According to the research of [1], the highly active sexual groups in the population play one of the most important roles in the sexual network. Therefore, the understanding of this core population is of major importance. The simulation model is mainly based on a study of statistical data from a survey that was directed by the “AIDS prevention and Research Center of National Yang Ming University - Taiwan” under the supervision of Professor Chen. This survey was conducted in 2003 in Taipei and Taichung, two major cities in Taiwan, and covers about 1000 samples of the homosexual population. This survey was lead in homosexual saunas and bars. The questionnaire covers different aspects in order to provide insight on the structure of this population as well as its behavior. It was used to give a global understanding and build the agents’ behavior.
Homosexual saunas and bars are referred as high risk places for they stand for locations where it is easy to encounter new sexual partners and are therefore frequented by sexually very active people who belong to the high risk population.
Different aspects need to be covered in the preliminary studies, such as the structure of the population, time scale in the frequentation of high risk places, the frequency of change of sexual partners, behavior regarding the establishment of new partners, the duration of a relationship between partners, usage of condoms, attitude regarding HIV testing, etc.
The data that are available and related to the population’s structure is not very important in this study because we do not have explicit relation between age, or marital status or education level and social behavior or impact on the HIV disease. Nevertheless,
it is important to shape the size of the high risk population in the entire network. In order to reflect the evolution of the HIV epidemic in the homosexual community in Taiwan, it is not possible to concentrate only on the high risk population for which we have statistical data. It is also necessary to make assumptions on a larger population which may have different behavior. The validity of these assumptions needs afterwards to be verified by simulation. The idea of the model is to have a majority of agents which are not active sexual agents, but more stable with a behavior that potentially represent a low risk for themselves. This category of agent represents the majority of the population and can be seen as a pool or reserve of susceptible agents from which the total number of HIV cases can grow. The high risk population is a minority but because of its important sexual activity acts as en engine to spread the virus inside and outside its population, and to increase the risk for other agent to be infected. Therefore the appellation of core population is justified we want to demonstrate that the behavior of this category of agent plays a major role.
In order to build this structure, we have based the distinction between high risk and low risk subpopulations according to their behavior regarding the number of partner one is willing to have, its condom usage policy, as well as its degree of “faithfulness”
regarding its long term partners. Therefore we make a distinction between short term partners that we call Free Links because this linkage between two agents moves freely from a partner to another; and the long term partners that we call Fix Links because the linkage between two agents is fixed over a long period of time (the order of a few years).
The small world model provides very interesting and powerful properties to a social network. We decide to build the agent network in order to give it small world properties.
To reach such a result, it is necessary to distribute the number of links of each agent among the network so that over a long period of time (typically many years) the distribution of the links of all the agents composing the population displays the pattern of a scale-free power-law.
A first approach of the power-law which is to be used can be retrieved from the result of the survey. Data of the cumulative number of sexual partners over the past three month, based on about 500 samples, actually do give a curve that is representative of a
power-law with a scaling exponent of 0.77 for a distribution of the number of partners k>1. See figure 3.1
We remind that scale-free networks are characterized by a power-law decay of cumulative distribution of the form:
λ
≈ k−
k P )( With:
k: Distribution of the number of partners λ: Scaling exponent
Figure 3.1: Scale-Free Distribution of the number of sexual partners in the "sexually active" homosexual community of Taiwan on log-log axis. The low value of the scaling exponent λ indicates that people in this population tend to have a lot of sexual partners, especially considering such a short period of time of 3 months.
As stated before, this survey only covers the high risk population. The majority of the population might bear a similar pattern but with a different scaling exponent and curve
shape. As we want to achieve a power-law distribution over a long time among all the agents of the simulation, we suppose that there exist such a function or class of functions Pf that represents a correct distribution of links among the agents. Such a function as the following general expression:
b ak k
P( )≈ −λ +
And it’s the plot of the general expression is as in Figure 3.2:
Figure 3.2: General curve of the distribution of partners among the population
We need to consider different parts in this graph. People having several sexual partners are more likely to have a different behavior than people with one only stable sexual partner. Therefore it is interesting to approach the problem by dividing the curve into different sections. Each section shall represent a type of subpopulation where each subpopulation may have a different profile. The choice here is to divide the population into 3 clusters. One cluster with a very high number of sexual partners can be correlated
see figure 3.3). We call it the alpha population. A second cluster called beta population which is characterized by an active sexuality but with a less extreme behavior as the alpha population and a higher number of agents. Then the gamma population is the third cluster and represents the rest of the population. As suggested by the power law (see figure 3.3) they have a few number of sexual partners, for most of them it is around 1, but they represent a high number of agents in the population.
Figure 3.3: General curve of the distribution of the alpha, beta and gamma populations
Thus, each part of the previous power law is a representation of the distribution of the links, or partners for each agent in the society. We will discuss in the chapter 4 the main parameters that define the profile and the behavior of each subpopulation.