By Warren C. Sanderson and Molly E. Hellmuth

1. Botswana Demographic Model

The Botswana demographic model was constructed as part of the project to provide information about what would happen to the population of Botswana, which is severely affected by HIV/AIDS, under various scenarios. For example, the model allows policy makers to determine the consequences of alternatives such as a successful program that reduces the riskiness of sexual behavior or a government program to provide HIV/AIDS medication to those in need. In these uncertain times, this kind of information can make the difference between policies that help and policies that do not. The philosophy behind all our models is that they should be as simple as possible, consistent with staying close to the data and capturing the major structural features of the phenomenon.

Categories

The population is divided (1) by age (100 ages from 0 through 99+); (2) by sex (female and male); (3) by education (primary and below, secondary, tertiary); (4) by HIV status (HIV negative; HIV positive, asymptomatic, and not on medication; HIV positive, asymptomatic, and on medication; and AIDS, i.e., symptomatic); (5) by number of years since HIV infection (15 categories from infected this year to infected 14 or more years, for people who are HIV positive, asymptomatic, and not on medication); (6) by sexual behavior risk group (not at risk, sometimes at risk); and (7) by onset of sexual activity (for young women and men).

Data on the initial population by age, sex, and education are taken from the 1991 Census of Botswana. Initial data on HIV prevalence by age for females are derived from the 1993 and 1997 Sentinel Surveillance Surveys after adjustment for geographical representativeness. There are no prevalence data for men. Before they can be used, the aggregate prevalence rates have to be adjusted for the relationship between education, fertility, and HIV prevalence and for the effect of HIV on fertility. Because there are no prevalence rate data on men, their incidence rates will be determined based on the incidence rates for females. The relationship between the incidence rates of men and women five years younger than they are is under the control of the user.

Forecasting the Non-HIV/AIDS Population

There has been a great deal written about population forecasting and we need not repeat it here. The non-HIV/AIDS population is projected using the standard cohort component approach. This involves forecasting the total fertility rate by education, life expectancy at birth by education, and migration rates. The time profile of total fertility rates by education and the time profile of life expectancy at birth are both under the control of the user. In the present version of the model, international migration is ignored. The time paths of the total fertility rates and the life expectancies at birth appear in the programs as lookup functions.

Forecasting HIV/AIDS Incidence and Prevalence Rates

The most difficult part of the program is the determination of the HIV incidence rates. This is done by adjusting prevalence rates for two years. In the case of Botswana, these are 1993 and 1997. Given consistent prevalence rates by age at these two dates, it is possible to estimate incidence rates. With incidence rates and prevalence rates, it is possible to estimate a set of age-specific prevalence-incidence relationship equations. This process requires a set of constants that can be specified by the user.

Three constants are required. One specifies the heterogeneity in the riskiness of sexual behavior. Another represents the manner in which those at risk interact with those not at risk. The third specifies the reduction in infectibility due to the use of medication. All appear on the relevant screen.

Forecasting the Number of New Infections

Once the initial prevalence rates and the prevalence-incidence relationships are determined for each single year of age (for 15 through 49 for women), we can compute age-specific incidence rates. Multiplying the number of women at risk of becoming infected at each age with the incidence rate yields the number of newly infected women at each age.

Forecasting the Number with Symptoms and the Number on Medication

The distribution of durations between infection and symptoms is assumed to be normal with a mean and standard deviation determined by the user. The mean can change over time in a way that users can control. The change in the mean duration to the onset of symptoms is also a lookup function and appears on the relevant screen.

With the onset of symptoms there are two possibilities: either the woman begins receiving medication or she does not. The user controls the probability that a newly symptomatic woman begins medication. If the woman begins medication, she is transferred into the status of being HIV positive, asymptomatic, and on medication. Otherwise she is transferred into the symptomatic category. In each year, a woman on medication has a probability of remaining on medication and a probability of becoming symptomatic. This probability is set by the user and can be found on the appropriate screen. Once a woman enters the symptomatic category, there is only one exit, death. The probability that a symptomatic woman dies each year is determined by the user.

Forecasting the Number of Deaths Due to HIV/AIDS

The only deaths due to HIV/AIDS are those of people in the symptomatic (AIDS) category. Deaths of HIV positive, but asymptomatic women are due to other causes. The number of deaths is the product of the number of women in the symptomatic (AIDS) category and the user-specified annual death rate. This death rate is not age specific.

2. Botswana Economic Model

The Botswana economic model is what economists call a CGE or computable general equilibrium model. The term "general equilibrium" is sometimes misunderstood to imply that the economy being studied is without distortions, rigidities or disequilibria. In fact, "general equilibrium" models can be used to investigate all sorts of economies from those that are heavily distorted to those that come close to the economists' view of perfect competition.

