.39753

126

5220040

0.11358

36

5210052

1.347185

427

5210047

2.565015

813

5230386

1.082165

343

5230387

1.22414

388

5230398

1.435525

455

5400040

2.735385

867

Table 3: Estimated Monthly Incidents

The method described here was discarded for the second run in favour or averages because of the inability to correlate the information. The method described here, however, would be the best means of proceeding if the data quality rendered it possible.

9.3 Determining Population Characteristics of Catchments

The EAs falling inside the drive time catchments defined the population characteristics of the catchments. The following graphic shows the EAs falling inside a sample catchment. Each dot is a census EA, with accompanying population total and population profile information (age, race, gender, and rural/urban split for the purposes of this analysis).

Figure 9: Enumerator Areas in sample catchment

Africon wrote analysis software in ESRI ArcView to determine how many times an EA fell into a drive time catchment. This showed how many ambulance satellite points were available to respond to incidents in that EA. The following graphic shows the analysis being undertaken for the West Cape.

Figure 10: EA presence in drive time catchments

The following table is a sample of the results of the analysis. NUMDRIVES shows the number of drive time catchments in which the EA has a presence (a value of 0 means that the EA is a candidate for service by aircraft. The information has been added to the EA table shown above in Section 9.2.

POLYGONID

NUMDRIVES

INCIDENTS

POP96

1010001

5

1.67215

530

1010002

5

1.72579

547

1010003

5

1.21152

384

1010004

5

2.01605

639

1010005

5

1.75734

557

1010006

5

1.93717

614

1010007

5

1.96241

622

1010008

5

2.06652

655

1010009

5

1.82674

579

1010010

5

4.15198

1316

1010012

5

2.26529

718

1010013

5

1.96556

623

1010014

5

2.07284

657

1010015

5

2.30315

730

1010016

5

2.61865

830

By this stage, the monthly expected incidents were known for individual EAs. It remained only to transform the information into monthly expected incidents per catchment. The transformation was complicated slightly by overlapping catchments, which meant that EAs could be serviced by more than one ambulance. The transformation process is described in the next section.

9.4 Estimating Incidents in Catchments

Africon wrote analysis software running in ESRI ArcView to transform the incident estimations to incident demands for each drive time catchment. The following graphic shows the analysis being done for the West Cape.

Figure 11: Estimating incidents in drive time catchments

The incident demand is simply the total incidents for the EA divided by the amount of catchments in which the EA has a presence. The reasoning is that available satellite points will contribute to responding to the incident demand within their service areas, and will therefore divide the incident load and the population serviced. The following table is a sample of the effective incidents per drive time catchment:

POINTNAME

DRIVETIME

INCDEMAND

623

40

9.8862

630

40

8.7805

636

40

11.1202

643

40

34.6999

657

40

9.223

661

40

9.4482

668

40

27.2028

675

40

15.7891

687

40

34.4225

697

40

8.6278

701

40

26.9578

706

40

17.2245

738

40

34.6438

Figure 12: Effective incidents per drive time catchment

(Dividing by the number of presences to determine the effective incidents and populations in the catchment areas introduced roundoff errors in the order of 3%, which were distributed back to the populations pro-rata as a correction to ensure that the entire population of South Africa was referenced.) As mentioned earlier, the final incident estimates had to be based on averages and not local population characteristics.

10 Hospital Catchment Analysis

The next part of the analysis was to determine how long an ambulance would take to deliver a patient to a hospital. The delivery time is essential in calculating the round trip (described in following section).

Africon used a hospital database and also the mandate from the DoH to position hospitals at likely locations. Concentric drive time analyses were done on each hospital: 30 minute, 60 minute, and, if necessary, 90 and 120 minute service areas, until the relevant provinces were covered. With this information it became possible to calculate the shortest drivetime to a hospital by merely selecting the hospital service area with the lowest time in which the point had a presence. Hospital service areas overlapped, which meant that the effective drive time of a point was dictated by the nearest hospital.

The following graphic shows the 30 minute catchments superimposed on the 60 minute catchments for hospitals.

Figure 13: Overlaid drive times for hospitals

Africon wrote software in ESRI ArcView to compute the shortest drive time to a hospital for all the ambulance satellite points. The following table shows a sample of the output.

