By Annababette Wils, Molly E. Hellmuth, and Maimuna Ibraimo

There are two integrated simulation models for Mozambique: (1) The Mozambique PDE Model; and (2) The Greater Maputo City Water Supply and Demand Model.

1. The Mozambique PDE Model

The Mozambique population-development-environment (PDE) model consists of five sectoral models which are incorporated into the integrated Mozambique PDE model. The "sub-models" are explained separately. They consist of the (1) Population and HIV/AIDS model; (2) education model; (3) labor force model; (4) economy; and (5) water model.

1.1. Population and HIV/AIDS Model

The population is projected with a cohort component model, the basic demographic tool for projection. It includes single-year age and gender, and age and gender-specific rates of fertility, mortality, and migration. What sets this model apart is that it includes the epidemiological dynamics of HIV/AIDS

HIV is an infectious disease, which means there is a relationship between prevalence, incidence, and susceptible population. The more people are infected, the more the disease spreads to the healthy people, so in turn, the more are infected. How quickly new people are infected depends on the relationship between prevalence and incidence, which is determined by biology and behavior.

If an infected person is healed or dies right away, the prevalence never has a chance to build up and cause an epidemic. On the other hand, if an infected person lives with the infection for a long time, prevalence has the opportunity to increase. This is the case with HIV, where the average time until the outbreak of full-blown AIDS in Africa is estimated to be 7-10 years. Once a person in Africa has AIDS, the annual mortality is very high, at least 50% annually.

Factors that can limit the spread of the HIV infection are safe sex practices (especially condom use), treatment of other sexually-transmitted diseases, bottle-feeding infants of HIV-positive mothers and other interventions. In the future a cheap vaccine might halt the disease.

Figure 1 shows these basic dynamics and the intervention points to limit HIV and AIDS. We have incorporated the relationship between prevalence and new incidence. If the relationship is higher, then HIV prevalence rises faster. The model also includes the three intervention possibilities in the figure. Further, all the dynamics are incorporated into a multi-state age and sex-specific population projection model [1]. With the model, we can make scenarios, which take into account how different rates of the diffusion of HIV and the effects of various policies impact population growth and age structure.

Figure 1. Flow diagram of HIV and AIDS dynamics.

We have incorporated these dynamics into the population projection by dividing the population into three sub-groups: those without HIV; the NEG population; the HIV-infected group; and those with full-blown AIDS. Each sub-group is divided by single-year age and sex, and the HIV group by years since infection. Basically, people move from the NEG to the HIV population, as given by the new infection rate derived from prevalence. Secondly, people move from the HIV to the AIDS population as determined by the years since infection and the likelihood of progressing to AIDS.

1.2 Education Model

Basically, the present low levels of educational achievement among Mozambican adults are the result of a past with low school enrollment rates. In the same way, to project future adult education - the essential ingredient for development - one needs to start by projecting school enrollment, including school intake and drop-out rates.

In Mozambique, school entry occurs at many ages, starting at age 5, and ranging up to young adulthood. Most people who enter school do so between the ages of 5 and 12. Similarly, school departure occurs throughout the school cycle. In each grade between 6% and 47% of the students leave (the higher drop-out rates occur at transitions from one school level to the next). Most, but not all, people who leave school are teenagers. This rather complex situation is captured in a model with school enrollment by single-year age groups and single grades from 1-12, as well as separate university enrollment (see Figure 2).

A particular concern for the country is whether or not there will be enough teachers, particularly at the lower primary school level. This concern is more acute in the face of the HIV/AIDS epidemic. Teachers are expected to have completed the teacher training program, but in many cases, the shortage of teachers leads to hiring people who have simply completed a certain minimum of general education [2]. The number of teachers is important because teachers are needed to fill new classrooms; also, the student/teacher ratio is a measure of school quality. A cross-sectional analysis of African countries in 1995 shows that where the student/teacher ratio is lower, the repetition rate is as well [3]. Repetition, which averages 23% in Mozambique, influences enrollment and greatly increases the inefficiency of school. This dynamic is also shown in Figure 2.

Figure 2. Flow diagram of school enrollment and teacher hiring dynamics captured in the education model.

The HIV/AIDS model gives the absolute size of each sex and age group. Within each group, the education model calculates the proportions who are in school and not in school, by grade. The same proportions are applied to the NEG, HIV, and AIDS statuses. Each sex and single-year age category has a total value of 1. Within that unit, the population is distributed over the education groups. For example, in 1997, at age 5, 0.951 of the boys and girls are in no school, and 0.049 are in grade 1. At age 6, 0.842 are in no school; 0.112 in grade 1; 0.041 in grade 2; and 0.005 in post school having achieved first grade.

1.3 Labor Force Model Description

Education does two things to the labor force: it increases the skill level and therewith the productivity of workers, and it moves people to cities (because the more educated a person is, the more likely he or she lives in an urban area). Meanwhile, AIDS takes people out of the labor force, through death and through home-nursing of AIDS patients. Our model calculates these effects for the urban and rural labor force.

From the HIV/AIDS and education models, we obtain the total population not in school by sex, age, and education achieved. Those with full-blown AIDS are not included. The average labor force participation rates by age, sex and urban or rural residence, from the 1997 Population Census are applied equally, regardless of HIV status or education. This is a simplification, which was dictated by the data. In reality, possibly, those with higher education are more likely to participate in the labor force. Only those with university degrees are assumed to have 100% labor force participation rate. The rates of urbanization are significantly higher for those with more schooling, as the 1997 Population Census shows. This difference is included in the model, so, as the labor force becomes more skilled, it automatically becomes more urban. Moreover, we include an independent, non-education related urban migration force, so that over time, even within each educational level, larger proportions live in cities.