We have designed the Botswana model to be simple, but yet to incorporate the main features of the Botswana economy. In the following we discuss the economy's production structure, the determination of wages and returns to capital, the structure of demand and savings, the important role played by the Government of Botswana in the economy, and the determination of investment flows.

When the model is run in the Vensim® Model Reader, the screens will guide the user.

Production and Output Prices

The economy is aggregated into three sectors: non-agricultural exports (NAE), non-tradables (NT), and agriculture (including agricultural exports) (AG). The NAE and NT sectors are represented at the upper-most level by Cobb-Douglas production functions in value-added, imports, and intermediate goods purchased from the other sectors. Value-added is represented by a nested constant elasticity of substitution production functions in skilled labor, unskilled labor, and capital. The agricultural sector is modeled on the basis of livestock herd dynamics and is made responsive to rainfall.

Non-agricultural exports include diamonds, other mining products, tourism, and manufacturing exports. The non-tradable sector includes a wide variety of activities from construction to health care. The agriculture sector includes the output of commercial and non-commercial farms and includes exports of live animals and meat.

The advantage of the nested constant elasticity of substitution form is that skilled labor and capital can be made complementary inputs, while the aggregate of the two can be substitutable for unskilled labor. This is the situation commonly found in developing countries.

The price and the quantity of NAE output are assumed to be determined exogenously by international conditions. This is certainly true about diamonds, Botswana's main export. The price and the quantity of NT output are both assumed to be determined endogenously. The price and the quantity of AG output are assumed to be determined exogenously. The price is determined internationally and the quantity is determined by rainfall and initial herd size relative to the level desired by the farmers.

Output in the NT sector and input demands are determined using the assumption of profit maximization. Output in the NAE sector is determined exogenously. Given the output level, inputs are determined so as to minimize the cost of production.

Determination of Wages and Returns to Capital

The supply of skilled labor is assumed to be exogenous and determined from the Botswana demographic model. The wage rate of skilled labor is determined so that the demand for labor at that wage rate is equal to the exogenous supply. The wage rate of unskilled labor is not assumed to clear the market for unskilled labor, allowing unemployment of unskilled labor to exist. In the NT sector, skilled and unskilled wage rates are equal to the respective values of their marginal products.

In Botswana, holding skill level constant, wages in the NAE sector are higher than they are in the NT sector. This is represented by a constant sectoral wage rate ratio. The model also includes a constant ratio of skilled to unskilled wages holding the sector constant. The model assumes that no skilled laborers work in the AG sector.

In the NT sector, the earnings of each unit of capital are equal to the value of the marginal product of that capital. In the NAE sector, return to each unit of capital is determined as a residual, given the price of output, the quantity of output, the prices of the other inputs, the quantities of the other inputs, and the initial stock of capital.

Structure of Income, Demand, and Savings

In the NAE and NT sectors, incomes are earned by skilled workers, unskilled workers, and capital. In the AG sector, all income is assumed to be earned by unskilled workers. Income flows are aggregated across sectors. What remains are the aggregate incomes of skilled workers, unskilled workers, and capital.

Some income goes to pay taxes. What remains can be used to buy the outputs of the NT sector, the AG sector, and imports, or it can be saved. The allocations of the three after-tax earnings to the four possible alternatives are made using three separate extended linear expenditure systems (ELES).

The Role of the Government

The Government of Botswana plays a number of crucial roles in the economy. It provides critical services such as education and health care. It invests in infrastructure, and it varies its level of spending so as to achieve macroeconomic balance. The Government is both a producer of services and a consumer of them. There is only one NT production function, so Government-produced services are not distinguished from other NT outputs. The model distinguishes between Government consumption (including education and health care) and Government investment. It does not subdivide Government consumption by activity, although this would be an easy extension to make. When the Government consumes and invests, it spends money on the outputs of the NT sector and on imports. The proportions spent on NT output and imports differ depending on whether the Government is consuming or investing.

Government revenues come from two main sources: (1) taxes and royalties on incomes that would otherwise go to capital, and (2) tariff revenues. Botswana is a member of SACU, the Southern African Customs Union, which collects all tariff revenue for all of its member countries and then allocates that revenue back to the member countries. Tariff revenue will significantly decrease in the future due to Botswana's international agreements and the EU-South African Free Trade Agreement. The model distinguishes between the two sources of income and allows the tariff rate to change over time. In the model tax rates differ by sector, but do not change over time. The incorporation of time varying tax rates would be an easy extension.

