List of Figures
Figure 1: Organization of chapters in this thesis: blue represents chapters contributing to case
study analysis; pink represents chapters related to social interaction and agent-based
simulation networks. ..............................................................................................................9
Figure 2: Impact of HIV/AIDS on a household (source: “Impact of AIDS,” United Nations
Population Division) ............................................................................................................ 13
Figure 3: Map showing Limpopo and the neighbouring provinces of South Africa (source:
Municipal Demarcation Board, South Africa) ..................................................................... 16
Figure 4: Map of the Greater Sekhukhune District showing locations of the Ga-Selala and
Mohlotsi villages (source: Ziervogel et al. 2006b) .............................................................. 17
Figure 5: Household size distribution in the Sekhukhune District for 830 households based on
the RADAR study. .............................................................................................................. 20
Figure 6: Distribution of household heads‟ age in the Sekhukhune District for 830 households
based on the RADAR study. .............................................................................................. 21
Figure 7: Frequency of the household members with respect to their relation with the household
head in the Sekhukhune District for 830 households based on the RADAR study. .......... 21
Figure 8: HIV arranged with other virus with respect to the degree of intimacy and
infectiousness (reproduced from: Liljeros et al. 2003) ....................................................... 30
Figure 9: Prevalence of HIV infections in Sub-Saharan Africa compared to global estimates
(1990-2007) (source: UNAIDS 2007; p.11) ........................................................................ 36
Figure 10: HIV prevalence estimates for 2001, 2003 and 2005 for 10 Sub-Saharan countries
based on the data reported by UNAIDS (2007) ................................................................. 36
Figure 11: Estimated HIV prevalence in South Africa for 2006 with respect to sex and age
groups (Dorrington 2006) ................................................................................................... 37
Figure 12: Province-based 2006 estimates for HIV prevalence in South Africa (Dorrington 2006)
............................................................................................................................................ 38
Figure 13: Location of the de Hoop Dam Project over the Olifants River in Limpopo (source:
Department of Water Affairs & Forestry, South Africa) ...................................................... 53
Figure 14: Agent-based social simulation (ABSS): as an intersection of social science, agentbased computing and computer simulation, related disciplines are Social Aspects of Agent
Systems (SAAS), Multi Agent Based Simulation (MABS) and Social Simulation (SocSim)
(source: Davisson 2002) .................................................................................................... 65
Figure 15: Association of Multiagent systems, role-playing game and field observations in a twocycle method (source: Barreteau et al. 2001) .................................................................... 70
Figure 16: A sketch of the major aspects of case study at the initial stages of this research. ... 73
Figure 17: Evidence-driven modelling methodology adopted in this thesis. ............................... 81
Figure 18: Random rewiring procedure in the Watts-Strogatz model (source: Albert and
Barabási 2002) ................................................................................................................... 87
Figure 19: Probability density function for the Pareto Distribution; an example of a heavy-tailed
distribution (source Wikipedia) ........................................................................................... 88
Figure 20: An illustration of the use of simulation to stage abstraction for social network models
(source: Edmonds and Chattoe 2005) ............................................................................... 96
Figure 21: A simulation run over time, where  is the lag size taken for different network
snapshots. .......................................................................................................................... 99
Figure 22: The model structure representing relation of social entities at individual and
household levels with respect to household composition. ............................................... 105
Figure 23: Flow chart showing the processes related to different aspects of the model in a
simulation step. ................................................................................................................. 106
Figure 24: Processes related to agents‟ characteristics described in Section 4.2.................... 107
Figure 25: Activity diagram for agent‟s death and profile update process at each time step. .. 112
Figure 26: Agent‟s update profile function called from the main schedule at each time step. .. 115
Figure 27: Processes related to formation of sexual relationships and marriages described in
Section 4.3. ....................................................................................................................... 116
Figure 28: An unmarried couple‟s update process for every time step (month). ...................... 120
Figure 29: Processes related to HIV spread in the model described in Section 4.4................. 122
Figure 30: Stages of progression to AIDS for agents in the model .......................................... 123
Figure 31: Frequency distribution for maximum number of concurrent sexual partners for: (left)
male and (right) female agents ......................................................................................... 124
Figure 32: Processes related to HIV spread in the model described in Section 4.5................. 129
Figure 33: Household main step function in the simulation. ..................................................... 136
299
Figure 34: Processes related to mining in the model described in Section 4.6. ....................... 138
Figure 35: Processes related to social networks in the model described in Section 4.7. ......... 141
Figure 36: Example of a social neighbourhood space of the village households in the model.