POINTNAME

DRIVETIME

BASEDRTM

INCDEMAND

623

40

60

9.8862

630

40

30

8.7805

636

40

60

11.1202

643

40

30

34.6999

657

40

30

9.223

661

40

30

9.4482

668

40

30

27.2028

675

40

30

15.7891

687

40

60

34.4225

697

40

30

8.6278

701

40

30

26.9578

706

40

30

17.2245

738

40

60

34.6438

741

40

30

11.7748

742

40

60

8.1142

Table 4: Shortest drive time to hospital

Point 623, for example, is within 60 min from a hospital, whereas point 630 is within 30 min from a hospital. This information is essential for the round trip analysis, described in the next section.

11 Round Trip and Incident Capacity Analysis

11.1 General Analysis

The ambulance must go through the following process:

  1. Respond to the incident within 40 min
  2. Stabilise the patient on scene
  3. Transport the patient to the hospital
  4. Hand over the patient to the hospital
  5. Travel back to the satellite point.

The time taken for this process determines how much time the ambulance spends on an incident, and therefore how many incidents an ambulance can service during a 24 hour period.

The following average times are used in the analysis:

Respond to the patient

30 min

Stabilise the patient on scene

20 min

Transport the patient to the hospital

75% of travel time

Hand over the patient to the hospital

20 min

Travel back to the satellite point

75% of travel time

Table 5: Round trip analysis parameters

Having determined the incident capacity of an ambulance stationed at a satellite point, the amount of ambulances necessary at that point is calculated by dividing the incident demand by the incident capacity.

A peak factor was applied to the incidents to predict the greatest incident demand. A study of information from kwaZulu-Natal and the Western Cape revealed that 18% of monthly incidents happen on Saturdays and that 33% of those incidents occur in a five hour period.

Africon wrote software in ESRI ArcView to perform this analysis for each point. The following table is a sample of the output.

POINTNAME

DRIVETIME

BASEDRTM

INCDEMAND

ROUNDTRIP

INCCAPACIT

NUMAMBUL

POPSERVED

623

40

60

9.8862

160

9

1.0985

43520.8333

630

40

30

8.7805

115

12.5217

0.7012

38653.5

636

40

60

11.1202

160

9

1.2356

48953

643

40

30

34.6999

115

12.5217

2.7712

152755.2

657

40

30

9.223

115

12.5217

0.7366

40601.3333

661

40

30

9.4482

115

12.5217

0.7545

41592.6667

668

40

30

27.2028

115

12.5217

2.1724

119751.8333

675

40

30

15.7891

115

12.5217

1.2609

69506.7667

687

40

60

34.4225

160

9

3.8247

151534.2667

697

40

30

8.6278

115

12.5217

0.689

37981.2167

701

40

30

26.9578

115

12.5217

2.1529

118673.3333

706

40

30

17.2245

115

12.5217

1.3756

75825.5167

738

40

60

34.6438

160

9

3.8493

152508.25

741

40

30

11.7748

115

12.5217

0.9403

51834.8333

742

40

60

8.1142

160

9

0.9016

35720.1667

746

40

30

17.6634

115

12.5217

1.4106

77757.5

749

40

30

7.8941

115

12.5217

0.6304

34751.2

Table 6: Incident capacity and ambulance demand for drive time catchments

Point 623, for example, has a round trip time of 160 minutes, and can thus service 9 incidents per day on average. The demand is 9.89 incidents per day, which means that 1.1 ambulances are needed. Since ambulances must be deployed in whole numbers, 2 ambulances will be necessary.

This is not the final output of the project analysis, however. Areas of the country have not been covered, and some areas covered by ambulance generate very low demands compared to the capacity provided by the mandatory minimum of one ambulance. These areas are candidates for area servicing, which is dealt with in the following sections.

11.2 Adjustment for Urban Areas

The response time in urban areas must be 15 minutes instead of 40 minutes. To accommodate this, the number of ambulances in urban areas was increased by multiplying the ambulance demands by 2.67 (40/15). The adjusted amount of ambulances have to be deployed sensibly within the drive time catchment.

The areas identified as urban are the entire Gauteng province and the urban region of the Western Cape. Other urban areas are sufficiently small to have a 15 minute response time from ambulances at the satellite stations.