Due to HIV/AIDS, a certain number of potential workers are lost, not only those who have the full-blown disease, but also family members who care for the sick. We assume that care for the sick is a quarter time job (this assumption can be changed) - for every four AIDS patients, one additional person is lost from the labor force because of care. After subtracting those who are caring for the AIDS patients, we have the actual labor force.

While the absolute size of the labor force says something, a true reflection of the economic potential of workers includes skill level as well as size. To capture this economic potential, we calculate the effective urban and rural labor separately from the absolute labor force size. The effective labor force incorporates relative productivity weights given to each skill level. The weights were estimated based on a comparison of incomes in different groups. They reflect the income distribution of the 1996 Household Survey. We assume income is ranked by skill - in other words, the unskilled have a lower income than the medium skilled, who have a lower income than the highly skilled. Figure 3 shows the flow diagram of the labor force model.

Figure 3. Flow diagram of the labor force model with actual and effective labor force.

1.4 Economic and water models

Figure 4 shows a flow diagram of the economic and water models. Economic production is divided into urban and rural sectors (equivalent to industry and services versus agriculture). Urban production is defined by a Cobb-Douglas function [4], which includes effective urban labor, capital stock, and productivity. Changes in the capital stock are determined by the rate of domestic investment as a proportion of GDP. Agricultural production is essentially a function of effective rural labor, productivity, and the effect of soil moisture and rainfall.

The model also calculates wage for highly skilled labor with a university degree or more, with a model developed by Kibuuka [5]. The basic assumption is that an increase in the demand for skilled labor is determined by economic growth: when the demand for skilled labor rises, wages rise. The supply of skilled labor is determined by two factors, namely the size of the skilled population, and the wage rate: a lower wage rate reduces the supply. The size of the professional labor force is increased by university graduates and foreign labor, and reduced by migration and deaths, which follow from the HIV/AIDS model.

The water model uses a physically-based hydrologic approach to calculate soil moisture [6]. The model includes 25 national and international rainfall catchment areas, which supply water for the major international rivers running through Mozambique. Not all water is available for extraction or crop growth. Most of it is lost through evapotranspiration and run-off. The model calculates the complex non-linear dynamics of these processes, including rainfall, temperature, vapor pressure, latitude, and soil moisture capacity. Unfortunately, it was not possible to find data, which would allow us to model in detail the effects of the timing and quantity of rainfall on agricultural output. The connection of rain and harvest is therefore very simple: a curve specifying the relative reduction of harvest as a function of rain shortfall in March.

Figure 4. Simplified flow diagram of economic and environmental dynamics captured in the economic and water model.

2. Greater Maputo City Water Supply and Demand Model

As the urban centers in Mozambique expand, so will the demands on the water infrastructure - namely the water pipes, treatment, and reservoirs. The Greater Maputo City water model focuses on the Pequenos Limbobos reservoir and the Umbeluzi River basin that feeds it. The river basin is modeled in the same way as the river basins in the Mozambique model (see previous section). The reservoir is basically a bathtub: the faucet is runoff from the river basin and the drain is the extraction of water for irrigation, household, and commercial or industrial use. The model also includes natural reservoir loss through evapotranspiration and excess drainage when the reservoir is full (see Figure 5).

The water demands for irrigation, household use and commercial/industrial use are each formulated separately. The growth in household water demand comes from the product of three trends: population growth, more people connected to pipes, and consumption increases for those who are connected to pipes. Each of these three factors is set in user-defined scenarios. Industrial and commercial water demands are linearly related to the total industrial and commercial output, and the user defined scenario for output growth rate. By far the biggest user of the water from Pequenos Limbobos and the Umbeluzi river that feeds it, is irrigated agriculture. Water demand is unequally distributed throughout the year, dependent on the growing cycle of crops. On average, 11-15,000 m3 per hectare is used every year, which means that irrigation technology is rather inefficient, and a little under 7000 hectare were irrigated in the Greater Maputo City area. The user can define the water use per hectare changes over time, and area irrigated.

Water demands drain the Pequenos Limbobos reservoir. Once the reservoir is dry, no more water is available. The model calculates the water deficits, but does not alter the demands. As water shortages are a possibility, the user can implement two types of policies when the reservoir reaches dangerously low levels: household water use rationing, and cutting off all irrigation water.

Figure 5. Flow diagram of the Greater Maputo City water model.

Endnotes

[1] The original version of this model was developed for Botswana by Warren Sanderson at the International Institute for Applied Systems Analysis, Laxenburg, Austria.

[2] According to data from the Ministry of Education, there were only 366 graduates from the training schools for lower primary education in 1998. This is far less than the increase of lower primary school teachers, from 30,513 in 1998 to 33,363 in 1999 (Instituto Nacional de Estatística, 2000, Moçambique em Números 1999, Maputo). In addition, teachers need to be hired to replace those who leave or die. We estimate that in 1998, about 6,000 new teachers were hired at the lower primary school level, far fewer than the qualified graduates.

[3] Using the database on the UNESCO website: www.unesco.org

[4]A standard economic formulation, which is discussed in most textbooks on macro-economics.

[5] "The projected supply and demand for professional and technical workforce in Botswana and the impact of AIDS 1991-2020," unpublished manuscript, 1997. Paper available from the author at paulk@dbsa.org.

[6] 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