Blue squares indicate households that have accommodated members of dissolved
households. ...................................................................................................................... 142
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Figure 37: Agents‟ savings clubs memberships at each 100 time step during a simulation run
illustrating the change in the network over time. .............................................................. 143
Figure 38: Example of the adult agents‟ friend network. ........................................................... 145
Figure 39: General Simulation run: agent population for 20 simulation runs; black line shows the
median. ............................................................................................................................. 154
Figure 40: General Simulation run: percentage HIV/AIDS prevalence in the population for 20
simulation runs; black line shows the median. ................................................................. 155
Figure 41: General Simulation run: average age of agents dying in a year for 20 simulation runs;
black line shows the median. ........................................................................................... 155
Figure 42: General Simulation run: average household size for 20 simulation runs; black line
shows the median............................................................................................................. 155
Figure 43: Role of Grants and State Pensions: average percentage of grants contribution to
households‟ monthly income for five cases concerning role of grants and state pensions.
.......................................................................................................................................... 162
Figure 44: Role of Grants and State Pensions: average percentage of agents on migration for
five cases concerning role of grants and state pensions. ................................................ 163
Figure 45: Role of Grants and State Pensions: households median income for five cases
concerning role of grants and state pensions. ................................................................. 164
Figure 46: Role of Grants and State Pensions: average household size for five cases
concerning role of grants and state pensions. ................................................................. 164
Figure 47: Outward Migration and Household Composition: average percentage of agents on
migration for the five cases concerning initial proportion of migrant agents. ................... 168
Figure 48: Outward Migration and Household Composition: average percentage of agents
without employment for the five cases concerning initial proportion of migrant agents. .. 168
Figure 49: Outward Migration and Household Composition: average percentage of households
lacking food for the five cases concerning initial proportion of migrant agents. ............... 169
Figure 50: Outward Migration and Household Composition: average percentage of households
headed by seniors for the five cases concerning initial proportion of migrant agents.
Above: original time series chart. Below: scaled vertical axis for the time series chart after
first 10 simulation years. ................................................................................................... 170
Figure 51: Outward Migration and Household Composition: median household monthly income
averaged over 30 simulation runs for the five cases concerning initial proportion of migrant
agents. .............................................................................................................................. 171
Figure 52: Graphical representation of the Gini coefficient where the area under the triangle is
defined as 1 (source: http://en.wikipedia.org/wiki/Gini_coefficient) .................................. 172
Figure 53: Outward Migration and Household Composition: Gini coefficient of the monthly
household income for the five cases concerning initial proportion of migrant agents. ..... 173
Figure 54: Outward Migration and Household Composition: average percentage of agents on
migration for the four cases concerning different chances for migration during simulation.
.......................................................................................................................................... 174
Figure 55: Outward Migration and Household Composition: average percentage of agents
without employment for the four cases concerning different chances for migration during
simulation. ........................................................................................................................ 175
Figure 56: Outward Migration and Household Composition: median household monthly income
averaged over 30 simulation runs for the four cases concerning different chances for
migration during simulation. ............................................................................................. 175
Figure 57: Outward Migration and Household Composition: gini coefficient of the monthly
household income for the four cases concerning different chances for migration during
simulation. ........................................................................................................................ 176
Figure 58: Outward Migration and Household Composition: average percentage of households
headed by seniors for the four cases concerning different chances for migration during
simulation: scaled vertical axis for the time series chart after first 10 simulation years. .. 176
Figure 59: Snapshots showing example of initialized kinship links to households for different
settings: (top-left) Watts-Strogatz network (WS) with radius 3; (top-right) WS with radius 5;
(bottom-left) Disjoint components with sizes from 7 to 15; (bottom-right) Random network
with 7% density. ................................................................................................................ 180
300
Figure 60: Funeral Costs and Traditional „Safety Nets‟: average number of household
memberships of funeral clubs for four cases based on initial extended family structure
(adjusted vertical scale). ................................................................................................... 181