12 Aircraft Areas

Aircraft may be fixed wing aircraft or helicopters.

Candidate aircraft areas are the areas not covered by satellite points and those covered where the incident demand is so low that stationed ambulances will be marginally used.

Africon analysed the country in ESRI ArcView to identify the aircraft areas. The following graphic demonstrates the identification of the aircraft areas:

Figure 14: Identification of aircraft areas

13 Aircraft Analysis

Having determined the areas and Census EAs that must be covered by aircraft, Africon covered the demand area with aircraft service zones. Information about helicopters was supplied by the DoH as follows, and applied to aircraft in general.

  1. Speed 234 km/h
  2. Range 3 hours.

Africon wrote software in ESRI ArcView to establish the incident demand and capacity for the aircraft. The process was practically identical to finding these factors for the road ambulances.

The following graphic shows the software:

Figure 15: Establishing incident demand and capacity for aircraft areas

The following average times were used in the roundtrip analysis:

Respond to the patient

20 min

Stabilise the patient on scene

20 min

Transport the patient to the hospital

20 min

Hand over the patient to the hospital

0 min

Travel back to the satellite point

20 min

Table 7: Parameters for aircraft analysis

This gave an average round trip time of 80 min, which yielded an incident capacity of 18 per aircraft per day.

14 Cross Border Analysis

The response policy will determine whether ambulances are limited to responding to incidents within their own province, or must service all incidents within range, including those across provincial borders. The aim of the cross border analysis was to establish the different implications of these two policies.

The implications were examined simply by running the analysis for the provinces individually, and then for the country as a whole. The incident demands and hence number of ambulances changed for each policy.

The difference between the two policies is shown in the satellite point reports in the sample outputs at the end of the report.

There is no significant difference between the two approaches (but see Mupumulanga for examples of local differences).

15 Sensitivity Analysis

15.1 Varying the Population Served by Road Ambulances

The sensitivity analysis shows the effects of varying the extent of coverage by road ambulance, and determining the amount of aircraft to complement them.

The current situation is as follows:

Mode

Incidents

Units

Population

Percentage

Ambulances

7989.5

1363

35171439.0

86.7

Aircraft

334.6

86

5392231.2

13.3

Total

8324.1

40563670.2

100.0

Table 8: Current totals of ambulances and aircraft

The sensitivity analysis depended on the ability to remove satellite polygons in the correct order. Removing a satellite polygon has the following effects:

  1. Removing the population that it exclusively serves from the demand on land ambulances (exclusively served populations are in EAs that appear only in that polygon, and not in the overlap of that polygon with other polygons). This reduces the number of ambulances.
  2. Shifting the demand to aircraft, and hence increasing the number of aircraft.

Using an ArcView script and information in an MSAccess database, it was possible to identify drive time contour polygons with high overlaps. These polygons were the best candidates for removal to examine the sensitivity.

The analysis is shown in the graphic below:

Figure 16: Ranking of polygons for removal during sensitivity analysis

A sample of the rankings appears below:

Figure 17: Sample of rankings

The removal of these polygons has to be approached sensibly. Polyons with an overlap index of n on average share each of their EAs with n – 1 polyons. This causes clustering of polygons of index n in groups of n. In practice the index is not exactly n, but close to it. Removing n-1 polygons from an n-sized cluster does not reduce the population dramatically, but removing the nth item from an n-sized cluster exposes all the EAs that were present in the overlaps and reduces the population significantly. Africon examined each cluster and left one representative polygon to make sure that the elimination of satellite points was in the marginal polygons. The nth polygon in the cluster was the opposite of marginal.

After filtering out the redundant polygons in each cluster, Africon removed the marginal ambulance presence polygons, starting with those that required an ambulance presence of less than one.

The results appear below:

Pop by Ambulances

Pop by Aircraft

Num ambulances

Num Aircraft

Tot Pop

Percent

Delta

Pop/amb

Pop/Aircraft

Base Line

35171439

5392231

1363

86

40563670

86.7%

25804.4

62700.4

First

34938171

5650716

1268

88

40588887

86.1%

0.6%

27553.8

64212.7

Second

34538452

6050435

1222

90

40588887

85.1%

1.0%

28263.9

67227.1

Third

34229787

6359100

1170

94

40588887

84.3%

0.8%

29256.2

67650.0

Fourth

33841750

6735131

1115

98

40576881

83.4%

0.9%

30351.3

68725.8

Fifth

33521823

7047780

1092

101

40569603

82.6%

0.8%

30697.6

69780.0

Sixth

31959113

8629774

1043

118

40588887

78.7%

3.9%

30641.5

73133.7

Table 9: Sensitivity analysis results

The results were examined in several ways.