The Government of Botswana normally runs a budget surplus in order to maintain macroeconomic balance. Government expenditures are adjusted downward when there is inflation in the Pula compared to the currencies of Botswana's main trading partners, and upward when the reverse is true. In the model, the rate of increase in Government spending changes each year depending on the previous year's growth rate of nominal income and on the previous year's rate of relative inflation. The sensitivity of changes in Government spending to the relative rate of inflation is a parameter that may be changed by the user.

Investment

The fraction of capital income saved and invested depends on the profitability of the NAE and the NT sectors. Returns experienced in those sectors in 1991 are taken as a benchmark. When returns exceed the benchmarks, investment rates increase and vice versa. The sensitivity of investment to profitability is set by the user.

3. Botswana Water Model Description

The water model is designed to provide forecasts of future regional water supply and demand for Botswana, in order to determine the sustainability of the water supply under various forecasts of economic, population, and climate changes. There are two models for Botswana, one for the specific case of Gaborone and one for the Socio-Ecological Region level [1].

Figure 1 shows a schematic of the water model. The water model breaks the region of interest down into the pertinent watersheds that contribute water to the surface and groundwater supply. The water that is available to consumers is the surface water runoff that is captured by surface infrastructure, or the groundwater recharge that allows sustainable abstraction. This water is then available as supply for the end users, or demand centers.

Figure 1: Water Model Schematic

3.1. Botswana SER Water Supply and Demand Model

The Socio-Ecological Regions (SERs) are shown in Figure 2.

Figure 2: Socio-Ecological Regions

There are five major hydrologic basins that were aggregated into macro basins from sub-basin maps (ALCOM, FAO) and delimited for analysis: Upper Zambezi, Okavango Delta, Orange River, Southern Interior, and the Limpopo. These basins are shown in Figure 3.

Figure 3: Modeled waterbasins

The modeled watershed sub-basins do not always directly correlate to the SERs. One could attribute the Okavango Basin to SER1, and the Orange, Southern Interior, and Upper Zambezi Basins to SER3. The Limpopo Basin and SER2 correspond directly. The amount of available water for each of these basins changes, depending on the scenario. The water is distributed amongst the SERs according to the percentage of the basin area they cover, the capacity of the infrastructure to store or transfer water to consumers, and the sustainable groundwater recharge rates. There is a macro reservoir for each SER center, which represents the total storage available for the SER. Similarly, the sustainable level of recharge which can be extracted for human consumption was modeled for each basin and then summed over the SER it supplies.

The connection of the water models to the population and development models occurs on both the water supply and demand sides. On the water demand side, population size, GDP per capita, and sectoral GDP drive the water use of the domestic, industrial, institutional, mining, energy, agricultural and livestock consumers. Domestic water use changes as a result of incomes (GDP per capita), urbanization, and population size. Industrial, Energy and Institutional water demands are linearly related to the total industrial and commercial output, which changes with each population scenario. The water demands for irrigation are unequally distributed throughout the year, depending on the growing cycle of crops. On average, 14,000 cubic meters per hectare are used every year, which means that irrigation technology is rather inefficient. The growth of water use in mining is driven by changes in the exports economic sector. Livestock water use changes as a result of changes in livestock production, which may grow or decline depending on the economic demand.

Scenario Options

The following variables may be changed or turned on (=1) or off (=0) depending on the choice of the modeler:

1. Time Scale: The model may be run at the monthly or yearly time scale, which allows the user to consider seasonal effects of water supply.
2. Start Time: Changing this value allows the user to consider scenario choices under different climate conditions. Since we do not know what future precipitation or temperature will be, the user may pick a number between 0 and 970 to choose a future climate [2].
3. Climate Change: This allows the user to run the model with future climate change assumptions incorporated. The Hadley Center Global Circulation Model produced predictions in future variations of precipitation and temperature by month. Set to 1 if you would like to consider the effects of climate change.
4. Groundwater Scenario: Turn on by setting equal to 1. Groundwater resources can be expanded to meet some of the growing pressure on the surface water supply [3].
5. Demand Side: Set this value to 1 if you would like to consider conservation measures in water consumption. This scenario reduces future industrial water consumption by changing the efficiency of water consumption over time. It reduces domestic water consumption by assuming zero growth in low and high income per capita domestic water use.
6. Percent Efficient: To consider the effects of higher water use efficiency in industrial use, please modify the Efficiency variable to incorporate the percentage of reduction in water use. This will gradually become more efficient as we move from 2002 to 2021.

3.2. Gaborone Water Supply and Demand Model

As Gaborone continues to grow as a result of urbanization, so will the city's water needs. The infrastructure of the existing water supply system as well as possible new sources were modeled. Figure 4 shows the existing infrastructure for Gaborone.