Figure 61: Funeral Costs and Traditional „Safety Nets‟: average number of households for four
cases based on initial extended family structure. ............................................................. 181
Figure 62: Funeral Costs and Traditional „Safety Nets‟: average number of individual
memberships of savings clubs (stokvels) for four cases based on initial extended family
structure. ........................................................................................................................... 182
Figure 63: Funeral Costs and Traditional „Safety Nets‟: average percentage of migrants for four
cases based on initial extended family structure. ............................................................. 183
Figure 64: Funeral Costs and Traditional „Safety Nets‟: average clustering coefficient of the
kinship network for four cases based on initial extended family structure. ...................... 184
Figure 65: Funeral Costs and Traditional „Safety Nets‟: total extended family contribution for the
funeral expenditure of bereaved households shown for four cases based on initial
extended family structure; averaged over 30 runs each. ................................................. 185
Figure 66: Mining Scenario: number of miners from outside the village for four cases concerning
mining activity in the case study region. ........................................................................... 189
Figure 67: Mining Scenario: number of miners from outside the village employed at mine for four
cases concerning mining activity in the case study region. ............................................. 190
Figure 68: Mining Scenario: number of villagers employed at mine for four cases concerning
mining activity in the case study region. ........................................................................... 190
Figure 69: Mining Scenario: percentage of migrant agents from village for four cases concerning
mining activity in the case study region. ........................................................................... 191
Figure 70: Mining Scenario: percentage of jobless villagers for four cases concerning mining
activity in the case study region. Above: original time series. Below: time series starting
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from 10 simulation year. ................................................................................................. 192
Figure 71: Mining Scenario: HIV/AIDS prevalence in village population for four cases concerning
mining activity in the case study region. ........................................................................... 193
Figure 72: Mining Scenario: frequency histogram for absolute relative change in prevalence for
case-I. Left: run with highest kurtosis value. Right: run with lowest kurtosis value. ......... 195
Figure 73: Mining Scenario: frequency histogram for absolute relative change in prevalence for
case-II. Left: simulation run with highest kurtosis value. Right: simulation run with lowest
kurtosis value.................................................................................................................... 197
Figure 74: Mining Scenario: frequency histogram for absolute relative change in prevalence for
case-I concerning mining scenario. Left: run with highest kurtosis value. Right: run with
lowest kurtosis value. ....................................................................................................... 198
Figure 75: Mining Scenario: frequency histogram for absolute relative change in prevalence for
case-IV concerning mining scenario. Left: run with highest kurtosis value. Right: run with
lowest kurtosis value. ....................................................................................................... 199
Figure 76: Mining Scenario: median household income for four cases concerning mining activity
in the case study region. .................................................................................................. 200
Figure 77: Percentage contribution of grants to household income for four cases concerning
mining activity in the case study region. Above: original time series. Below: shifted time
series from start of mining activities with adjusted vertical axis. ...................................... 201
Figure 78: Population Pyramid and Adult Dependency: median population size for three cases
regarding adult mortality based on 10 simulation runs..................................................... 202
Figure 79: Population Pyramid and Adult Dependency: median percentage of HIV prevalence
for three cases regarding adult mortality based on 10 simulation runs. ........................... 203
Figure 80: Population Pyramid and Adult Dependency: age-group wise bar chart of population
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in case-I for (left) male; (right) female for 0 , 20 , 40 and 60 years shown in each row
respectively. ...................................................................................................................... 207
Figure 81: Population Pyramid and Adult Dependency : age-group wise bar chart of population
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in case-II for (left) male; (right) female for 0 , 20 , 40 and 60 years shown in each row
respectively. ...................................................................................................................... 208
Figure 82: Population Pyramid and Adult Dependency : age-group wise bar chart of population
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in case-III for (left) male; (right) female for 0 , 20 , 40 and 60 years shown in each row
respectively. ...................................................................................................................... 209
Figure 83: Population Pyramid and Adult Dependency: population pyramid for the years 2000
and 2020 (estimated) for South Africa and Botswana (original source: US Census Bureau;
cited at http://www.fao.org/sd/2002/PE0101a_en.htm) .................................................... 210
Figure 84: Population Pyramid and Adult Dependency: median dependency ratio for three
cases regarding adult mortality based on 10 simulation runs (adjusted vertical scale) ... 212
301
Figure 85: Macro-level Validation: number of out-migrants and jobless persons without mining.