First, the road ambulances and aircraft were plotted against population covered by road ambulance, in linear and logarithmic scale.

Figure 18: Sensitivity analysis plots of ambulance and aircraft variations (linear scale)

Figure 19: Sensitivity analysis plots of ambulance and aircraft variations (logarithmic scale)

Second, the population per ambulance and per aircraft at each percent were plotted, in linear and logarithmic scale.

Figure 20: Variation of population/ambulance (linear scale)

Figure 21: Variation of population/ambulance (logarithmic scale)

Figure 22: Variation of aircraft/ambulance (linear scale)

Figure 23: Variation of aircraft/ambulance (logarithmic scale)

From these graphs, it is apparent that the Fifth reduction is an optimum for both population served per aircraft and per ambulance.

The population served per ambulance was investigated in greater detail.

Figure 24: Investigation of population/ambulance

15.2 Road Ambulance Results by Province

The total road ambulances in the sensitivity analysis are arranged in provinces as follows:

EC

FS

GP

KZN

MP

NC

NP

NW

WC

Total

Base Line

147

91

364

253

80

69

89

65

205

1363

First

132

97

325

216

72

69

89

73

195

1268

Second

111

80

332

224

70

66

89

75

175

1222

Third

108

67

332

221

69

49

84

69

171

1170

Fourth

110

68

333

219

59

20

73

62

171

1115

Fifth

102

62

333

219

60

14

73

62

167

1092

Sixth

96

57

333

217

50

9

67

54

160

1043

Table 10: Ambulances by province in sensitivity analysis

It is worth noting that the ambulance totals for individual provinces can rise with reduction of satellite points because of the loss of cross border servicing from an adjacent province.

15.3 Inherent Factor of Safety in the Deployment

The deployment contains an inherent safety factor because the calculated numbers of ambulances were rounded up to the nearest whole number. This automatically leads to an over-deployment of ambulances (and aircraft).

The ratios of rounded ambulances to original ambulances and rounded aircraft to original aircraft are shown in the table below.

Rounded Ambulances

Original Ambulances

Ratio

Rounded Aircraft

Original Aircraft

Ratio

Base Line

1363

1086.5

1.25

86

68.1

1.26

First

1268

1025.0

1.24

88

71.3

1.23

Second

1222

1036.8

1.18

90

76.3

1.18

Third

1170

1031.7

1.13

94

80.2

1.17

Fourth

1115

1024.4

1.09

98

84.9

1.15

Fifth

1092

1018.4

1.07

101

88.8

1.14

Sixth

1043

987.0

1.06

118

108.0

1.09

Table 11: Inherent factor of safety in deployments due to roundup

15.4 Extending the Road Network

The previous analyses were performed on the primary road network, which led to several clusters of population not being serviced by road ambulance. The road network was extended by incorporating secondary roads as shown by the blue roads in the following graphic.

Figure 25: Extended road network

The analysis was done for the extended road network to examine the population that would be covered by road ambulance and the resulting demand on the aircraft. It must be emphasised that the quality of roads may warrant the use of aircraft.

The results of the analysis are as follows:

Pop by Ambulances

Pop by Aircraft

Num ambulances

Num Aircraft

Tot Pop

Percent

Pop/amb

Pop/Aircraft

Fifth

33521823

7047780

1092

101

40569603

82.6%

30697.6

69780.0

Extended Fifth

35851203

4718400

1172

74

40569603

88.4%

30589.8

63762.2

Table 12: Implications of extending the road network

The factors of safety due to roundup of ambulances are as follows:

Rounded Ambulances

Original Ambulances

Ratio

Rounded Aircraft

Original Aircraft

Ratio

Fifth

1092

1018.4

1.07

101

88.8

1.14

Extended Fifth

1172

1077.9

1.09

74

59.5

1.24

Table 13: Inherent factors of safety after extending the road network

15.5 Allowing a 60 minute Response Time

The fifth reduction is the optimal point for the 40 minute response, and so was chosen as the point from which to investigate the effect of relaxing the response time to 60 minutes (the urban areas are relaxed in the same proportion, i.e. by a factor of 0.5, from a response time of 15 minutes to 22.5 minutes).