Figure 4: Existing infrastructure for Gaborone

Greater Gaborone's water supply currently comes from four main reservoirs: the Gaborone Reservoir, the Bokaa Reservoir, the Nnywane Reservoir, and the Molatedi Reservoir (South Africa). Additionally, the North South Carrier (NSC), which began operating in 1999, provides water from the Letsibogo Dam. The Palla Road wellfield groundwater supplies for the greater Gaborone region were also modeled. Four main demand nodes were included in the model: Greater Gaborone [4], Palapye [5], Mahalapye [6], and Selebi-Phikwe [7]. It was necessary to incorporate these additional centers as they share water supplies with Gaborone through the NSC. Gaborone was given priority for the water supply from the NSC.

Additionally, there are rule curves that are applied to each of these sources to allow for efficient use of storage. The demand was allocated in the following manner:

1. Water demands are calculated at each node. The Gaborone demand is at the top of the hierarchy.
2. Water is transferred to the Gaborone Dam from the Molatedi Dam following the agreement made between Botswana and South Africa: If the Molatedi Dam is more than 25% full, 7.2 million cubic meters per year may be transferred, otherwise Botswana receives only half of this entitlement.
3. Water is transferred from the Bokaa and Nnywane Dams [8] to Gaborone (if necessary).
4. Gaborone demands are first met by the sustainable amount of groundwater which is available from recharge, then by surface supplies.
5. If the Gaborone Dam is less than 50% capacity, water is transferred from the north via the NSC.
6. Water is transferred from the NSC to meet the demands in Palapye and Mahalapye.

The water demands that are modeled for each of the above demand nodes are Domestic, Industrial, Institutional and Energy. The population, which is broken into urban and rural water users drive the Domestic demands. The per capita water use rate for these two categories is allowed to grow as per capita income grows, until they eventually reach a maximum water use saturation level. Industrial, Institutional and Energy consumption are driven by changes in annual GDP in the non-tradables economic sector (described in the Economic Model Description). This is assumed to be a linear relationship.

Scenario Options

The following variables may be changed or turned on (=1) or off (=0) depending on the choice of the modeler:

1. Time Scale: The model may be run at the monthly or yearly time scale, which allows the user to consider seasonal effects of water supply.
2. Start Time: Changing this value allows the user to consider scenario choices under different climate conditions. Since we do not know what future precipitation or temperature will be, the user may pick a number between 0 and 970 to choose a future climate.
3. Climate Change: This allows the user to run the model with future climate change assumptions incorporated. The Hadley Center Global Circulation Model produced predictions in future variations of precipitation and temperature by month. Set to 1 if you would like to consider the effects of climate change.
4. Demand Side: Set this value to 1 if you would like to consider conservation measures in water consumption. This scenario reduces future industrial water consumption by changing the efficiency of water consumption over time. It reduces domestic water consumption by assuming zero growth in low and high income per capita domestic water use.
5. Percent Efficient: To consider the effects of higher water use efficiency in industrial use, please modify the Efficiency variable to incorporate the percentage of reduction in water use. This will gradually become more efficient as we move from 2002 to 2021.

In addition, experienced users may wish to change other variables, such as initial storage capacities or water losses. The user can change the dates that the satellite cities of Palapye and Mahalapye are connected to the NSC supply.

Endnotes Water Model Description

[1] Hellmuth, M., K.M. Strzepek, and D.N.Yates. 2000. Methodological Framework of the Southern African Integrated (SAINT) Model of Water Supply and Demand. Draft available from the author at hellmuth@iiasa.ac.at

[2] The start time is a random number to start the model with a different climate. For instance, if you type in 12, it will take the first month of precipitation (i.e., January, "year 12"). If you type in 780, it will take the first month of precipitation that is found in data series 780. Since we do not know what the future climate will be, auto- and cross-correlated 1000-year monthly data series of precipitation, temperature and vapor pressure were created.

[3] This option must be used with caution and knowledge of realistic future sustainable groundwater abstractions. Figures of expected future groundwater extractions for each SER are turned on if the groundwater scenario is used.

[4] Includes Gaborone, Lobatse, Tlokweng, Mogoditshane, Mochudi, Ramotswa, Metsemetlhabe, Gabane, Oodi, Modipane, Packlani, Mokolodi, Otse, and Mogobane.

[5] Includes Palapye and Morupule.

[6] Includes Mahalapye, Kalamare, and Shoshong.

[7] Includes Selebi-Phikwe and Mmadinare. They currently consume water from the Shashe Dam and are expected to be connected to the NSC to relieve pressure on the Shashe Dam which also feeds Francistown's demands.

[8] Nnywane storage was transferred into Gaborone Dam to simplify the modeling process.