.......................................................................................................................................... 215
Figure 86: Macro-level Validation: number of out-migrants, mineworkers, and jobless persons
with mining. ....................................................................................................................... 215
Figure 87: Macro-level Validation: average household monthly income of the simulated
population. ........................................................................................................................ 216
Figure 88: Macro-level Validation: median household monthly income of the simulated
population. ........................................................................................................................ 217
Figure 89: Macro-level Validation: percentage of households not fully fed. ............................. 219
Figure 90: Macro-level Validation: number of children pulling out from schools. ..................... 220
Figure 91: Average (left), Maximum (middle) and Minimum (right) population size of agents for
60 simulation years for parameters chanceLooseJob and initPropMigration .................. 229
Figure 92: Average (left), Maximum (middle) and Minimum (right) percentage prevalence of
HIV/AIDS for 60 simulation years for parameters chanceLooseJob and initPropMigration
.......................................................................................................................................... 230
Figure 93: Average (left), Maximum (middle) and Minimum (right) population size of agents for
60 simulation years for parameters chanceLooseJob and randomSelectChance ........... 231
Figure 94: Average (left), Maximum (middle) and Minimum (right) percentage prevalence of
HIV/AIDS for 60 simulation years for parameters chanceLooseJob and
randomSelectChance ....................................................................................................... 232
Figure 95: Average (left), Maximum (middle) and Minimum (right) population size of agents for
60 simulation years for parameters initPropMigration and randomSelectChance ........... 233
Figure 96: Average (left), Maximum (middle) and Minimum (right) percentage prevalence of
HIV/AIDS for 60 simulation years for parameters initPropMigration and
randomSelectChance ....................................................................................................... 234
Figure 97: Average percentage of HIV infected agents with 5% (left), 15% (middle) and 25%
(right) chance for a random search; ................................................................................. 236
Figure 98: Role of Different Transmission Probabilities: average percentage prevalence of HIV
infected agents for five cases based on different transmission probability settings. ....... 238
Figure 99: Partnership Fluctuations: average percentage of HIV/AIDS prevalence in agent
population for three cases based on different fluctuation rates and initial assignment of
aspiration. ......................................................................................................................... 242
Figure 100: Partnership Fluctuations: average agent population for three cases based on
different fluctuation rates and initial assignment of aspiration. ........................................ 242
Figure 101: Partnership Fluctuations: average number of dyads in the heterosexual networks
three cases based on different fluctuation rates and initial assignment of aspiration. ..... 243
Figure 102: Partnership Fluctuations: average percentage of married agents for three cases
based on different fluctuation rates and initial assignment of aspiration.......................... 243
Figure 103: Heterosexual Networks: snapshots of the heterosexual networks resulting from
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case-I, taken at the 10 and 240 time step (simulation month); blue denotes male agents
and yellow denotes female agents. .................................................................................. 244
Figure 104: Heterosexual Networks: snapshots of the heterosexual networks resulting from
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case-III, taken at the 10 and 240 time step (simulation month); blue denotes male
agents and yellow denotes female agents. ...................................................................... 245
Figure 105: Heterosexual Networks: degree centralization of heterosexual networks for three
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cases based on different fluctuation rates and initial assignment of aspiration at every 10
time step. .......................................................................................................................... 246
Figure 106: Heterosexual Networks: betweenness centralization of heterosexual networks for
three cases based on different fluctuation rates and initial assignment of aspiration taken
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at every 10 time step. ..................................................................................................... 247
Figure 107: Structural Changes in Networks: clustering coefficient of friendship network (Jin et
al. 2001) over a simulation run. ........................................................................................ 251
Figure 108: Structural Changes in Networks: p-score of the KS test for the degree distribution of
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the friendship network compared for consecutive snapshots taken at every (left) 100 tick
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and (right) 25 time step................................................................................................... 251
Figure 109: Structural Changes in Networks: p-score of the KS test for degree distribution of the
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friendship network compared for consecutive snapshots taken at every 5 time step for
first 125 time steps of simulation. ..................................................................................... 252
Figure 110: Structural Changes in Networks: clustering coefficient of the agents‟ friendship
network in the model for impact of HIV/AIDS. .................................................................. 254
Figure 111: Structural Changes in Networks: p-score of the KS test for the degree distribution
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taken at every 50 time step for the three different simulation settings. .......................... 254
302
Figure 112: Structural Changes in Networks: clustering coefficient of the agents‟ friendship
network. ............................................................................................................................ 255
Figure 113: Structural Changes in Networks: p-score of the KS test for the degree distribution
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taken consecutively at every 50 time step, with HIV/AIDS prevalence. ......................... 255
Figure 114: Structural Changes in Networks: clustering coefficient of the agents‟ friendship
network. ............................................................................................................................ 256
Figure 115: Structural Changes in Networks: p-score of the KS test for the degree distribution
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taken consecutively at every 50 time step for the three different simulation settings. ... 256
Figure 116: An illustration of the bottom-up way of model development using Keep It
Descriptive, Stupid (KIDS) Approach (source: Edmonds and Moss 2005). ..................... 273
Figure 117: UML class diagram showing the class relations and hierarchy in the model ........ 296
Figure 118: Screenshot of the model with the GUI ................................................................... 297
303