The round trip time had to be adjusted to accommodate the greater response time, but apart from that the analysis was identical.

The 60 minute results were then refined by a thinning procedure similar to that described previously. Thinning was necessary because using greater drive times (i.e. 60 minute instead of 40 minute) tended to increase the overlaps.

The results are as follows:

Pop by Ambulances

Pop by Aircraft

Num ambulances

Num Aircraft

Tot Pop

Percent

Pop/amb

Pop/Aircraft

40 Minute

33521823

7047780

1092

101

40569603

82.6%

30697.6

69780.0

60 Minute

33848138

6723208

1216

100

40571346

83.4%

27835.6

67232.1

60 Minute Thinned

32332929

8255958

1172

118

40588887

79.7%

27587.8

69965.7

Table 14: Implications of a 60 minute response time

The factors of safety due to roundup of ambulances are as follows:

Rounded Ambulances

Original Ambulances

Ratio

Rounded Aircraft

Original Aircraft

Ratio

40 Minute

1092

1018.4

1.07

101

88.8

1.14

60 Minute

1216

1132.8

1.07

100

84.6

1.18

60 Minute Thinned

1172

1128.6

1.04

118

108.0

1.09

Table 15: Inherent factors of safety if allowing a 60 minute response time

The 40 minute scenario amounted to 160 ambulance satellite points, and the thinned 60 minute scenario amounted to 85 satellite points.

16 Comment on Increasing the Response Time

Changing the response time from 40 minutes to 60 minutes reveals behaviour that is not necessarily intuitive: the amount of ambulances increases. Africon therefore undertook a high level theoretical investigation of the effect of varying the response time.

The approach involved choosing a drivetime of a certain number of minutes, finding the area of a circle based on the radius (assuming 60 km/h speed), and then proportioning the surface area of South Africa by the area of the circles. Assuming a uniform population distribution, the populations in each circle could be calculated, and thus the incidents determined.

A round trip was determined for each radius assuming a 30 minute drive time to the receiving hospital.

The following information was used:

South African Population: 41 000 000 (rounded from Census Data)

The previously described methods were used to apply peak factors to find daily incidents, and the following table resulted:

Drive Time

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

120.0

130.0

140.0

150.0

Roundtrip

92.5

100.0

107.5

115.0

122.5

130.0

137.5

145.0

152.5

160.0

167.5

175.0

182.5

190.0

197.5

Inc capacity

15.6

14.4

13.4

12.5

11.8

11.1

10.5

9.9

9.4

9.0

8.6

8.2

7.9

7.6

7.3

Area (km2) at 60 km/h

314.2

1256.6

2827.4

5026.5

7854.0

11309.7

15393.8

20106.2

25446.9

31415.9

38013.3

45238.9

53092.9

61575.2

70685.8

Points in SA

3881.9

970.5

431.3

242.6

155.3

107.8

79.2

60.7

47.9

38.8

32.1

27.0

23.0

19.8

17.3

Pop per point

10561.8

42247.3

95056.5

168989.4

264045.9

380226.0

517529.9

675957.4

855508.6

1056183.5

1277982.0

1520904.2

1784950.1

2070119.6

2376412.8

Incidents per point (0.7%)

2.4

9.6

21.6

38.4

60.0

86.4

117.6

153.6

194.3

239.9

290.3

345.5

405.5

470.2

539.8

Num Ambulances

0.2

0.7

1.6

3.1

5.1

7.8

11.2

15.5

20.6

26.7

33.8

42.0

51.4

62.0

74.0

Total amb

598.3

646.8

695.3

743.8

792.3

840.8

889.3

937.8

986.3

1034.8

1083.3

1131.9

1180.4

1228.9

1277.4

Rounded amb

1.0

2.0

3.0

4.0

6.0

9.0

12.0

16.0

22.0

28.0

35.0

43.0

52.0

63.0

75.0

Total rounded amb

3882.0

1941.0

1294.0

971.0

932.0

971.0

951.0

971.0

1055.0

1087.0

1123.0

1160.0

1195.0

1248.0

1294.0

Table 16: Results of theoretical response time analysis

The results produce the following graph:

Figure 26: Response Times

The blue line shows the total ambulance needed to service incidents in South Africa for the response times. The blue line shows that theoretically, smaller response times lead to fewer ambulances. The problem however is that ambulances cannot be deployed in fractions, and thus each area must have an integer number of ambulances. The pink line shows rounded up ambulances.

Several interesting results emerge:

17 Comment on the possibility of incidents coinciding

Data from the West Cape suggests a consistent ratio of 6% of incidents not being able to be accommodated because of non-availability of the response unit. The current analysis does not attempt to explore this, but the approach would involved a time probability distribution calibrated with results such as those mentioned from the West Cape.

It must also be recognised that the rounding up factor in the ambulance deployment provides additional margins of safety, some of which can absorb the likelihood of coinciding incidents.

18 Accommodating the Seasonal Factor

The current model is based on a moderate month (August 2001), factoring the month’s incidents to produce daily peaks. It is recommended that exceptional months (April and January) be accommodated by sensible scheduling of planned fleet downtime.

The following data was received from the West Cape:

Figure 27: Monthly Call Rates

The final ambulance deployment figures suggested by the model reflect fleets that must be active during peak times. This implies a larger ambulance pool to allow maintenance. It is recommended that maintenance be schedules for non-peak months to provide additional capacity.

19 Sample Outputs

20 Appendix A: Bases with Matched Incidents

20.1 KwaZulu-Natal

Base

Incidents

APPLESBOSCH

128

ASSISI

1

BENEDICTINE

3

CEZA

119

DUNDEE

408

EKHOMBE

2

ESTCOURT

66

EZAKHENI

1

GREYTOWN

591

HARDING

1

HOWICK

179

IMBALI

756

IXOPO

708

KINGSBURGH

1

KOKSTAD

318

LADYSMITH

208

MADADENI

195

MATATIELE

89

MONTEBELLO

146

MPUMALANGA

2

NEWCASTLE

486

NONGOMA

51

NQUTU

88

NTUNJAMBILI

27

PAULPIETERSBURG

47

PIETERMARITZBURG

2553

PONGOLA

332

PORT SHEPSTONE

966

RICHMOND

231

TUGELA FERRY

71

ULUNDI

335

UMLAZI

1

UMZINTO

587

UNDERBERG

216

VRYHEID

664

WARTBURG

5

20.2 Western Cape

Base

Incidents

Cape Town

1050

Pinelands

0

GF Jooste

129

Atlantis

9

Bellville

15

Khayelitsha

0

Mitchell's Plain

0

Retreat

0

Somerset West

441

Stellenbosch

129

Paarl

477

West Coast

0

Malmesbury

200

Hopefield

0

Vredenburg

259

Moorreesburg

71

Piketberg

119

Porterville

65

Citrusdal

55

Clanwilliam

78

Lambert's Bay

0

Vanrynsdorp

82

Vredendal

153

Boland

5

Worcester

324

Ceres

151

Wolseley

23

Tulbagh

2

De Doorns

7

Touws River

0

Laingsburg

100

Montagu

78

Roberston

0

Ashton

132

Bonnievale

0

Overberg

0

Caledon

184

Grabouw

638

Bredasdorp

213

Hermanus

255

Still Bay

26

Gansbaai

32

Riviersonderend

48

Barrydale

5

Swellendam

37

Southern Cape

0

Riversdale

155

Albertinia

18

Mossel Bay

308

George

1053

Knysna

356

Plettenberg Bay

5

Ladismith

0

Calitzdorp

0

Oudtshoorn

773

Uniondale

91

Murraysburg

14

Beaufort West

372

Prince Albert

0

Villiersdorp

79

Strand

14

Eerste Rivier

32

Faure

76

20.3 Northern Province

Base

Incidents

Tzaneen

129

Ellisras

147

Messina

221

Louis Trichardt

248

Phalaborwa

199

Thabazimbi

54

Warmbad

199

St Ritas

114

Nylstroom

100

Naboomspruit

149

Lestitele

9